2.0 Schemes Considered for Constellation Deployment

2.1 Phase I Design: In-Plane Single Orbit configuration

2.2 Phase II: Two Orbit Primary/Secondary Configuration

Primary Transponder Ring and Gravitational Effects of Jupiter

Therefore, a test mass was simulated in a position 90º forward of Jupiter's orbit for a period of approximately 96 years (8 Jovian orbital periods).   The interest was not in accuracy of orbital determination, but rather in the general effect of third-body Jovian gravity on the displacement of the mass from Jupiter.   The simulation was carried out numerically by integrating the mass trajectory as a two body system about the Sun with Jovian gravity as a perturbation using a 7-8 order Runge-Kutte integrator with a step size of .001*TJ (TJ=Jovian orbital period), approximately 4 days.   During this integration step, the Jovian gravity effect was considered to be a constant value.   After 8*TJ the forward orbital displacement of the mass has deteriorated to approximately 65º from 90º and was much nearer the Jovian Lagrange point.

Although this represented a downtrack motion of 25º relative to Jupiter, the mass was still in a stable orbit with a semi-major axis of approximately 5.5 AU.   The interpretation of this motion was that for a period of 100 years a primary P-STAR transponder ring of three spacecraft operating at 90º, 180º, and -90º displaced from Jupiter's orbit at 5.2 AU would maintain stability and substantial displacement from each other.

Secondary Transponder Ring and Extra-Ecliptic Displacement

With three stations placed in a 'four corners' arrangement with Jupiter, the Heliocentric X-Y position of a spacecraft can be passively determined.   However, P-STAR is required to:

1. Achieve accurate Z axis positioning.
2. Provide a fourth transponder for time variable estimation.
3. Provide alternate transponders in the event that the line of sight between a spacecraft and a transponder passes through the Solar blind spot.

The establishment of such a system can be nominally achieved if one assumes certain convenient parameters.   Plausibly, one can estimate circular non-inclined orbits for Earth and Jupiter.   Also, one can assume frequent Hohmann transfer launch opportunities given the 13 month synodic period of the Earth-Jupiter system.   One can assume:

1. existing motors with unspecified masses and Specific Impulses (Isp's) of 400 seconds and mass fractions of 0.1 for tailor made staging - very unrealistic
2. placement in non-inclined Earth orbit by a large delivery system (the Titan IV was approximated) without penalty to spacecraft mass - only simplifies launch window timing
3. zero inclination of the Earth's rotational axis to the ecliptic - only simplifies launch window timing
4. maximum payload delivery for the approximated systems

The circularization DV for the primary transponder ring (calculated from 35flyby.tk) required such a large mass that, given a Titan IV mass limit for LEO, only 275 kg could be placed in a 5 AU heliocentric circular orbit.   While the technology and mass involved with each transponder will not be analytically explored, it is assumed that a minimum mass of 500 kg would be required for an operational unit.  

However, it was felt that the inclined orbits of the secondary transponder ring (calculated in rctooe.tk):

corresponded to a promising enough payload to become the basis for a more realistic final launch and delivery scheme.  

2.3 Final Selection: Six Inclined Elliptical Orbits

Given the synodic period of the Earth-Jupiter system it will be possible to launch toward Jupiter approximately every 13 months.   The Hohmann transfer orbit time from Earth to Jupiter is 2.73 years.   During this time Jupiter moves through 83º of its orbit.   Since the Hohmann orbit's argument of ascending node is aligned with the Earth-Sun line at time of launch, Jupiter must be 97º ahead of Earth in the ecliptic plane at time of interplanetary injection.   Therefore, the hohangle.f and the position.f F77 programs were used to determine potential launch dates.   A note should be made here that the positions calculated from these routines were based upon the 1984 Astronomical Almanac ephemeris tables which contains the 'actual' inclinations and eccentricies of Earth and Jupiter rather than the noninclined circular approximations used here.   However, since these eccentricies and inclinations are small, a tolerance value is included in the hohangle.f launch criterion, and booster fuel calculations include contingency burns, the launch dates provided should suffice for the scope of this study.

Thus, in hohangle.f and position.f the orbits of Earth and Jupiter were both assumed to be circular and noninclined, which is more or less true, and the Space Shuttle and Titan IV were again used as LEO delivery systems.   However, the following assumptions were adapted from Phase II:

1. only existing upper stage motors would be used with fuel restrictions and launch system fairing in place
2. placement in Earth orbit at approximately 28º inclination to the equator
3. 23º inclination of the Earth's rotational axis to the ecliptic
4. maximum payload delivery for the approximated systems (Titan IV and Shuttle)

Contents | Texas Space Grant | CSR Homepage | NASA | UT Aerospace