Ares Industries wishes to thank all of those in industry and academia who helped make the Percival Mission to Mars possible.
Among those we wish to thank from industry are Dr. Paul Robinson, Assistant Chief Technologist for JPL; Bill Blume, Mars Observer Mission Planner at JPL; and Dave Kaplan and John Conolly, both of the Lunar and Mars Exploration Office.
Many of the people from the University of Texas at Austin were very helpful in the design of the Percival mission. We would like to thank Dr. Wallace Fowler, Aerospace professor; Dr. John Lundberg, Aerospace professor; Mr. Sirnivas Bettadpur, Aerospace graduate student; and Mr. Elfego Pinon, Aerospace graduate student.
We would especially like to thank Dr. George Botbyl and Mr. Tony Economopoulos for their direction and guidance through the course of this design.
Introduction
With the downturn of the world economy, the priority of unmanned exploration of the solar system has been lowered. Instead of foregoing all missions to our neighbors in the solar system, a new philosophy of exploration mission design has evolved to insure the continued exploration of the solar system. The "Discovery-class" design philosophy uses a low cost, limited mission, available technology spacecraft instead of the previous "Voyager-class" design philosophy that uses a "do-everything at any cost" spacecraft. The "Voyager-class" philosophy is no longer feasible. The Percival Mission to Mars has been proposed by Ares Industries as one of the new "Discovery-class" of exploration missions. The spacecraft will be christened Percival in honor of American astronomer Percival Lowell who proposed the existence of life on Mars in the early twentieth century.
The main purpose of the Percival mission to Mars is to collect and relay scientific data to Earth suitable for designing future manned and unmanned missions to Mars. The measurements and observations made by Percival will help future mission designers to choose among landing sites based on the feasibility and scientific interest of the sites. The primary measurements conducted by the Percival mission include gravity field determination, surface and atmospheric composition, sub-surface soil composition, sub-surface seismic activity, surface weather patterns, and surface imaging. These measurements will be taken from the orbiting Percival spacecraft and from surface penetrators deployed from Mars orbit.
Percival has been designed as a follow-up mission to the Mars Observer (MO) spacecraft that is currently in route to Mars. As a follow-up mission , it will augment the Mars Observer mission by improving the gravity field map created by MO and by supporting the Visual and Infrared Mapping Spectrometer (VIMS), which was originally planned for the Mars Observer mission. In addition, images and data taken by MO will be used to determine the desired impact sites for the three surface penetrators included within the Percival mission.
As a secondary mission, Percival will
support the Mars Balloon Relay (MBR) communications system, similar
to the one used on Mars Observer. This system is a separate communications
package directed towards the surface of Mars to receive and transmit
data from surface landers. During the science phase of the Percival
mission, this system will be used for data relay between the surface
penetrators and Earth. After the completion of the science phase
of the mission, the MBR will be used to support future Mars landers.
The Percival mission scenario consists of the following elements:
Launch using modified Delta-class launcher.
Use a broken-plane Hohmann transfer trajectory between Earth and Mars.
Insert into a low altitude, circular, sun-synchronous Mars orbit.
Determine gravity field using gravity gradiometer and Doppler- shift measurements as a backup.
Release each penetrator individually from Percival in Mars orbit.
Use the Mars Balloon Relay communications system for data relay from surface penetrators and future surface missions.
Support both real-time and store-and-forward data transmission to Earth.
Conduct scientific measurements for approximately
1-2 Martian years.
The design work for the Percival Mission
to Mars has been divided among four technical areas: Orbits and
Propulsion System, Surface Penetrators, Gravity and Science Instruments,
and Spacecraft Structure and Systems. This overview summarizes
the results for each of the technical areas followed by a design
cost analysis and recommendations for future analyses.
Orbits and Propulsion System
The main objective of the orbits and propulsion group was to develop the best combination of launch system and transfer trajectory that would maximize the allowable mass in Martian orbit. The design of the final Mars orbit was designed to accommodate the gradiometer, the VIMS, and the relay communications packages. The spacecraft propulsion system was designed to provide transfer trajectory corrections, Mars orbit insertion, and end-of-mission boost burns.
The choice of launch system and the design of the transfer trajectory was heavily impacted by the low cost objective of the Percival mission and the Delta-class launch vehicle constraint stated in the Request For Proposal. The Delta launch system is one of the less expensive launch systems, but it is also one of the lower performance vehicles among those capable of supporting an interplanetary payload. To maximize the amount of mass that can be placed into a Martian transfer trajectory, a Delta 7925 with an additional upper stage motor has been chosen. The first two stages of the Delta will place the boost stages and the spacecraft into Earth orbit, while the two Star-48B motors will provide the thrust for the Mars transfer injection burn.
To compromise between minimal energy transfer and time of flight, a broken-plane Hohmann transfer, shown in Figure 2.3, was chosen. This trajectory requires a 3576 m/s DV, provided by the Star 48B's, for transfer insertion. The plane change burn is performed at a true anomaly of 90°, requiring a 258 m/s DV to change the orbital plane by 0.53°. Course corrections will also be made during this burn. The Mars insertion burn will require a 2178 m/s DV by the spacecraft propulsion system. The time of flight will be approximately 11 months.
The design of the final Mars orbit was driven by the instrument packages onboard Percival. To increase the accuracy and precision of the gradiometer data, a low-altitude (179.4 km), circular orbit was chosen. To increase the groundtrack coverage of Mars, a high inclination orbit was necessary. A sun-synchronous orbit was chosen for this reason as well as to reduce thermal variations on the spacecraft. The sun-synchronous orbit also minimizes the pointing requirements of the high-gain antenna used to communicate with Earth. The period of the Martian orbit will be 108 minutes. The groundtrack for this orbit allows for communication with each penetrator every two to three days and allows for a complete VIMS mapping cycle in 82 days.
Percival's propulsion system is designed
to provide the plane change burn, course corrections, Mars orbit
insertion, and end-of-mission orbit boost. These maneuvers will
require a DV
of 2436 m/s. The resulting propulsion system will have approximately
60 kg of hardware mass and 730 kg of propellant mass.
Surface Penetrators
The surface penetrators group was tasked to design the penetrator system, which includes deployment methods, deceleration methods, impact and stress analysis, structural design, subsystem design, and scientific instrumentation of the penetrators. The purpose of the penetrator system is to provide scientific data from the surface and sub-surface of Mars as an aid to designing future manned and unmanned missions. The data returned by the penetrators will help determine the feasibility of a landing site and the scientific interest of a site.
Each of the three penetrators will be deployed separately from Martian orbit and impact at a different location on the Martian surface. The deployment and deceleration system uses a spring for the initial separation from Percival, a 500 m/s DV deorbit motor for entry, and a 1.14 m diameter drag chute for deceleration and stability through the atmosphere. The transfer from Mars orbit to impact takes approximately 4.5 minutes and results in a 235 m/s impact velocity.
Upon impact the forebody and afterbody of the penetrator separate as shown in Figure 3.1. The umbilical cord connecting the two sections of the penetrator contains power and communications lines. Both hard and soft soil models were used to analyze the impact. The forebody must penetrate deep enough to isolate the seismic instruments from surface wind disturbances, but must not separate from the afterbody farther than the umbilical cord will allow. The penetration of the afterbody must be minimized so that the communications and surface instruments will remain on the surface. The results of the penetration analysis are summarized in Table 3.2.
Each penetrator contains instrumentation that will carry out four scientific objectives: planetary science, imaging, soil analysis, and meteorology. Planetary science is the determination of the interior structure of Mars. This involves the study of the surface structure, global seismology, and the magnetic field of the planet using a seismometer and a magnetometer. Imaging systems on the penetrators will provide information on the geology of the Martian surface. Two imaging systems will be on each penetrator: a descent imager located on the nose of the penetrator and a panoramic imaging system located in the top of the afterbody. Soil analysis is the study of the chemical composition, water content, and physical properties of the subsurface soil. The physical properties of the soil include the subsurface temperature and conductivity. A meteorology package containing four distinct instruments will measure the temperature, pressure, humidity, and wind speed and direction of the local atmosphere.
The necessary subsystems for each penetrator
are power, communications, and thermal control. The power subsystem
is composed of a 0.5 W Radioisotope Thermoelectric Generator (RTG)
and a 20 W Nickel-hydrogen battery. The RTG handles all continuous
power requirements and recharges the battery. The battery will
provide for peak power requirements, such as transmission of data
to Percival. This type of power system provides for a penetrator
with an operating life of one year. The communications system
uses a helix antenna on the penetrator afterbody for receiving
and transmitting data. The thermal system uses thermal blankets
and excess heat from the RTG to keep the battery in the proper
temperature range. The remainder of the excess heat is transferred
to the soil using a heat pipe. Figure 3.3 shows a layout of the
penetrator subsystems and instrumentation. Table 3.6 shows a
breakdown of the mass and power requirements of the penetrator.
Gravity and Science Instruments
Two of the main objectives of the Percival mission are to augment and improve the gravity field mapping being done by MO and to serve as a support platform for scientific instrumentation that was originally planned for MO. The gravity and science instruments group chose the instruments to accomplish these objectives and developed the constraints that the instruments placed on the Percival spacecraft.
Mars Observer will be using radioscience techniques (Doppler shift measurements) to carry out gravity mapping of Mars. Percival will improve upon the accuracy of the MO gravity map by using a two-axis gravity gradiometer, sensitive in the radial and transverse directions. This instrument uses highly sensitive accelerometers to measure the local gravity field. It is expected that an accuracy of 1 Eotvos will be obtained by using the gradiometer without cryogenic cooling. Since gradiometers have never been used in space, Percival will also have the capability to support radioscience techniques. Doppler shift measurements will still augment the gravity map created by MO, though the accuracy of the map will not be improved.
To achieve the desired accuracy and sensitivity of the gravity field map, mechanical vibrations and accelerations generated by the spacecraft must be eliminated or minimized. The gradiometer also requires that attitude position and rates be known very precisely. Table 4.1 summarizes the requirements placed on the GN&C system. While attitude maneuvers are being conducted, the gradiometer will not make gravity field measurements.
The Visual and Infrared Mapping Spectrometer
(VIMS) will also be flown on Percival. This instrument, originally
designed for MO, will determine the composition of the Martian
atmosphere and surface. The VIMS mapping mission requires the
Percival spacecraft to maintain a nadir orientation. This type
of orientation requires the spacecraft to maintain a constant
revolution rate of one revolution per orbit. This rotation rate
is not high enough to significantly affect the gradiometer measurements.
A more sensitive, cryogenically-cooled gradiometer would need
to take the rotational acceleration terms into account. With
an orbital altitude of 179.4 km, one VIMS mapping cycle of Mars
will take 82 days.
Spacecraft Structure and Subsystems
The Spacecraft group was responsible for designing the basic structure and the subsystems of the Percival spacecraft. To eliminate the need for a complete redesign of the spacecraft bus, the Percival spacecraft bus was based on a scaled down version of the Planetary Observer bus used for the MO mission. Systems design was done for the communications, power, thermal, and GN&C subsystems. A schematic of the spacecraft is shown in Figure 5.1. A summary of the mass and power requirements of each spacecraft system is shown in Table 5.1.
The communications system consists of a high-gain antenna and a backup low-gain antenna for communication with Earth. The high-gain antenna will transmit at a frequency of 8.4 GHz with a data rate of 150 kbps. Since Percival will not be able to transmit at all times, the capability to store data in addition to real-time transmission will be used. Ares Industries expects that Percival will receive an allocation of Deep Space Network (DSN) time roughly equivalent to the 8 hours per day that MO receives currently. During the 8 hour period, Percival would be able to transmit approximately 1622 megabits of data.
For communications with the surface of Mars, Percival will use the Mars Balloon Relay (MBR) communications system currently used on MO. This system consists of a low-gain antenna pointed towards the surface of Mars. The antenna will transmit at 401 MHz and receive at 406 MHz with a data rate of 8 kbs. This communications system will support the surface penetrators during the science phase of the Percival mission. Beyond the science phase, the MBR system will support other future surface missions.
An RTG and battery combination was chosen to provide power for the Percival spacecraft. The RTG was chosen for its good mass to power rating (5.4 W/kg) and for its ability to generate power without repointing as solar panels are required to do. The battery would be used to provide power during peak power consumption phases of the mission. Today's RTGs use Plutonium 238 as the radioactive isotope. This isotope is not commonly available, making the RTG very expensive. A less expensive alternative would be to make RTGs that utilize a more readily available isotope, such as Strontium 90. This isotope is a common daughter isotope in all nuclear reactors. In the past, Strontium 90 has been used for SNAP reactors on spacecraft.
