Spacecraft Orbit Determination Errors
The forces, in order of their significance, that contribute to perturbations in the satellite orbit error are parameterized as:
- Radiation Pressure
- Atmospheric Pressure
- Geoid Modeling
- Solid Earth & Ocean Tides
- Troposphere and
- Station Location.
The fact that the earth is not perfectly spherical in nature but rather shaped as an oblate spheroid creates an asymmetric potential in earth's gravitational field. The cyclical characterization of this perturbation requires a rather high level of degree and order in the spherical harmonic expansion representation in order to predict precise effects on the satellite orbit.
Radiation Pressure/Spacecraft Radiation
Solar, albedo and infrared emissions are the three external radiative fluxes acting on a spacecraft. The two separate types of flux influencing a spacecraft's temperature are internal and external. Internally the equipment dissipates heat. Externally, the solar radiation, albedo, and infrared fluxes cause surface heating. These types of forces vary with spacecraft shape, orientation and reflectivity during the different phase events of orbit such as
- occultation effects
- oblique illumination
- spacecraft's thermal inertia changes.
The effect of earth's atmosphere at orbit altitude is calculated using empirical relationships for air density, together with the known shape and orientation of the satellite.
As indicated previously, current geoid models have relatively low orders of degree and order upon which their spherical harmonic expansions are based. These discrepancies combine to perturb the satellite's estimated orbit away from the true orbit.
Solid Earth & Ocean Tides
As noted above, both oceanic & solid earth tides perturb the gravitational potential. Their influence on satellite orbits is calculated from a spherical harmonic expansion involving terms to a relatively low degree and order calculated from hydrodynamic models. It is meaningful to note that the largest amplitude M2 tide constituent is not the dominant contributor to satellite orbit anomalies. However, this same factor plays a significant role in tide frequency vs. altimeter signal aliasing and thus requires highly accurate tracking data in order to best define an adequate representation. Thus, the two most important tide modeling strategies are:
- to improve the long wavelength tide terms which are in resonance with near-earth satellites and have distinctly large long period orbital effects
- to produce as many as feasibly practical tidal coefficients which encompass many tide lines for inclusion in models thereby creating a whole category of short period perturbations.
As discussed in propagation medium corrections above, the signal delay
caused by water vapor content and other gases present in the
troposphere must be accounted for in satellite tracking theory and
perturbation analysis. Typically, satellite laser ranging (SLR) techniques are involved which use frequencies in the visible portion of the electromagnetic spectrum and thus are not as susceptible as the radio frequency ranging methods to the delays listed.
Station position, i.e. the inability to know the precise location of the tracking stations relative to the center of the earth, used to be the dominant problem in this category. However, with satellite laser ranging (SLR), extremely accurate measurements are now common place; the only exception being in cases of severe weather conditions in which data outages can and do last indefinitely. Station distribution is also a significant hindrance, with most SLR's concentrated in the northern hemisphere and on continents rather than being evenly dispersed around the globe. With the advent of the DORIS tracking system, these too may no longer pose a concern. Another, smaller in magnitude yet still present, discrepancy is that the coordinatesystem used to determine the station positions is not precisely known because of polar motion and the variations in the length of the day.
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