The thermal control methods will be based primarily on passive methods to reduce the mechanical noise produced by the system. Passive methods of thermal control will include thermal blankets and surface coatings. The active thermal control methods used will include freon radiators and heaters.
The Guidance, Navigation, and Control
system consists of sensors and thrusters to determine and control
the spacecraft's position, velocity, and attitude. The GN&C
system is designed to be completely autonomous with the capability
of ground override. Attitude and position determination will
be done using a sun sensor and a fixed-head star tracker. Rate
determination will be done using a ring laser gyro. The control
system will use 24 reaction control jets divided among two independent
systems. One system will use hot gas, while the other will use
cold gas. The cold gas thrusters will allow the spacecraft to
be controlled more precisely than the hot gas thrusters will allow.
Recommendations
As designed, the Percival spacecraft is not capable of supporting all mission objectives. The constraint of the Delta launch vehicle has limited the allowable mass of the spacecraft to 460 kg dry mass at Mars. This is 75 kg higher than the mass estimate for Percival of 535 kg. To come within the mass budget, one or more mission objectives may have to be eliminated or a higher performance launch vehicle must be used. It may also be possible to take advantage of larger GEMs (Graphite-Epoxy Motors) to provide the additional boost, if they become available in the future.
A preliminary estimate of the development and production cost for the Percival mission has shown that, as designed, Percival exceeds the desired "Discovery-class" budget of $150 million. The current estimate of $270 million includes the development, production, and launch costs for the Percival mission. The cost estimate does not include program costs, operation costs, or other long term management costs. Ares Industries has concluded that the numerous mission objectives of the Percival mission make it unsuitable for a true Discovery-class mission. If a Discovery-class mission is required, one of the three major scientific objectives, gradiometer, penetrator, or the VIMS, should be chosen as the single, primary mission objective.
To design the Percival Mission to Mars
beyond the preliminary design phase, detailed design must be done
for all portions of the project. The following issues must also
be considered. For the propulsion system, the type of propellant
must be chosen to give a more precise estimate of the fuel mass
required. The penetrator system requires the accuracy of the
penetrator targeting to be determined in addition to the effects
of winds on the entry trajectory and attitude of the penetrator.
Also, the susceptibility of the penetrator structure to failure
during an oblique impact must also be considered. The feasibility
of increasing the data rate of the Mars Balloon Relay should be
determined. For the spacecraft power system, the feasibility
of using a Strontium 90 RTG should be further analyzed. The GN&C
system of Percival should be analyzed in more detail to determine
if it satisfies the position and rate determination and control
requirements defined by the gradiometer.
1.0 Overview1.0 Overview
This report describes the design work
done by Ares Industries to complete the preliminary design of
the Percival spacecraft. This design was done in response to
the Request for Proposal (RFP) for an unmanned Martian gravity
mapper.
1.1 Mission Objectives1.1 Mission Objectives
The following mission objectives, taken
from the RFP, were the basis of the Percival mission design:
To augment and improve the Martian gravity field determination being carried out by Mars Observer.
To deploy a set of instrumented penetrators in selected regions of Mars as a precursor to future manned and unmanned Mars missions.
To relay penetrator and gravity field data back to Earth
To provide a platform for scientific instrumentation cut from the Mars Observer mission due to funding cutbacks.
Low cost, available technology design.
The last mission objective was not explicitly
stated in the RFP, but was implied through the specification of
a Delta class launcher.
1.2 Mission Scenario1.2 Mission Scenario
The above objectives are met by the current
mission scenario, listed below.
Launch using modified Delta-class launcher.
Use a broken-plane Hohmann transfer trajectory between Earth and Mars.
Insert into a low altitude, circular, sun-synchronous Mars orbit.
Determine Mars gravity field using gravity gradiometer and Doppler- shift measurements as a backup.
Release each penetrator individually from Percival in Mars orbit.
Use the "Mars Balloon Relay" communications system for data relay from surface penetrators and future surface missions.
Support both real-time and store-and-forward data transmission to Earth.
Conduct scientific measurements for approximately
1-2 Martian years.
1.3 Design Drivers1.3 Design Drivers
The design of the Percival spacecraft
was driven by the specification of the Delta-class launcher for
the mission and the "Discovery-class" design philosophy
(1). The Delta-class launcher necessitates a low mass due to
the limited performance launchers. The "Discovery-class"
design philosophy specifies a low-cost, limited objective, and
available technology design. This design philosophy has developed
in response to the limited funding that is now available to exploration
spacecraft. Instead of foregoing all space exploration missions,
"Discovery-class" missions may be used to continue the
unmanned exploration of the solar system.
1.4 Report Overview1.4 Report Overview
The technical work done by Ares Industries has been divided among four technical areas: Orbits and Propulsion System Design, Surface Penetrator Design, Gravity Field Mapping and Science Instruments, and Spacecraft and Subsystems Design. The remainder of this report consists of descriptions of the technical work done by each element, a brief section on management and project costs, and the conclusions and recommendations of the Percival design study.
2.0 Orbits and Propulsion System
Design2.0 Orbits and Propulsion System Design
The primary considerations for selecting
an orbital trajectory and propulsion system are the following:
Design must accommodate the mass of the entire spacecraft
Trajectories must minimize the total DV required in order to maximize the available mass
Mission scenario should result in a Mars
orbit that best enables Percival to carry out its objectives
The basic mission scenario as outlined in the request for proposal (RFP) consists of a near-Hohmann trajectory to Mars initiated by a Delta class launcher. The near-Hohmann transfer enables a larger mass to be placed in orbit than most other trajectories. Ares Industries looked into two other types of trajectories: Lambert targeting trajectories and gravity assist trajectories. The Delta class launcher was specified in the RFP because of its low cost. The RFP further specified a final Mars orbit that would trail Mars Observer or be in a high-low configuration with it. However, after consideration of the projected lifetime of Mars Observer and the operational independence inherent in the spacecraft instruments onboard Percival, Ares Industries has decided that this constraint is unnecessary, and will establish an independent orbit.
The considerations affecting the choice
for the final Mars orbit are outlined below:
Low altitude, for sensitivity of measurements
Near circular, for uniformity of measurements
Sun-synchronous, for minimizing thermal
variations
The Percival spacecraft will use a chemical
propulsion system. This system will be used to provide the thrust
for the plane change at the broken plane maneuver and for the
Mars Orbit Insertion burn.
2.1 Launch Vehicle2.1 Launch Vehicle
The Delta 7925 with an additional Star 48B upper stage has been selected as Percival's launch vehicle. The 7925 and its various configurations are the only commercial Delta launch vehicles in production (2). The addition of a second upper stage allows a greater spacecraft mass to be placed into orbit than does a single upper stage; however, the highest allowable spacecraft mass, 1187 kilograms, is achieved when the second Star 48B has only 1587 kg of fuel loaded on it, about three-fourths of its standard amount. Fuel offloading for the Star series of motors is a routine process and should pose no problem (3). The Delta's full launching power was used in creating this configuration, so the two upper stage/spacecraft combination are placed into a low, 185 km circular orbit about the Earth, into which the Delta can lift the most payload mass. From low Earth orbit, the two upper stages successively burn to inject Percival into its transfer trajectory.
The Delta 7925 can not lift as much mass
into orbit as some other commercially available launch vehicles,
but cost is a major constraint in the Percival mission. The 7925
is a good compromise between performance and cost. Figure 2.1
shows a schematic of the Delta 7925.
Figure 2.1 Delta
7925 Launch Vehicle Schematic.
2.2 Earth-Mars Transfer Trajectory2.2 Earth-Mars Transfer Trajectory
Three types of trajectories were considered
for Percival's Earth-Mars trajectory. These three trajectories
are:
1. Hohmann transfer with broken plane maneuver (BPM) at n=90°
2. Lambert-targeted trajectories
3. Gravity assist
2.2.1 Hohmann Transfer
Hohmann transfer trajectories utilize
a minimum DV
transfer by traveling on the smallest ellipse connecting the original
and final orbits. Figure 2.2 illustrates the Hohmann transfer
trajectory.
Figure 2.2 Hohmann
Transfer from Earth to Mars.
The transfer to Mars, however, requires a plane change. A broken plane maneuver performed at a true anomaly of 90° along the Hohmann trajectory will require the smallest amount of DV. The amount of plane change required in such a case is the target's ecliptic latitude, b (4). The following figure (Figure 2.3) illustrates a Hohmann transfer with a broken plane maneuver.
Hohmann transfer trajectories from Earth
to Mars have launch opportunities that repeat every 2.1 years.
Table 2.1 gives the allowable masses and DV's
for the next three launch opportunities. The launch opportunity
in 1996 is the optimum launch date of the three, allowing a spacecraft
dry mass of 460 kg. The calculations were made using the programs
listed in Appendix A.
Figure 2.3 Hohmann
Transfer with Broken Plane Maneuver.
Table 2.1 Comparison
of Three Hohmann Transfer Opportunities.
Time of Flight | |||
Total DV | |||
Percival DV | |||
Total Spacecraft mass | |||
Approximate dry mass |
2.2.2 Lambert Targeting
Lambert Targeting does not require a spacecraft
to follow just one highly-defined trajectory like the Hohmann
transfer. Therefore, a Lambert targeting solution can be found
for more flexible launch windows. Initially, only Lambert targeting
solutions allowing Percival to arrive when Mars is at one of its
orbital nodes were considered in order to eliminate the need for
a plane change. A Lambert targeting trajectory to a descending
node is illustrated in Figure 2.4.
Figure 2.4 Lambert
Targeting Trajectory.
Optimization of the Lambert targeting
solution considers launch date, time of flight, and the required
DV's.
The goal for this type of trajectory was again to maximize the
dry mass of the spacecraft. The results of this optimization
are listed in Table 2.2. As can be seen, neither solution benefits
the mission more than the Hohmann trajectory; thus, no total DV
would be lower than that of the Hohmann trajectory, and no larger
spacecraft dry mass could be attained.
Table 2.2 Lambert
Targeting Options.
Launch date | ||
Time of Flight | ||
DV from LEO | ||
DV for MOI | ||
Total spacecraft mass | ||
Approximate dry mass |
note: LEO - Low Earth Orbit
MOI - Mars Orbit Insertion
More general Lambert targeting solutions
were also investigated. These were Lambert trajectories with
a Broken Plane Maneuver performed 90° before intercepting
Mars. As for the Hohmann trajectory with BPM, performing the
BPM on a Lambert trajectory 90° before target intercept also
requires the least DV
(4). The characteristics of the Lambert solutions calculated
were those with launch dates on each of the 800 consecutive days
beginning in mid-November 1996, and having times-of-flight from
200 to 400 days. The launch dates were chosen to encompass an
entire Earth-Mars synodic period, and also, combined with the
relatively short times-of flight chosen for investigation, to
allow for Percival's arrival at Mars in a timely manner to allow
it to carry out one of its important functions after its primary
science missions have been completed--to provide a communications
link to Earth for future missions to Mars. The results of all
of these calculations are too lengthy to display here, but the
important result is that none of the solutions provided a lower
total DV
or a higher dry mass than did the Hohmann trajectory described
above. Therefore, the broken-plane Hohmann trajectory is preferred
over the Lambert trajectories.
2.2.3 Gravity Assist Trajectories
Gravity assist trajectories utilize the
gravitational attraction of a planet or other large mass to provide
a positive DV
to the spacecraft during a flyby with the planet. The best option
for a gravity assist trajectory from Earth to Mars would utilize
Venus, which is closer to Earth and Mars than Jupiter. But the
additional weight acquired through radiation protection does not
make this option appealing. Since Percival is already over budget
in terms of mass, any added weight can not be allowed. Also,
the longer times of flight would inhibit the types of instruments
that Percival could carry. Therefore, gravity assist is not a
viable option.
2.2.4 Baseline Trajectory
After consideration of all of the options,
the baseline trajectory for the Percival mission to Mars was chosen
to be the Hohmann transfer with BPM. The optimum launch date
is November 28, 1996. The geometry for Earth departure is shown
in Figure 2.5. All relevant numbers are given in Appendix A.
Figure 2.5 Earth
Departure Geometry.
One reason for the appeal of the 1996
opportunity is the small plane change required for it compared
to later opportunities. The plane change angle is only 0.53°,
which translates into a relatively small DV
of 258 m/s. Thirty five extra kilograms of propellant have been
added to Percival to accommodate a total of about 85 m/s of trajectory
corrections. This additional propellant should be sufficient
for any necessary corrections considering that this is approximately
the amount allowed for Mars Observer, a much larger spacecraft
than Percival (5). After a time of flight of 254 days, Percival
should arrive at Mars on August 9, 1997. The approach geometry
is shown in Figure 2.6. Again, all relevant numbers are given
in Appendix A.
Figure 2.6 Mars
Approach Geometry.
2.3 Final Mars Orbit2.3 Final Mars Orbit
For insertion into the final Mars orbit, aerobraking was considered as a propellant-saving option. However, the atmosphere of Mars is very thin (5), so that appreciable results from an aerobraking maneuver could not be obtained without performing a dangerously low passage above the Martian surface. Therefore, this option was discounted, and Mars orbit insertion will be performed by Percival's thrusters so as to directly enter the final Mars orbit.
The final Mars orbit itself will be a circular, sun-synchronous orbit. A sun-synchronous orbit was chosen because it minimizes thermal variations on the scientific instruments, primarily the gradiometer, which could affect their measurements. A low-altitude orbit, 179.4 km, was selected because it allows more accurate gravity readings and the atmosphere is still thin enough at that altitude that the orbit will not decay because of drag (6). The actual altitude was chosen because it allows communications with the penetrators every two to three Martian days, and also allows an orderly coverage of the Martian surface by the VIMS that results in a complete mapping cycle every 82 Martian days. Figure 2.7 summarizes the final Martian orbit. A schematic representation of the groundtracks produced by the orbit design is shown in Figure 2.8.
As shown in Figure 2.7, the orbital plane
is roughly perpendicular to the direction of the sun, and will
remain in this configuration for the duration of the mission.
Therefore, the pointing requirements for Percival's Earth-facing
antenna only encompass a limited range of angles, minimizing repositioning
demands on the antenna which produce mechanical noise disruptive
to the gradiometer.
Circular, sun-synchronous orbit
Altitude: 179.4 km
Inclination: 92.36°
Period: 108.2 minutes
Figure 2.7
Final Mars Orbit.Figure 2.7 Final Mars Orbit.
Figure 2.8 Groundtracks
of Martian Orbit.
Upon completion of its one to two year
mission, Percival will boost itself into a permanent 375 km circular
orbit above the Martian surface. This is to obey international
contamination requirements of ensuring a less-than 0.0001 probability
that the spacecraft will impact Mars before January 1, 2009, and
a less-than 0.05 probability that an impact will occur between
January 1, 2009, and January 1, 2039. To satisfy these requirements,
an orbit with a semi-major axis of at least 3767.2 km is required
(5). A 375 km circular orbit satisfies this requirement. An
orbit of this altitude will also provide better coverage of Mars
and better access to Earth for future missions that may utilize
the Mars Balloon Relay on Percival for communications.
2.4 Orbital Mission Scenario2.4 Orbital Mission Scenario
To summarize, the scenario for the Earth
to Mars trajectory is outlined below.
Launch
Launch optimally on November 28, 1996
Launch on Delta 7925 with second, partially-fueled Star 48B upper stage
Upper stages and spacecraft placed in 185 km circular orbit about Earth
Total spacecraft mass of 1187 kg
Hohmann Transfer with Broken Plane Maneuver
Hohmann transfer with BPM at n=90°
Time of flight - 254 days
DV required to initiate Hohmann transfer - 3576 m/s
Plane change required of 0.53°
DV required for plane change - 258 m/s
Arrival at Mars
Arrival date - August 9, 1997
Direct insertion to 179.4 km circular orbit
DV required for insertion - 2178 m/s
Spacecraft dry mass - 460 kg
Boost Percival at end of mission to 375 km circular orbit
DV
required - 90.9 m/s
2.5 Spacecraft Propulsion System2.5 Spacecraft Propulsion System
The primary option being considered for
the propulsion system is chemical fueled thrusters because they
are well tested, reliable, and low cost. The DV
required of these thrusters is 2436 m/s. The estimated hardware
mass is 60 kg and the estimated propellant mass is 730 kg.
2.6 Summary2.6 Summary
In order to fulfill all of the requirements
and considerations of the orbits and propulsion design of the
Percival mission, many options were considered and some assumptions
were made. The mission scenario and final Mars orbit have been
chosen so as to minimize the DV's
required to execute the mission. This is primarily to maximize
the allowable spacecraft mass at Mars, but also to help lower
the cost of the mission. The addition of a second upper stage
on the Delta to allow more mass will result in a higher cost and
more design effort, but the increased cost should be small compared
to the total cost of the launch system. Furthermore, having a
more powerful upper stage system facilitates the design of a mission
that will accommodate all of the proposed objectives. Nevertheless,
other options for third stages and transfer trajectories should
be investigated in an attempt to further improve the efficiency
of the mission and to increase its scientific potential.
3.0 Surface Penetrator Design3.0 Surface Penetrator Design
One of Percival's primary objectives is to land surface penetrators on Mars in order to deploy instruments on and below the surface. The penetrator instruments will be used to acquire scientific data about Mars in order to advance planetary science and to provide a precursor for future unmanned and manned missions to Mars. The impact sites for the penetrators will be selected on the basis of scientific value and potential for future manned missions.
The basic penetrator mission scenario consists of the following stages:
1) Release from Percival
2) Deorbit and descent to the Martian surface
3) Impact with surface
4) Relay of scientific data back to Percival and then to Earth
for a mission lifetime of one Earth year
Each penetrator consists of a forebody
which penetrates deep into the surface and an afterbody with remains
on the surface. Both the forebody and the afterbody contain
scientific instruments and are connected by an umbilical cord
designed to transfer data and power between the two sections.
Figure 3.1 shows how the penetrator deploys upon reaching the
Martian surface.
Figure 3.1
Surface Penetrator Deployment.
3.1 Deployment and Atmospheric Entry3.1 Deployment and Atmospheric Entry
The penetrators will be released from Mars orbit from Percival, instead of the transfer orbit specified in the Proposal. There are two reasons for this. First, release from Mars orbit lowers the impact velocity that the penetrator must be designed to survive. Second, the required precision in the propulsion and attitude control system is lower when the penetrators are released from the Earth-Mars transfer trajectory, which lowers the weight and complexity of the guidance and control systems.
A spring or similar device will be used to separate each penetrator from the Percival spacecraft. Once the penetrator has moved away from the Percival spacecraft, a small motor will burn to deorbit the penetrator. For preliminary calculations, a 500 m/s DV deorbit motor was assumed. Future analyses will consider the sizing of the deorbit motor and the descent trajectory of the penetrator.
Some form of deceleration during the descent
form orbit will be necessary to reduce the impact loads on the
penetrator. A solid rocket motor was chosen for deorbit and a
drag chute for atmospheric deceleration. The optimum size for
the drag chute was determined to be 1.14 m in diameter. The chute
deploys after about 200 seconds when the penetrator reaches the
tangible atmosphere. After deployment, it takes about 80 seconds
for the penetrator to impact the surface. A smaller drogue chute
is also deployed behind the large chute to assist in the deployment
of the large chute and to increase the aerodynamic stability.
Table 3.1 shows the results of preliminary drag chute sizing.
The 1.14 m drag chute was chosen since it slowed the penetrator
sufficiently without being too large.
Table 3.1 Drag Chute Sizing
3.2 Penetrator Structure and Emplacement3.2 Penetrator Structure and Emplacement
The structure of the penetrators must
withstand the large deceleration loads that occur during impact
with the surface of Mars. The structure must also protect the
scientific instrumentation and penetrator subsystems from being
damaged during the impact. The analysis method used for the penetrator
emplacement and the structural design are taken from Mars Balloon
and Surface Penetrator Study by Mark E. Johnson. This method
is described in detail in Appendix B of this report. Any equations
or related data not mentioned in the following text may be found
in this Appendix. The results of the penetration and stress analysis
for the Percival mission penetrators are given in the following
sections.
3.2.1 Impact Conditions
To determine the necessary strength of the penetrator structure and the depth of penetration, the initial impact conditions must be determined. The primary concern is the impact velocity, since the penetration depth equations use impact velocity as an input. Using a 1.14 m diameter drag chutes yields a 235 m/s impact velocity.
The obliquity of the impact is also a
concern. Stress analysis of the penetrators is based on a normal
impact with the surface (longitudinal axis of penetrator oriented
perpendicular to the surface). Any deviation from a normal impact
will induce bending stresses in the penetrator structure. Future
analysis will determine the oblique impact tolerance of the penetrator
structure.
3.2.2 Penetrator Emplacement
Penetrator emplacement describes the loading and penetration of the penetrator once it impacts with the surface. The depth of penetration, the velocities, and the accelerations experienced by the penetrator during impact are given here.
Equations for the depth of penetration take into account soil characteristics, penetrator nose shape, mass to cross-sectional area ratio, impact velocity, and the varying mass and shape of the penetrator sections. This analysis assumes that the soil cross-section is homogenous.
To account for unknown conditions at Mars, both hard and soft soil penetration models were created. The primary concern for a hard soil model is obtaining sufficient penetration without excessive loads. For the soft soil model, the primary concern is limiting the penetration of the aft section of the penetrator. Excessive aft body penetration would prohibit the antenna and afterbody instruments from operating properly. Another soft soil concern involves the design of the umbilical cord connecting the two penetrator sections. If the forebody separated from the afterbody too much, the umbilical cord would break.
The input quantities for the penetration
analysis are shown in Table 3.2. Table 3.3 shows the results
of the penetration analysis. The results show that the critical
accelerations occur in the aft section of the penetrator since
its penetration depth is much smaller.
Table 3.2
Penetration Analysis Input Quantities.
Impact Velocity | |
Nose Performance Coefficient | |
Low-mass Scaling Coefficient | |
Hard Soil Coefficient | |
Soft Soil Coefficient |
Table 3.3 Penetrator
Performance.
Impact velocity | 235 m/s | 235 m/s |
Maximum deceleration | Fore Section: 2,420 g
Aft section: 8,455 g | Fore Section: 855 g
Aft section: 2,990 g |
Total Forebody Penetration | 1.54 m | 3.66 m |
Antenna height (above surface) | 0.24 m | -0.3 m |
3.2.3 Structural Design
The penetrator must maintain its structural
integrity so that the internal instruments and subsystems are
not damaged. The penetrator is modeled here as a thin cylinder
with titanium as the primary structural material. Steel was also
considered as a primary structural material, but titanium saves
approximately 5 kg per penetrator in structural mass. The instruments
and subsystems are housed in aluminum caging and crushable aluminum
honeycomb. The dimensions and relevant information of the penetrator
design are given in Table 3.4. A dimensioned schematic of the
penetrator design is given in Figure 3.2. The stiffness of the
penetrator will be enhanced by the presence of internal structures.
This effect will not be considered in this analysis. The following
analysis examines the two primary expected failure modes: Euler
column buckling and local wall crippling. Future analyses will
consider the effect of the internal structures and crushable aluminum
honeycomb structure on protecting the internal instruments and
subsystems.
Table 3.4 Penetrator
Dimensions.
Composition | Titanium nose and walls, with aluminum honeycomb impact attenuators |
Nose cone length | |
Nose cone, fore section diameter | |
Fore section length (incl. cone) | |
Fore section wall thickness | |
Aft section diameter | |
Aft section length (not incl. antenna) | |
Aft section wall thickness | |
Total enclosed volume | |
Total structural mass |
Figure 3.2 Penetrator
Dimensions.
For each failure mode, the highest stress
experienced within the penetrator wall is used as the basis of
the structural design. Only hard soil stresses are considered
since soft soil stresses will be lower. The resulting stresses
for the hard soil case are shown in Table 3.5. Critical stresses
for each failure mode and the corresponding safety factors are
given in Table 3.6. These results show that local wall crippling
is the limiting failure mode.
Table 3.5 Maximum
Stress in Penetrator Walls.
Table 3.6 Critical
Stresses for Penetrator Loading.
3.3 Scientific Instruments3.3 Scientific Instruments
The scientific instruments placed on the
surface penetrators will carry out four primary scientific objectives.
These four objectives are planetary science, soil analysis, surface
imaging, and in situ atmospheric measurements. Each penetrator
will contain the same scientific payload. The instruments were
evaluated based on the following criteria:
Scientific value
Weight
Impact Survivability
Power requirements
Cost
Data requirements
Operational lifetime
Compatibility
3.3.1 Planetary Science Instruments
Planetary science is the determination of the interior structure of Mars. This involves the study of the surface structure, global seismology and magnetic field of the planet. Planetary science measurements will be carried out by a seismometer, a decelerometer, and a magnetometer.
Table 3.7 contains a description and the
weight, power, and data rate requirements for each instrument.
The seismometer is the primary planetary science instrument on
the penetrator. The network of three penetrators will provide
information on the interior structure of the entire planet. Information
on the local surface structure is obtained from the decelerometer
which records data as the penetrator impacts the surface. The
magnetometer will provide information on the local and global
magnetic fields.
Table 3.7 Mass, power, and data rate requirements for the planetary science
instrumentation. (7).
3.3.2 Soil Analysis Instruments
Soil analysis is the study of the chemical composition, water content, and physical properties of the subsurface soil. The physical properties of the soil include the subsurface temperature and conductivity.
Table 3.8 contains a summary of the soil
analysis instrumentation. The a-backscatter
spectrometer will be the primary instrument for determining chemical
composition. A g-ray
spectrometer could provide complementary data to the a-backscatter
spectrometer data, but the g-ray
spectrometer is not compatible with the RTG power source. The
radioisotopes emitted by the RTG would contaminate the data taken
by a g-ray
spectrometer (8). The water detector uses a P2O5
electrolytic cell to measure the presence of water vapor in a
soil sample. The thermoprobe is a set of thermocouples located
on the umbilical cord of the penetrator which can measure subsurface
temperatures. The permittivity meter will provide information
about the electrical properties of the ground. The information
from the thermocouple array and permittivity meter will enhance
the soil composition data obtained from the spectrometers and
water detector.
3.3.3 Imaging Systems
Imaging systems on the penetrators will
provide information on the geology of the Martian surface. Two
imaging systems will be on each penetrator: a descent imager located
on the nose of the penetrator and a panoramic imaging system located
in the top of the afterbody. The descent imager is a monochrome
camera, which is based on a frame-transfer CCD, and is not designed
to survive the impact with the Martian surface. The descent imager
has a wide angle lens with a field-of-view of 40° (8). The
panoramic imaging system consists of a television camera with
black & white and color capabilities. Table 3.9 summarizes
the design parameters of the descent and panoramic imaging systems.
Table 3.8 Mass, power, and data rate requirements for the soil analysis
Instrumentation (7).
Table 3.9 Mass, power, and data rate requirements for the penetrator
imaging systems (8).
3.3.4 Atmospheric Measurements
A meteorology package containing four
distinct instruments will measure the temperature, pressure,
humidity, and wind speed and direction of the local atmosphere.
The meteorology package must be located near the end of the afterbody
of the penetrator. The sensors should be deployed above the
penetrator to reduce the effect of the heat flux generated by
the other subsystems and to insure that the meteorology package
is sufficiently elevated above the surface of Mars. Further investigation
of possible deployment methods is necessary. Table 3.10 contains
the design parameters for the meteorology package.
Table 3.10 Mass, power, and data rate requirements for the meteorology
package instrumentation (8).
| ||||
3.3.5 Instrumentation Layout
The scientific instruments must be arranged
with the penetrator subsystems according to the objectives and
requirements of each instrument. The seismometers, for example,
must be placed in the forebody of the penetrator structure to
eliminate the errors induced by the wind on the surface of the
planet. Figure 3.3 is a schematic of the instrument layout within
each penetrator.
Figure 3.3
Schematic of Penetrator Scientific Instrument and Subsystems
Layout.
3.4 Penetrator Subsystems3.4 Penetrator Subsystems
Each penetrator subsystem was chosen on the basis of performance, weight, cost, power requirements, and impact survivability. Each subsystem is detailed in the following section. The mass, power, and volume requirements are based on the analysis done by Mark E. Johnson in his thesis titled Mars Balloon and Surface Penetrator Study.
For the long-term life of the Mars penetrator, the only two viable choices for the power subsystem are solar arrays and radioisotope thermoelectric generators (RTG's). However, solar arrays have the serious liabilities of poor impact survivability and difficulty in continuous service on the active and harsh environment of the Martian surface. Even though RTG's are expensive and complicated, they have been tested to several thousand g's of loading. Nickel-hydrogen batteries will be used to supply short-term power requirements such as communication with Percival. A 0.5 W RTG with a 20 W battery requires about 2.5 kg of mass and 1000 cm3 of volume.
Communications between the penetrator and Percival is essential. A helix antenna was chosen because a traditional dish antenna could not survive the impact of landing on the surface of Mars. A helix antenna requires about 1.5 kg of mass and a continuous 0.2 W of power for the receiver and a short-term power of 5 W for transmission. A helix antenna of this sort is expected to survive as much as 10,000 g's.
Thermal control is another concern for the harsh environment of the Martian surface. Temperatures on the surface vary from 130 K to 300 K. The batteries need to always operate in the upper range of this band, so they must be heated. Fortunately, RTG's produce waste heat which can warm the batteries. A thermal blanket to surround the batteries and RTG will weigh about 0.3 kg. However, the excess waste heat from the RTG must be transferred away from the penetrator by heat pipes. The heat pipes connect the RTG to the aft section of the forebody. The heat is conducted out of the penetrator and into the soil on the side opposite that of the soil composition instruments to minimize heat contamination of the soil.
The computer and data storage requirements
for each penetrator must also be considered. A typical space-certified
computer system to meet our requirements has a mass of about 0.25
kg, a power requirement of 0.05 W, a volume of 200 cm3, and can
survive about 10,000 g's.
3.5 Low-Cost Alternative3.5 Low-Cost Alternative
Because of the complexity of the penetrators
(such as the use of RTG's and impact hardened components), concerns
have been raised about the total cost of each penetrator. If
it becomes necessary to lower the cost of the penetrator, a new
simpler design must be pursued. First, the RTG's would be replaced
with batteries. This would lower the lifetime of the penetrators
drastically, lessening the usefulness of instruments such as seismometers,
which could then be eliminated. It is also possible that the
penetrator structural design can be made into one piece, because
the seismometer requirements will not have to be considered if
they are eliminated. All of the above changes will significantly
lower the cost of the penetrators.
3.6 Summary3.6 Summary
In summary, the surface penetrators are composed to two primary sections; the forebody, which penetrates into the surface, and the afterbody, which remains on the surface. A small solid rocket deorbit motor provides for deceleration from orbit, and a 1.14 m diameter drag chute slows the penetrator down to acceptable velocities. An umbilical cord containing power and communication lines connects the two sections. Each penetrator contains instruments for planetary science, soil composition, imaging, and meteorology. An RTG provides power for the penetrator, with a nickel-hydrogen battery providing for short-term power needs.
Table 3.11 contains the mass and power
summary for each penetrator. The penetrators were allotted 75
kg of total mass, so three penetrators can be carried by Percival.
The total power of the instruments and subsystems is also less
than the maximum power provided by the RTG's.
Table 3.11
Penetrator Mass and Power Summary.
4.0 Gravity Field Mapping and
Science Instruments4.0 Gravity Field Mapping and Science Instruments
As a precursor to future manned and unmanned
missions, Percival is responsible for collecting a multitude of
data about Mars. Instruments onboard Percival will provide detailed
information about the Martian gravity field and the surface composition
of Mars, adding to the data that will be compiled by the Mars
Observer spacecraft. Mars Observer will be measuring the Martian
gravity field using radioscience techniques. The Percival mission
plans to improve and augment on the gravity field mapping carried
out by Mars Observer. The surface composition instrument has
been placed aboard Percival since this instrument was not within
the Mars Observer budget. By adding to and improving the data
that Mars Observer is collecting, a better understanding of Mars
will be achieved.
4.1 Gravity Determination Techniques4.1 Gravity Determination Techniques
One of the primary mission objectives
of the Percival mission to Mars is to improve and augment the
gravity map determined by Mars Observer. In order to accomplish
this goal, Ares Industries considered three gravity measuring
techniques. These three techniques are listed below:
Gradiometers
Doppler tracking
Spacecraft to spacecraft
Earth to spacecraft
RADAR tracking
4.1.1 Gravity Gradiometry
Gradiometers map the gravity field by measuring changes in accelerations using sensitive accelerometers. Figure 4.1 is a schematic design of a single accelerometer.
Changes in acceleration are measured as changes in capacitance along the radial and transverse directions. Measuring the gravity field with gradiometers is a simple concept and one that has been tested on the ground and in aircraft, however, it has never been proven in space nor has the proposed accuracy of 10-2 to 10-4 Eotvos been achieved. There are professionals working on space based gradiometers such as Dr. Paik at the University of Maryland,
Figure 4.1
Dual Axis Accelerometer Preliminary Design (9).
who believe that it is possible to put
gradiometers in space with available technology (10). Such a
system would not achieve our proposed accuracy but it may be able
to achieve an acceptable accuracy of 1 to 10-1 Eotvos, which would
still be an improvement over the Mars Observer measurements.
The difficulty with this system is that any slight acceleration
not caused by the gravity field around Mars will pollute the data.
These accelerations could be caused by a number of things such
as fuel sloshing, thermal variations, antenna movements, and
attitude adjustments. However, if the acceleration is known and
is not too large, it can be accounted for in the data reduction.
The challenge is thus designing a guidance and control system
capable of providing and maintaining a highly accurate attitude.
4.1.2 Radioscience Gravity Mapping (Doppler shift measurements)
Doppler tracking measures the gravity
field of a planet indirectly by tracking the changes of a spacecraft
in orbit. More specifically, this method measures the change
in frequency of the tracking signal. These determinations can
be performed from one spacecraft to another or from Earth to a
spacecraft. If the spacecraft to spacecraft approach is considered
the receiving spacecraft, or target spacecraft, must be capable
of receiving and returning a radio signal sent from the measurement
spacecraft, causing the operating lifetime of the target spacecraft
becomes a constraint on mission design. Further, the target spacecraft
must be in view of the measurement spacecraft. In this approach,
too much of the gravity field measurement is dependent on the
target spacecraft. The Earth to spacecraft approach on the other
hand is a well proven technique which does not rely on a second
spacecraft. Percival does however have to compete with Magellan,
Galileo, Mars Observer and other planetary explorers for Deep
Space Network (DSN) time. Doppler tracking is a low cost, well
proven method and is currently being used by Mars Observer to
map the gravity field around Mars (10).
4.1.3 RADAR Tracking Gravity Mapping
RADAR tracking is similar to Doppler tracking
measurements, but the signal from one spacecraft to another or
from Earth to a spacecraft is measured after it rebounds off the
target. RADAR tracking requires more power than Doppler because
it must send out a signal strong enough that its reflection can
be sensed. The RADAR tracker must also be capable of accurately
tracking its target. For the above reasons, RADAR tracking was
eliminated as a feasible method of gravity field determination.
4.2 Spacecraft Interface4.2 Spacecraft Interface
The choice to use gradiometers to map
the gravity of field of Mars affects the rest of the spacecraft.
There are three main areas affected which will each be discussed
in the following sections. They are:
Attitude determination
Spacecraft orientation
Subsystem interface
4.2.1 Attitude Determination
Gradiometers are more sensitive than Doppler
or RADAR measurements, and therefore require more precise knowledge
of the attitude of the spacecraft. The precision with which Percival
will need to be able to determine its attitude are listed in Table
4.1 (12).
Table 4.1 Gradiometer
Attitude Control Constraints.
Pitch, yaw, and roll | < 0.05° |
Angular rate | < 0.106 rad/sec |
Angular Acceleration | < 10-8 rad/sec2 |
Linear Acceleration | < 10-8 m/sec2 |
The instruments used to determine the
attitude of the spacecraft must not create vibrations which would
affect the gradiometer readings. The following instruments will
be used to determine the attitude of Percival.
Fixed head star tracker
Sun sensor
Ring laser gyroscopes
4.2.2 Spacecraft Orientation
In order to measure the gravity field of a planet, gradiometers sense changes in acceleration. As a consequence, anything that produces an acceleration will affect the gravity field measurement. Most planetary spacecraft orbit in a local vertical - local horizon reference frame. In this reference frame, one axis in the spacecraft is always pointed perpendicular to the local horizon and usually the spacecraft is spin stabilized. This orientation has the advantage that the scientific instruments are always pointing toward the planet that they are observing. However, in this reference frame, the (w2r ) centrifugal acceleration will affect the gradiometer readings. For an accurate measurement, the w2r must be known precisely so that it may be taken out of the data or the gradiometer must be a single axis gradiometer. When using a single axis gradiometer, two accelerometers (one for redundancy) are placed on the spin axis of the spacecraft so that there is no w2r term to determine (6). This limits the spacecraft to measuring changes in gravity in only the local vertical direction but this is still an improvement on Mars Observer's data.
The inertial reference frame orientation,
in which one axis of the spacecraft is always pointed toward a
distant object and the spacecraft does not rotate as illustrated
in Figure 4.2, eliminates the centrifugal acceleration term.
However, now the scientific instruments can not always observe
the planet and the direction of the transmitting and receiving
communication antennae change position with respect to the Earth.
This is not a convenient attitude for the Visible Infrared Mapping
Spectrometer (VIMS). In addition, the movement of the antenna
will create unwanted accelerations.
Figure 4.2 Inertial
Reference Frame.
4.2.3 Subsystem Implications
The two other subsystems that the gradiometers
and attitude control affect are the propulsion and thermal systems.
The propulsion system must be designed to prevent fuel sloshing
because the resulting vibrations affect the gravity measurements.
Multiple fuel tanks would lessen fuel sloshing (13). Also, cryogenic
cooling would increase the accuracy of the gravity measurements.
In our proposal, Ares Industries initially proposed a level
of accuracy of 10-2 to 10-4 Eotvos. To achieve this level of
accuracy, Percival's gradiometers would have to be cryogenically
cooled (12). However, cryogenic cooling would add extra mass
to the Percival spacecraft. A level of accuracy of 1 to 10-1
Eotvos is possible without cryogenic cooling and is still considerably
more accurate than the readings of Mars Observer (10).
4.2.4 Mass, Volume, and Power Requirements
The following table (Table 4.2) summarizes
the mass, volume, and power requirements for the gradiometers
and the two scientific instruments.
Table 4.2 Mass,
Volume, and Power Requirements of Gradiometer and Science instruments.
Dimensions | Mass | Power | |
Each Gradiometer | 60x60x90 cm | 50 kg | 65 - 125 W |
VIMS | 120x64x52 cm | 22 kg | 74 W |
Balloon Relay | dia 5 cm
length 60 cm | 6.8 kg | 12.5 W |
note: VIMS - Visible Infrared Mapping
Spectrometer
4.3 Scientific Instruments4.3 Scientific Instruments
The two instruments carried on Percival are a Visible and Infrared Mapping Spectrometer (VIMS), shown in Figure 4.3, which was cut from Mars observer due to funding, and a Mars Balloon Relay (MBR) communications system (14). The VIMS instrument uses imaging spectrometry to identify the spectral features of Mars in the visible and infrared regions. The spectral data will provide a mineralogical map of the Martian surface and a concentration map of water and carbon dioxide in the atmosphere (clouds) and on the surface (frost and snow) of Mars (14). The MBR serves as a communications link between surface vehicles and Earth (11). The MBR will operate beyond the science phase of the Percival mission.
The VIMS has two data acquisition modes: mapping mode and snapshot mode. Mapping mode takes a representative sample of the surface. In this mode every other 182 m pixel is read and every other scan line is skipped. The snapshot mode is a much more comprehensive sampling mode. In this mode every pixel is read and every line at full resolution. A maximum area of 53.46 km2 may be mapped in this mode. Typically, the mapping mode will be used for most data acquisition while the snapshot mode will be used for detailed maps of specific areas of interest. VIMS provides a 512 kbyte buffer to accommodate both modes of data acquisition.
Figure 4.3 Visible
and Infrared Mapping Spectrometer Schematic (14).
4.4 Summary4.4 Summary
To summarize, the gravity mission objective
will be achieved through the use of gravity gradiometers. Following
lists the major points of the gradiometers:
Accelerometers on the axis of rotation
Reads lower and higher order gravity terms
Precise attitude and position necessary
Local vertical - local horizon orientation
Propulsion system - multiple fuel tanks
No cryogenic cooling necessary
Readings from 1 to 10-1 Eotvos
Readings taken for 1 - 2 Martian years
Doppler shift measurements used as backup
Doppler shift measurements augment Mars
Observer's data if resonance designed accordingly
For the future, costs for these instruments
need to be determined, radioscience techniques need to be investigated
further, and the design of the gradiometer needs to be refined.
5.0 Spacecraft Structure and
Subsystems Design5.0 Spacecraft Structure and Subsystems Design
The purpose of this section is to consider options for the spacecraft structure (bus) and subsystems. Two potential spacecraft busses were being considered prior to the PDR1 phase, one of which included a new design using aerobraking. The second option for the spacecraft bus was a scaled down version of the Planetary Observer class spacecraft. These two alternatives were examined carefully and a decision was made based on mission requirements and costs.
In addition to determination of the spacecraft
structure, this section also examines the subsystems that will
be used on the Percival spacecraft. The subsystems included are
power systems, thermal control, communications, and guidance,
navigation, and control (GN&C). Where applicable, there is
a brief discussion as to why a particular subsystem was chosen
over a competing subsystem.
5.1 Spacecraft Structure5.1 Spacecraft Structure
As mentioned previously, one consideration
for the spacecraft bus was a new design utilizing aerobraking.
This design was ruled out because the thin Martian atmosphere
will not be able to supply the necessary drag required for considerable
propellant savings. Also, a new design, which would incorporate
an aeroshell to protect the spacecraft, would require extensive
research and development (R&D). Thus, a scaled down version
of the Planetary Observer class spacecraft (currently used on
the Mars Observer mission), with slight modifications, will be
used (see Figure 5.1). Ares Industries feels that this design
will minimize R&D costs and provide valuable feedback on the
reliability and performance of the bus (based on information attained
from the Mars Observer mission).
5.2 Power Subsystem5.2 Power Subsystem
Figure 5.1 Scaled
Down Version of Planetary Observer Spacecraft.
use a Plutonium 238 isotope that can only be irradiated at the Savannah River Reactor, it is extremely expensive to manufacture an RTG (estimated at $20,000 per watt produced by the RTG). Currently, the Savannah River Reactor is not operable and will require several months of start up time in addition to at least 30 months for production of the 238 isotope (15). Because of the present costs and time constraints, other sources of plutonium 238 should be found, such as the stores which were previously reserved for the now canceled CRAF mission. Strontium 90, an isotope that is produced as a byproduct in nuclear power reactors, is also being considered as a potential fuel for the RTG. This material is readily available and also has an excellent mass to power ratio (16). Strontium 90 was used in SNAP devices (early RTG's) but has never been used on RTG's in space (16). It may be expensive to separate Strontium 90 from other reactor products, and the feasibility of using this material in space has not been investigated fully.
At one point in the mission design, consideration
was given to the use of solar arrays as a potential power source.
They were discarded as an option because of the creation of mechanical
noise that would occur during realignment phases. The gradiometer
that will be used for gravity mapping is highly sensitive to mechanical
noise. Therefore, unnecessary mechanical noise could bias scientific
data. Also, because the solar arrays occupy a considerable area
around the spacecraft, they could infringe upon the reception
and transmission of telemetry data.
5.3 Thermal Control Subsystems5.3 Thermal Control Subsystems
Both active and passive thermal control
measures will be used by the Percival spacecraft. Passive thermal
control devices include thermal blankets and surface coatings
(15). Ares Industries felt that the active thermal control devices
should be limited to those that create the least mechanical noise
while still meeting the requirements of both subsystems and science
instruments. Therefore, freon radiators will be used by Percival
for cooling where required. Heaters will supply any necessary
temperature increases on the spacecraft.
5.4 Communications Subsystem5.4 Communications Subsystem
The Percival spacecraft has two independent communications systems. First, the Mars Balloon Relay (MBR) instrument will relay data between the penetrators or future surface missions and Percival. This instrument comprises an antenna, transmitter, and receiver in one package. The penetrator data is relayed between 401 and 406 MHz. The MBR antenna has no pointing capabilities and is fixed to the "Mars-facing" side of the spacecraft. The spacecraft will be in view of the penetrators for a maximum of 215 seconds on each pass, and during this time, the MBR and the penetrator will establish communications and relay the penetrator's accumulated data. The data transfer rate for the MBR is limited to 16 kbps (thousand bits per second); therefore 200 kilobytes of data can be transferred in a typical 100 second pass.
A parabolic high-gain antenna will provide communications with Earth. An antenna size of 1 m will provide acceptable performance. The system will operate in the X band at 8.4 GHz, which is a standard frequency for space communications. Calculations of the total system performance show that for a transmitter output power of 5 watts RF and a data rate of 150 kbps, for the worst case scenario when Earth and Mars are 2.5 AU apart, the received signal to noise ratio will be 9 dB for the 34-m and 15 dB for the 70-m Deep Space Network (DSN) antennas (16, 17). This signal to noise ratio is sufficient to ensure reliable communications with Earth. The transmitter will use solid-state electronics and will require 20 watts of electrical power when operating. The half-power beamwidth of the 1-meter antenna, at this frequency, is 2.5°. In the worst case, when Earth is at its maximum elongation as seen from Mars, this beamwidth will require that the antenna be repointed every two minutes. Due to the accelerations and rotations caused by antenna movement, no gravity gradiometer data can be taken during the repositioning. A low-gain antenna will also be included on Percival for contingency communications if the high-gain antenna cannot be used or loses Earth point. The low-gain antenna will be helical with a beamwidth of 67°, which is sufficient to maintain communications without the need to repoint the antenna. The maximum data rate if the low-gain antenna must be used is 1200 bps.
The mapping orbit has a period of 108 minutes, with 52 minutes available for data playback to the DSN antennas on Earth. It is anticipated that the Percival mission will receive a DSN allocation equal to that of Mars Observer, which uses one 8-hour period per day on the 34-meter HEF subnet antennas to transmit to Earth. In one 8-hour DSN pass, Percival can transmit data over four orbits, for a total of 1622 megabits of data transmitted to Earth per day.
The data sent to Earth will be encoded
by the Reed-Solomon method, which encodes redundant bits with
data bits in such a way that if errors are introduced during transmission,
the original data can be recovered if the errors are not too serious.
The Reed-Solomon code replaces every 218 bits of data with 250
bits of encoded data, resulting in a communications throughput
speed of 130 kbps.
5.5 Guidance, Navigation, and Control5.5 Guidance, Navigation, and Control
A precise and reliable guidance, navigation,
and control system is essential to the successful completion of
Percival's mission objectives. Each subsystem is designed to
meet the requirements imposed by the overall spacecraft and scientific
objects. The guidance system determines where the spacecraft
needs to go, the navigation system determines where the spacecraft
is, and the control system performs the acts necessary to get
the spacecraft from where it is to where it needs to go. The
guidance, navigation, and control subsystems are described in
the following paragraphs.
5.5.1 Guidance
The guidance system for Percival is contained
on the spacecraft. Percival will utilize autonomous guidance
with ground based override capability. Spacecraft-based guidance
does impose slightly more weight, power, and cost penalties on
Percival than does ground-based guidance. However, for reasons
of practicality and mission safety, ground-based override capability
will be used.
5.5.2 Navigation
Percival will have a variety of navigation
instruments, such as sun sensors, a star sensor, and a ring-laser
gyroscope. The sun sensor is used as a coarse acquisition sensor.
In other words, it is used to estimate the attitude of the spacecraft,
to an accuracy between 0.01 and 0.1 degrees, so that the star
sensor can then be used to improve the accuracy of the attitude
determination. Percival will have four sun sensors, which will
allow the spacecraft attitude to be determined from any initially
unknown position. Percival will also have a fixed-head star tracker,
which will provide a very accurate position measurement for Percival
on the order of 0.001 degrees of accuracy. The fixed-head tracker
will be used in lieu of a gimbaled star tracker in order to minimize
mechanical noise, weight, and cost. Finally, Percival will contain
a ring-laser gyroscope. Ring-laser gyroscopes use certain properties
of light to determine attitude rates. The ring-laser gyroscope
has many advantages over conventional gyroscopes, including greater
accuracy and reliability and lower weight. The gyroscope will
keep track of the attitude in between star tracker measurements,
and the star tracker will update the gyroscope in order to minimize
drift error. Ring-laser gyroscopes are a new technology, but
they have been proven on the Boeing 757 and 767 as well as the
Orbital Sciences Transfer Orbit Stage. This combination of instruments
will satisfy all of the navigation requirements for Percival (15).
5.5.3 Control
Twenty-four reaction control jets will
be used for attitude control on Percival. Two separate attitude
control systems will be used for reliability purposes, with each
system containing its own independent fuel system. Three-axis
control capability will be available because of the distribution
of the twelve jets in each control system. The distribution also
allows the control system to survive a single jet failure without
impairing the ability of the control system. Figure 5.2 shows
a schematic representation of the control system. One of the
control systems will contain hydrogen, or cold-gas, thrusters
for fine attitude control. The other control system will be composed
of hydrazine, or hot-gas, thrusters with a catalyst for higher
thrust and lower accuracy requirements. Two control systems were
considered essential to meet mission requirements in the event
of a single system failure.
Figure 5.2 Dual
Attitude Control System for Percival Spacecraft.
5.6 Summary5.6 Summary
In summary, the Percival spacecraft will utilize a scaled down Planetary Observer with power supplied by an RTG and battery. Thermal control devices include thermal blankets, surface coatings, heaters, and freon radiators. Percival will use the Mars Balloon Relay System for reception of penetrator data and a high gain antenna for penetrator and science instrument data transmission to earth in real time. The onboard computer system will also have the ability to store data for periods when Percival is not in its transmission zone. A low-gain antenna will be used for backup and redundancy purposes. The spacecraft will have completely autonomous guidance with ground based override capability. Sun sensors, a star sensor, and a star tracker will be used for attitude determination, while ring laser-gyroscopes will be used for rotation rate determination. Percival will contain 24 hot and cold gas reaction control jets capable of both low and high precision attitude control maneuvers.
Finally, Table 5.1 contains the mass and
power requirements of the spacecraft structure and systems. The
total mass, 1262 kg, shown in Table 5.1 is inclusive of a 10%
safety factor. However, this spacecraft mass is 75 kg over the
mass budget for Percival. The power requirement of 299 W (this
is a peak value) does fall within the 300 W that can be produced
by the RTG.
Table 5.1 Mass
and Power Requirements for Percival.
Penetrators | ||
MBRS | ||
VIMS | ||
Gradiometer | ||
GN&C | ||
Communications | ||
Computer System | ||
RTG | ||
Batteries | ||
Propulsion | ||
Thermal Control | ||
Spacecraft Structure | ||
6.0 Management Structure and
Cost Summary6.0 Management Structure and Cost Summary
6.1 Management Structure6.1 Management Structure
The organizational structure of the Percival
mission design team is shown in Figure 6.1. The project was managed
by three upper management personnel: the Team Leader, the Chief
Engineer, and the Chief Administrator. The design work was divided
among four technical areas: Orbital and Propulsion System Design,
Surface Penetrator Design, Gravity Field Mapping and Science Instrumentation,
and Spacecraft Structure and Subsystems Design. Each technical
element was composed of three engineers and was headed by an element
leader. This organizational structure remained essentially the
same since the project start. Workload demands in the elements
necessitated shifting of engineering personnel between elements
to accommodate increased or reduced workloads.
Figure 6.1 Percival
Design Team Organizational Structure
Integration efforts were conducted by the element leaders, headed by the Chief Engineer. The task of building a spacecraft model was headed by the Spacecraft Systems element lead. Personnel for this task were taken from all elements. The task of creating a poster describing the mission was given to the upper management personnel.
The client for the Percival project asked
that the Ares Industries management use and evaluate MicrosoftProject®
software designed to help create scheduling and critical path
charts. Initial work was done to create Gantt and PERT charts
for the Percival project using MicrosoftProject®. Recommendations
for use of this software product will be made to the contract
monitor.
6.2 Cost Summary6.2 Cost Summary
The cost for the preliminary design portion
of the project has been broken into personnel cost and material
cost. A preliminary cost for the Percival Mission to Mars launch
and space segments was also calculated using parametric cost estimating
relationships (19). The following sections discuss each of these
cost areas.
6.2.1 Personnel Cost
Personnel cost have been tracked using
weekly progress reports from each design team member. The personnel
cost for the design effort up to the end of week 13 is shown in
Figure 6.2. The total personnel cost is currently $24,786. This
is approximately $4,500 below the proposed cost expected at this
date. The discrepancy is due to an overestimate of the number
of hours worked weekly by the engineering personnel. Appendix
C contains a detailed breakdown of the personnel cost by team
member.
6.2.2 Material Cost
The material costs used in the design
effort came in on schedule with the proposed material costs.
6.2.3 Preliminary Cost Estimate
The total cost of the Percival Mission to Mars is estimated to be $271 million (fiscal year 1990 constant dollars). Appendix C contains a summary of the cost for each portion of the space segment of the mission (32). The total cost is over the proposed "discovery class" mission philosophy cost of $150 million. Ares Industries has concluded that the primary scientific goals of the Percival mission (improved gravity mapping and penetrators) cannot be accomplished within the current discovery class definition. The gravity gradiometer and penetrators are new technologies that are costly additions to the Percival Mission to Mars.
Figure 6.2 Personnel
Cost Status
7.0 Conclusions7.0 Conclusions
The main objectives of the Percival mission are to make gravity field measurements at Mars that will augment and improve the Mars Observer gravity mapping, to deploy penetrators to Mars as a precursor to future missions, and to provide a platform for scientific instrumentation that was originally planned for Mars Observer. These objectives were to be designed into the mission with a low-cost "Discovery-class" design philosophy as the driver.
Each of the three scientific payloads on Percival was designed to meet the desired objectives. The gravity gradiometer will provide more accurate data than Mars Observer's gravity map will contain. The Doppler-shift measurement capability, used as a backup to the gradiometer, will still augment the Mars Observer gravity map, though the accuracy of the map will not be improved. Three individual penetrators will be deployed to separate regions of Mars to collect surface and sub-surface data. This data will help future mission designers to chose the most feasible and most scientifically interesting landing sites on Mars. The VIMS will be carried aboard Percival, fulfilling the scientific platform objective.
The "Discovery-class" design philosophy specifies a low-cost, limited mission, and available technology design. This design philosophy was violated in several areas. Though Percival has fewer primary scientific packages than previous spacecraft, such as the seven instruments on Mars Observer, three primary scientific objectives may still be too high for a "Discovery-class" mission.
Spaceborne gradiometers can not be considered as available technology. Gradiometers have been used in aircraft and on ships, but never in space. Much disagreement about the obtainable accuracy of gradiometers exists. Ares Industries has claimed only a moderate accuracy of 1 Eotvos is possible with spaceborne gradiometers. Since this technology is untested, Doppler-shift measurement capabilities will be designed into Percival with negligible additional weight or cost.
The most prominent violation of the "Discovery-class" design philosophy was the low-cost specification. The estimated design, development, and production costs for the Percival mission is $270 million, compared to the "Discovery-class" goal of $150 million. The scientific instruments and the RTG's are major contributors to the cost estimate. The nature of the gradiometer and the VIMS as single-use instruments makes them more expensive than other spacecraft instruments. Impact-hardened instruments on the penetrators will cost considerably more than their standard counterparts. Also, the extremely limited availability of RTG's makes them very expensive.
Though each of the scientific payloads was integrated into the Percival spacecraft design, the total spacecraft mass is greater than the specified launch system can support. The Delta 7925 with an additional upper stage allows for a spacecraft dry mass of 460 kg at Mars. The current integrated spacecraft which meets all of the mission objectives has an estimated mass of 535 kg. Ares Industries has concluded that the primary scientific goals of the Percival mission cannot be accomplished within the current "Discovery-class" definition and cannot be accomplished with a Delta-class launch vehicle.
8.0 Recommendations8.0 Recommendations
With the constraint of the Delta-class launch vehicle, Ares Industries was not able to design the Percival mission to include all of the mission objectives within the allowable weight. The spacecraft as designed is 75 kg over the mass budget, which is the exact weight of the penetrator system. Although undesirable, it would be possible to use the Delta vehicle to launch the Percival mission without the penetrator system. At this time, the only alternative available to launch the full Percival mission would be to choose a larger, more expensive launch vehicle.
Technology must be developed further for the full Percival mission to be launched using a Delta-class launch system. One modification that has been examined is the modification of the GEM motors. The performance of the GEMs would be increased by lengthening the motors. Other future alternatives might be the use of upper stage motors with better performance characteristics than the Star 48B's currently used.
Ares Industries has concluded that the current mission objectives cannot be accomplished within the current definition of the "Discovery-class" design philosophy. If the "Discovery-class" mission becomes a necessary constraint, one of the three primary scientific packages should be chosen as the single, primary mission of the Percival spacecraft. This choice will reduce both the complexity and the cost of the mission.
To design the Percival Mission to Mars
beyond the preliminary design phase, detailed design must be done
for all portions of the project. The following issues must also
be considered. For the propulsion system, the type of propellant
must be chosen to give a more precise estimate of the fuel mass
required. The penetrator system requires the accuracy of the
penetrator targeting to be determined in addition to the effects
of winds on the entry trajectory and attitude of the penetrator.
Also, the susceptibility of the penetrator structure to failure
during an oblique impact must also be considered. The feasibility
of increasing the data rate of the Mars Balloon Relay should be
determined. For the spacecraft power system, the feasibility
of using a Strontium 90 RTG should be further analyzed. The GN&C
system of Percival should be analyzed in more detail to determine
if it satisfies the position and rate determination and control
requirements defined by the gradiometer.
9.0 References9.0 References
1. Robinson, Dr. Paul, Assistant Chief
Technologist for JPL, Phone interview on 10/06/92.
2. ------,"Delta", Delta Systems
Program Office, Los Angeles, California, 1990.
3. ------,"Star Motor Data",
in ASE 166M Class Notes, University of Texas at Austin, 1986.
4. Bate, Roger R., Donald D. Mueller, and
Jerry E. White, Fundamentals of Astrodynamics, Dover Publications,
Inc.: New York, 1971.
5. Beerer, Joseph G. and Ralph B. Roncoli,
"Mars Observer Trajectory and Orbit Design", Journal
of Spacecraft and Rockets, Sept-Oct 1991, American Institute
of Aeronautics and Astronautics, Washington, D.C.
6. Fowler, Dr. Wallace, Professor Department
of Aerospace Engineering and Engineering Mechanics, University
of Texas at Austin, Personal Interview.
7. Johnson, Mark E. "Mars Balloon
and Surface Penetrator Design Study," Master's Thesis,
University of Texas at Austin College of Engineering, May 1990.
8. Chicarro, A.F., et al, "MARSNET
Report on the Assessment Study", ESA Publication SCI(91),
6 January 1991.
9. Bettadpur, Srinivas, Department of Aerospace
Engineering and Engineering Mechanics (Graduate student), University
of Texas at Austin, Personal Interview.
10. Lundberg, Professor Department of Aerospace
Engineering and Engineering Mechanics, University of Texas at
Austin, Personal Interview.
11. McKinley, E.L., "Mars Observer
Project: An Introduction", AIAA Journal of Spacecraft
and Rockets, vol. 28, No. 5, 489-490, Sept.-Oct. 1991.
12. Sanso, F. and Rummel, R. Theory
of Satellite Geodosy and Gravity Field Determination - Notes
compiled from a symposium, New York, 1988.
13. Griffin and French, "Space Vehicle
Design", AIAA, Inc., 1991.
14. Blume, Bill, Mission Planner for Mars
Observer, Jet Propulsion Laboratory, Pasadena, CA, Phone interview.
15. ------,Spacecraft Subsystems (Student
Spacecraft Subsystems Descriptions), Department of Aerospace
Engineering and Engineering Mechanics, University of Texas at
Austin, January 1992.
16. CRC Handbook of Physics and Chemistry,
49th Edition, Chemical Rubber Publishing Company: Cleveland,
Ohio 1968.
17. Cogdell, J. R., Foundations of Electrical
Engineering, Prentice Hall: Englewood Cliffs, New Jersey,
1990.
18. The 1989 ARRL Handbook, The
American Radio Relay League, Newington, Connecticut, 1988,
19. Wong, Robert, "Cost Modeling",
in Space Mission Analysis and Design, ed. J. Wertz and
W. Larson, Kluwer Academic Publishers, The Netherlands,1991.
10.0 Bibliography10.0 Bibliography
Bate, Roger R., Donald D. Mueller, and
Jerry E. White, Fundamentals of Astrodynamics, Dover Publications,
Inc.: New York, 1971.
Bettadpur, Sirnivas, ASE Graduate student,
University of Texas at Austin, Personal Interview.
Beerer, Joseph G. and Ralph B. Roncoli,
"Mars Observer Trajectory and Orbit Design", Journal
of Spacecraft and Rockets, Sept-Oct 1991, American Institute
of Aeronautics and Astronautics, Washington, D.C.
Blume, Bill, Mission Planner Mars Observer
JPL, Phone interview.
Braun,R. "Aerodynamic Requirements
of a Manned Mars Aerobraking Transfer Vehicle", Journal
of Spacecraft and Rockets, June 1988.
Burgess, Eric, Return to the Red Planet,
Columbia University Press, New York, 1990, p. 137.
Chicarro, A.F., et al, "MARSNET Report
on the Assessment Study", ESA Publication SCI(91), 6 January
1991.
Conolly, John, Lunar and Mars Exploration
Office, Phone Interview.
Covault, Craig, "U.S. Satellite Launch
to Renew Mars Exploration" in Aviation Week and Space
Technology, Aug. 17,1992, p. 42.
Dubrawsky, Ido, "Design of an Unmanned
Robotic Mission to Mars", Master's Thesis, University of
Texas at Austin College of Engineering, May 1992.
Esposito, Pasquale and Duane Roth, "Mars
Observer Orbit Determination Analysis", Journal of Spacecraft
and Rockets, American Institute of Aeronautics and Astronautics,
Washington, D.C., Sept-Oct 1991.
Fenlason et al.,"A Phobos Industrial
Production and Supply Base", UT-Austin, Dec. 8, 1986.
Fowler, Dr. Wallace, Professor ASE Department,
University of Texas at Austin, Personal Interview.
Griffin and French, "Space Vehicle
Design", AIAA, Inc., 1991.
Joels, Kerry M.,The Mars One Crew Manual,
Ballantine Books, 1985.
Johnson, Mark E. "Mars Balloon and
Surface Penetrator Design Study," Master's Thesis,
University of Texas at Austin College of Engineering, May 1990.
Kaplan, Dave, Lunar and Mars Exploration
Office, Phone Interview.
Lewis, John S., "The History of Mars,"
The NASA Mars Conference, American Astronautical
Society, 1988.
Lundberg, Dr. John, Professor ASE Department,
University of Texas at Austin, Personal Interview.
McKinley, E.L., "Mars Observer Project:
An Introduction", AIAA Journal of Spacecraft and Rockets,
vol. 28, No. 5, 489-490, Sept.-Oct. 1991.
Palocz, Suzanne, "Mars Observer Mission
and Systems Overview", AIAA Journal of Spacecraft and
Rockets, Vol. 28, No. 5, 491-497, Sept.-Oct. 1991.
Report of 90-Day Study on Human Exploration
of the Moon and Mars, Task force of NASA for the National Space
Council, November 1989.
Robinson, Dr. Paul, Assistant Chief Technologist
for JPL, Phone interview on 10/06/92.
Sanso, F. and Rummel, R. Theory of
Satellite Geodosy and Gravity Field Determination - Notes
compiled from a symposium, New York, 1988.
U.S. Congress, Office of Technology Assessment,
"Exploring the Moon and Mars; Choices for the Nation,"
OTA-ISC-502, Washington, DC: U.S. Government Printing Office,
July 199.
The following analysis was taken form Mars Balloon and Surface Penetrator Study by Mark E. Johnson. The equations and empirical data were originally developed at Sandia National Laboratories. Given the dimensions and mass of a penetrator, soil characterization, and an impact velocity, the depth of penetration, the maximum accelerations, and the maximum stresses present in the penetrator walls can be calculated. Equations are also given for the calculation of critical stresses for Euler column buckling and local wall crippling.
The equation used to predict the depth
of penetration is as follows:
where dn is the penetration depth (m), Kn is the low-mass scaling coefficient, Sn is the characteristic soil coefficient, Nn is the nose performance coefficient, M/A is the mass-to-cross-sectional area ratio (kg/cm2), and Vn is the impact velocity.
The subscripts allow for differing soil characteristics and different penetrator mass and cross-sectional areas. Each "layer" calculation represents a layer of homogeneous soil or a thickness through which the penetrator's cross-sectional area and mass are the same. The soil will be assumed to be homogenous for all calculations. Thus, each calculation represents a different section or configuration of the penetrator.
Three penetration calculations are necessary for the fore and aft design of the penetrator. The first determines the penetration of the penetrator before the aft section separation. This calculation ensures that the depth of penetration is enough to cause the fore and aft sections to separate (dn must be greater than the length of the forebody). If dn is greater than the forebody length, the initial penetration is set equal to the forebody length. The second calculation determines the depth of the forebody after the aft section separates. The last calculation determines the depth of penetration of the aft section. The final depth of penetration of the forebody is the sum of the first two depth calculations.
The low-mass scaling coefficient is determined
from the graph shown in Figure B.1. The nose performance coefficients
are determined from Table B.1. Guidelines for the choice of soil
coefficients are given in Table B.2. The shaded region indicates
the soil characteristics considered by the Percival project.
The data in these graphs and tables was empirically developed
at Sandia National Laboratories.
Figure B.1 Low-mass
scaling coefficients
Table B.1 Nose
Performance Coefficients, N
|
| |
|
| |
|
| |
Table B.2 Characteristic
Soil Coefficients, S
Massive medium to high-strength rock, with few fractures; Concrete, 2-5 ksi, reinforced. | |
Silt or clay, frozen, saturated, very hard; Rock, weathered, low-strength, fractured; Sea or freshwater ice more than 10 feet thick. | |
Massive gypsite deposits; Sand and gravel, coarse, well-cemented; Caliche, dry; Silt or clay, frozen, moist. | |
Sea or freshwater ice from 1 to 3 feet thick; Sand, medium to coarse, medium dense, no cementation, wet or dry; Silt or clay, hard, dry, dense; Desert alluvium. | |
Fine sand, very loose, excluding topsoil; Silt or clay, moist, stiff, medium dense, less than about 50% sand. | |
Topsoil, moist, loose with some clay or silt; Clay, moist, medium stiff and dense, with some sand. | |
Topsoil, loose, moist, with humus material, mostly sand and silt, soft, low shear strength. | |
Topsoil, very loose, dry, sandy; Silt or clay. saturated, very soft, low shear strength, high plasticity; Wet lateritic clays. | |
Snow, loose. |
For each new calculation beyond the first,
the new initial "impact" velocity must be determined.
This velocity can be found using the acceleration and velocity
equations shown below:
where an is the deceleration over the penetration
(m/s2), Vn is the impact velocity for the previous layer (m/s),
and dn is the penetration depth or "thickness" of the
layer (m). Experiments done at Sandia National Laboratories have
shown that the deceleration due to penetration is essentially
a step function rather than an impulse function. Thus, the deceleration
is considered to be constant for each layer calculation. The
new initial velocity is given by:
where Vn-1 is the initial velocity for
the previous layer (m/s), an-1 is the acceleration through the
previous layer (m/s2), Tn-1 is the thickness of the previous layer
(m), Ln-1 is the length of the previous Penetrator section's nose
(m).
Stress Analysis
The following analysis examines the two
primary expected failure modes for a penetrator: Euler column
buckling and local wall crippling. For each failure mode, the
highest stress experienced within the penetrator wall is used
for comparison. The following equation gives the maximum stress:
where smax is the maximum stress (MPa), mmax is the largest mass that the penetrator section must support (kg), amax is the largest acceleration that the penetrator section experiences, and Awallmin is the minimum cross-sectional area of the penetrator wall.
The critical stress for Euler column buckling
is given by the following:
where sc is the critical stress (MPa), E is the Young's modulus for the material (MPa), L is the longest column length (m), and r is the minimum radius of gyration of the cross-section (m).
The critical stress for local wall crippling
is a characteristic of the material used. For titanium, the following
equations were used to estimate the allowable stress before onset
of local wall crippling:
L/r ²
10
10 ²
L/r ² 54
L/r ³
54
where L and r are defined as above.
Program to find Hohmann transfer opportunities
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DOUBLE PRECISION MUSUN
DIMENSION XE(3),XEDOT(3),XM(3),XMDOT(3),TEST1(3),TEST2(3)
RTD=180.D0/PI()
AUTOM=1.49599D11
MUSUN=1.32718D20
C
C Get range of launch dates to try
C
WRITE(6,*)'Possible launch dates from JD:'
READ(5,*)UTCLA
WRITE(6,*)'To JD:'
READ(5,*)UTCLB
C
C If 0 input for second date, just look at first date
C
IF(UTCLB.EQ.0.D0)UTCLB=UTCLA
C
C Set up step value (1 day) and tolerances
C
TSTEP=1.D0
ANGTOL=0.5D0
C
C Start iteration
C
200 DO 10 UTCL=UTCLA,UTCLB,TSTEP
C
C Find Earth's position at current launch date
C
CALL SOLAR(XE,XEDOT,UTCL,3)
TEST1(1)=XE(1)
TEST1(2)=XE(2)
TEST1(3)=0.D0
RMAG1=ABV(TEST1)
DO 20 I=1,3
TEST1(I)=TEST1(I)/RMAG1
20 CONTINUE
UTCA=UTCL
C
C Find Mercury's position at launch date
C
CALL SOLAR(XM,XMDOT,UTCA,4)
C
C Just look at projection on ecliptic, and begin propagating
C Mars' position forward by day to find when angle between
C Earth and Mars is 180 degrees.
C
500 TEST2(1)=XM(1)
TEST2(2)=XM(2)
TEST2(3)=0.D0
RMAG2=ABV(TEST2)
DO 30 I=1,3
TEST2(I)=TEST2(I)/RMAG2
30 CONTINUE
C
C Find the angle between Earth and Mars
C
COSANG=DOTP(TEST1,TEST2)
DIFF=DACOS(COSANG)*RTD
C
C See if angle near 180
C
IF(DABS(180.D0-DABS(DIFF)).LE.ANGTOL) GOTO 100
C
C Increment arrival date
C
UTCA=UTCA+TSTEP
C
C Find Mars' position at arrival date
C
CALL SOLAR(XM,XMDOT,UTCA,4)
GOTO 500
C
C If found when Earth and Mars directly opposite each other,
C write out time it took
C
100 WRITE(6,*)'TOF at launch date',UTCL,' =',UTCA-UTCL
WRITE(6,*)'Phase angle=',DIFF
C
C From positions, calculate Hohmann trajectory and TOF
C spacecraft would follow if on this trajectory.
C
R1=ABV(XE)*AUTOM
R2=ABV(XM)*AUTOM
AT=(R1+R2)/2.D0
TOF=PI()*DSQRT(AT**3/MUSUN)/86400.D0
WRITE(6,*)'Semi-major axis=',AT
WRITE(6,*)'Calculated TOF=',TOF
C
10 CONTINUE
C
STOP
END
Program to calculate Hohmann/BPM trajectory
details
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION MUSUN,MUE,MUM,NMTOFT,KMTOFT
DIMENSION XE(3),XEDOT(3),XM(3),XMDOT(3)
OPEN(9,FILE='PLAN.DAT')
MUSUN=1.32718D20
MUE=3.98603D14
MUM=4.2828D13
RE=6378.D0
RM=3397.D0
KMTOFT=3280.8D0
AUTOM=1.49599D11
RTD=180.D0/PI()
C
C Get inputs and write to output file
C
WRITE(6,*)'Julian date of launch:'
READ(5,*)TLNCH
WRITE(9,*)'Julian date of launch:',TLNCH
WRITE(6,*)'Time of flight:'
READ(5,*)TOF
WRITE(9,*)'Time of flight:',TOF
C
C Find position of Earth at launch and Mars at arrival
C
TARR=TLNCH+TOF
CALL SOLAR(XE,XEDOT,TLNCH,3)
CALL SOLAR(XM,XMDOT,TARR,4)
C
C Calculate semi-major axis of Hohmann transfer
C
RSUNE=ABV(XE)*AUTOM
RSUNM=ABV(XM)*AUTOM
AT=(RSUNE+RSUNM)/2.D0
WRITE(6,*)'Semi-major axis of transfer:',AT
WRITE(9,*)'Semi-major axis of transfer:',AT
C
C Calculate hyperbolic excess velocity at Earth
C
VEARTH=ABV(XEDOT)*AUTOM/86400.
VINERE=DSQRT(MUSUN*((2.D0/RSUNE)-(1.D0/AT)))
VINFE=VINERE-VEARTH
WRITE(6,*)'V-inf at Earth=',VINFE
WRITE(9,*)'V-inf at Earth=',VINFE
C
C Input altitude of orbit around Earth; then can determine
C delta-V for transfer insertion
C
WRITE(6,*)'Altitude of Earth parking orbit (km):'
READ(5,*)RNOTE
WRITE(9,*)'Altitude of Earth parking orbit (km):',RNOTE
RNOTE=(RNOTE+RE)*1000.D0
VNOTE=DSQRT(VINFE**2+(2.D0*MUE/RNOTE))
WRITE(6,*)'V-not at Earth=',VNOTE
WRITE(9,*)'V-not at Earth=',VNOTE
C
C Calculate departure geometry
C
CALL GEOM('Earth',RNOTE,VNOTE,VINFE,MUE)
C
C Calculate delta-V for transfer insertion
C
VCIRCE=DSQRT(MUE/RNOTE)
WRITE(6,*)'V-circ at Earth=',VCIRCE
WRITE(9,*)'V-circ at Earth=',VCIRCE
DVE=VNOTE-VCIRCE
WRITE(6,*)'Delta-V from LEO=',DVE
WRITE(6,*)
WRITE(9,*)'Delta-V from LEO=',DVE
WRITE(9,*)
C
C Calculate plane change angle for BPM at true anomaly of
C 90 deg., and delta-V
C
P=(RSUNE*VINERE)**2/MUSUN
WRITE(6,*)'P=',P
WRITE(9,*)'P=',P
E=DSQRT(1.D0-(P/AT))
WRITE(6,*)'E=',E
WRITE(9,*)'E=',E
VNINE=DSQRT(MUSUN*((2.D0/P)-(1.D0/AT)))
RMXY=DSQRT(XM(1)**2+XM(2)**2)
DINC=DABS(DATAN(XM(3)/RMXY))
WRITE(6,*)'Plane change required at 90 (deg):',DINC*RTD
WRITE(9,*)'Plane change required at 90 (deg):',DINC*RTD
DVPC=2.D0*VNINE*DSIN(DINC/2.D0)
WRITE(6,*)'Delta-V for plane change=',DVPC
WRITE(6,*)
WRITE(9,*)'Delta-V for plane change=',DVPC
WRITE(9,*)
C
C Calculate hyperbolic excess velocity at Mars
C
VMARS=ABV(XMDOT)*AUTOM/86400.
VINERM=DSQRT(MUSUN*((2.D0/RSUNM)-(1.D0/AT)))
VINFM=VINERM-VMARS
WRITE(6,*)'V-inf at Mars=',VINFM
WRITE(9,*)'V-inf at Mars=',VINFM
C
C Input altitude of final Mars orbit to determine
C delta-V necessary for insertion
C
WRITE(6,*)'Altitude of Mars final orbit (km):'
READ(5,*)RNOTM
WRITE(9,*)'Altitude of Mars final orbit (km):',RNOTM
RNOTM=(RNOTM+RM)*1000.D0
C
C Calculate period
C
PERMRS=2.D0*PI()*DSQRT(RNOTM**3/MUM)
WRITE(6,*)'Period of Mars orbit=',PERMRS/60.D0
WRITE(9,*)'Period of Mars orbit=',PERMRS/60.D0
C
C Calculate inclination for sun-synchronous orbit
C
OMEGAD=1.05851D-7
ORBINC=DACOS(-OMEGAD*2.D0/3.D0/0.001965D0*(RNOTM/1000.D0/RM)**2*
1 PERMRS/(2.D0*PI()))
WRITE(6,*)'Inclination of Mars orbit=',ORBINC*RTD
WRITE(9,*)'Inclination of Mars orbit=',ORBINC*RTD
VNOTM=DSQRT(VINFM**2+(2.D0*MUM/RNOTM))
WRITE(6,*)'V-not at Mars=',VNOTM
WRITE(9,*)'V-not at Mars=',VNOTM
C
C Calculate arrival geometry
C
CALL GEOM('Mars ',RNOTM,VNOTM,VINFM,MUM)
C
C Calculate delta-V for orbit insertion
C
VCIRCM=DSQRT(MUM/RNOTM)
WRITE(6,*)'V-circ at Mars=',VCIRCM
WRITE(9,*)'V-circ at Mars=',VCIRCM
DVM=VNOTM-VCIRCM
WRITE(6,*)'Delta-V for Mars orbit insertion=',DVM
WRITE(6,*)
WRITE(9,*)'Delta-V for Mars orbit insertion=',DVM
WRITE(9,*)
C
C Determine total delta-V, and delta-V required of spacecraft
C
DVTOT=DVE+DVPC+DVM
DVPER=DVPC+DVM
WRITE(6,*)'Total delta-V:',DVTOT
WRITE(6,*)'Total delta-V required of Percival:',DVPER
WRITE(6,*)
WRITE(9,*)'Total delta-V:',DVTOT
WRITE(9,*)'Total delta-V required of Percival:',DVPER
WRITE(9,*)
C
C Input specific impulse of spacecraft's engines to
C determine final mass ratio
C
WRITE(6,*)'Specific impulse of Percival''s propulsion system:'
READ(5,*)SPIMP
WRITE(9,*)'Specific impulse of Percival''s propulsion system:'
1 ,SPIMP
RATMAS=EXP(DVPER/(SPIMP*9.81))
WRITE(6,*)'Final mass ratio=',RATMAS
WRITE(6,*)
WRITE(9,*)'Final mass ratio=',RATMAS
WRITE(9,*)
CLOSE(9)
STOP
END
C
C
C
SUBROUTINE GEOM(TITLE,RNOTE,VNOTE,VINFE,MUE)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION MUE
CHARACTER*5 TITLE
RTD=180.D0/PI()
C
C Calculate eccentricity, true anomaly of asymptote, turning angle,
C semi-major axis, and distance from asymptote for escape hyperbola.
C
ECC=1.D0+(RNOTE*VINFE**2)/MUE
THINF=DACOS(-1.D0/ECC)
TRNANG=2.D0*DASIN(1.D0/ECC)
A=-MUE/(VINFE**2)
DELTA=(RNOTE*VNOTE)/VINFE
WRITE(6,*)
WRITE(9,*)
WRITE(6,*)'*****',TITLE,' escape hyperbola*****'
WRITE(9,*)'*****',TITLE,' escape hyperbola*****'
WRITE(6,*)'Semi-major axis:',A
WRITE(9,*)'Semi-major axis:',A
WRITE(6,*)'Eccentricity:',ECC
WRITE(9,*)'Eccentricity:',ECC
WRITE(6,*)'Delta:',DELTA
WRITE(9,*)'Delta:',DELTA
WRITE(6,*)'Turning angle (deg):',TRNANG*RTD
WRITE(9,*)'Turning angle (deg):',TRNANG*RTD
WRITE(6,*)'True anomaly of asymptote (deg):',THINF*RTD
WRITE(9,*)'True anomaly of asymptote (deg):',THINF*RTD
WRITE(6,*)'********************'
WRITE(9,*)'********************'
WRITE(6,*)
WRITE(9,*)
RETURN
END
Program to calculate groundtracks on
Mars
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION MUM
RMARS=3397.D0
MUM=4.2828D13
DTR=PI()/180.D0
OPEN(9,FILE='GROUND.DAT')
C
C Enter type of function to do
C
5 WRITE(6,*)'1) Full, 2) List, 3) Large Prog-VIMS, 4) Quit:'
WRITE(9,*)'1) Full, 2) List, 3) Large Prog-VIMS, 4) Quit:'
READ(5,*)ITYPE
IF(ITYPE.EQ.4)GOTO 99
C
C If full list:
C
IF(ITYPE.EQ.1)THEN
C
C Input altitude at which information desired
C
WRITE(6,*)'Altitude of orbit(km):'
WRITE(9,*)'Altitude of orbit(km):'
READ(5,*)ALT
C
C Calculate period
C
PER=2.D0*PI()*DSQRT(((ALT+RMARS)*1000.D0)**3/MUM)
WRITE(6,*)'Period=',PER/60.D0,' minutes'
WRITE(9,*)'Period=',PER/60.D0,' minutes'
C
C Caculate number of orbits per day
C
ORBS=88772.D0/PER
IORB=INT(ORBS)+1
WRITE(6,*)'Number of orbits per day:',ORBS,IORB
WRITE(9,*)'Number of orbits per day:',ORBS,IORB
C
C Caculate swath angle VIMS has at this altitude
C
VIMS=0.115703948D0*ALT
WRITE(6,*)'Swath of VIMS (km):',VIMS
WRITE(9,*)'Swath of VIMS (km):',VIMS
C
C Caculate range of penetrator
C
PEN=2.D0*2.144506921D0*ALT
WRITE(6,*)'Maximum range allowed from penetrator (km):',PEN
WRITE(9,*)'Maximum range allowed from penetrator (km):',PEN
C
C Caculate distance along equator between consecutive orbits
C
DORB=(0.0040553D0*PER)*DTR*RMARS
WRITE(6,*)'Distance groundtrack moves each orbit (km):',DORB
WRITE(9,*)'Distance groundtrack moves each orbit (km):',DORB
C
C Caculate distance along equator between passes on
C consecutive days
C
TIMDAY=DBLE(IORB)*PER
DANGLE=(0.0040553D0*TIMDAY)-360.D0
DGRND=DANGLE*DTR*RMARS
WRITE(6,*)'Distance groundtrack moves west each day (km):',DGRND
WRITE(9,*)'Distance groundtrack moves west each day (km):',DGRND
C
C Caculate distance between passes of short-distance repeat cycle
C
GRNDS=DORB/DGRND
IGRND=INT(GRNDS)+1
DVIMS=(DBLE(IGRND)*DGRND)-DORB
IF(DVIMS.GT.100.D0)DVIMS=DVIMS-DGRND
WRITE(6,*)'''VIMS'' distance (km):',DVIMS
WRITE(9,*)'''VIMS'' distance (km):',DVIMS
C REPEAT=DGRND/ABS(DVIMS)
C WRITE(6,*)'Number of days for complete mapping cycle:',REPEAT
C WRITE(9,*)'Number of days for complete mapping cycle:',REPEAT
C
C If lists of vital information for several altitudes desired:
C
ELSEIF(ITYPE.EQ.2)THEN
WRITE(6,*)'Starting altitude (km):'
READ(5,*)ALTST
WRITE(6,*)'Final altitude (km):'
READ(5,*)ALTFN
DO 10 ALT=ALTST,ALTFN,1.D0
PER=2.D0*PI()*DSQRT(((ALT+RMARS)*1000.D0)**3/MUM)
ORBS=88772.D0/PER
VIMS=0.115703948D0*ALT
PEN=2.D0*2.144506921D0*ALT
DORB=(0.0040553D0*PER)*DTR*RMARS
IORB=INT(ORBS)+1
TIMDAY=DBLE(IORB)*PER
DANGLE=(0.0040553D0*TIMDAY)-360.D0
DGRND=DANGLE*DTR*RMARS
WRITE(6,*)' Altitude (km):',ALT
WRITE(6,*)'Distance groundtrack moves each orbit (km):',DORB
WRITE(6,*)'Distance groundtrack moves west each day (km):',DGRND
10 CONTINUE
C
C If lists for several altitudes desired in order to find good
C short-distance repeat cycles
C
ELSEIF(ITYPE.EQ.3)THEN
WRITE(6,*)'Starting altitude (km):'
READ(5,*)ALTST
WRITE(6,*)'Final altitude (km):'
READ(5,*)ALTFN
DO 20 ALT=ALTST,ALTFN,.1D0
PER=2.D0*PI()*DSQRT(((ALT+RMARS)*1000.D0)**3/MUM)
ORBS=88772.D0/PER
VIMS=0.115703948D0*ALT
PEN=2.D0*2.144506921D0*ALT
DORB=(0.0040553D0*PER)*DTR*RMARS
IORB=INT(ORBS)+1
TIMDAY=DBLE(IORB)*PER
DANGLE=(0.0040553D0*TIMDAY)-360.D0
DGRND=DANGLE*DTR*RMARS
GRNDS=DORB/DGRND
IGRND=INT(GRNDS)+1
DVIMS=(DBLE(IGRND)*DGRND)-DORB
WRITE(6,*)' Altitude (km):',ALT
WRITE(6,*)'Distance groundtrack moves each orbit (km):',DORB
WRITE(6,*)'Distance groundtrack moves west each day (km):',DGRND
WRITE(6,*)'''VIMS'' distance (km):',DVIMS
20 CONTINUE
ENDIF
GOTO 5
99 STOP
END
Hohmann Output Data
Julian date of launch: 2450416.00
Time of flight: 254.00 days
Semi-major axis of transfer: 1.8670514293D+011 km
V-inf at Earth= 2791.45700209158 km/s
Altitude of Earth parking orbit : 185.0000 km
V-not at Earth= 11369.344171054200
km/s
*****Earth escape hyperbola*****
Semi-major axis: -5.115389147D+007 km
Eccentricity: 1.128299134458780
Delta: 2.67304872468D+007
Turning angle : 124.8213265086500 deg
True anomaly of asymptote : 152.4106632543250 deg
********************
V-circ at Earth= 7793.258454759390 km/s
Delta-V from LEO= 3576.085716294780
km/s
P= 1.78500852649D+011
E= 0.209624658694674
Plane change required at 90 (deg): 0.529605136990626
Delta-V for plane change= 257.5200606530690
V-inf at Mars= -2800.80238948
Altitude of Mars final orbit (km): 179.40000
Period of Mars orbit= 108.2265589
Inclination of Mars orbit= 92.35772239
V-not at Mars= 5638.6909074
*****Mars escape hyperbola*****
Semi-major axis: -5459625.549319550
Eccentricity: 1.655063239720850
Delta: -7200156.011446760
Turning angle (deg): 74.3435304598782
True anomaly of asymptote (deg): 127.1717652299390
********************
V-circ at Mars= 3460.51593878382
Delta-V for Mars orbit insertion=
178.17496869507
Total delta-V: 6011.78074564293
Total delta-V required of Percival:
2435.69502934814
Specific impulse of Percival's propulsion system: 289.900
Final mass ratio= 2.35480331874
Groundtrack Output Data
Altitude of orbit: 179.4 km
Period: 108.227 minutes
Number of orbits per day: 13.670
Swath of VIMS : 20.757 km
Maximum range allowed from penetrator : 769.449 km
Distance groundtrack moves each orbit : 1561.280 km
Distance groundtrack moves west each day : 513.9498 km
'VIMS' distance : -19.4310 km
Personnel Cost
Preliminary Design Cost Estimate
B1 B2 B3 B4 B5 B6 B7 B8 B9 B10
C1 C2
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10