Solar force modeling of block IIR Global Positioning System satellites

Scientific applications of the Global Positioning System require that the space vehicles be located with an accuracy of a few centimeters. The most important uncertainties in position estimation are the result of direct and indirect solar forces. Perhaps as early as late 1996, Block IIR space vehicles will begin to replace the existing Blocks II and IIA. We give formulas for the solar force to be expected on Block IIR and evaluate their probable accuracy based on our previous experience. These a priori formulas include indirect solar forces, including the reradiation of sunlight in the form of heat from the space vehicle's body and solar panels, but do not include radiation-induced outgassing, especially from the multilayered insulation that wraps the space vehicle body. We discuss the best way to combine these a priori models with real-time tracking data to optimize ephemeris accuracy. MONG the many unique features of the Global Positioning System (GPS), one fact is of primary importance for its use in geodesy, studies of crustal dynamics, and support of such space missions as TOPEX/Poseidon: it is the first system of navigational satellites in which errors in knowledge of the Earth's gravitational field have negligible effect, and orbit accuracy is limited almost entirely by errors in modeling the force of solar radiation on the space vehicles (SVs). These SVs are high altitude (semimajor axes = 26,560 km = 4.16 Earth radii) and relatively insensitive to the higher-order gravitational harmonics, which are well known in any case via satellites such as LAGEOS. But GPS SVs have a large cross- sectional area (about 13.6 m2 for Block II/IIA) and are accelerated about 1 x 10~7 m/s by direct solar radiation. Table 1 shows our calculation (using the Aerospace TRACE program) of perturbations on a typical GPS orbit over 12 h. After the Earth oblateness J2, the sun, and the moon, solar radiation is the most important. An a priori model calculates the solar force to be expected on the vehicle as a function of its orientation and of its cross-sectional area and optical properties. Direct solar pressure can be pictured as the net momentum imparted to the S V by photons striking and recoil- ing from its opaque surfaces. Indirect solar pressure is caused, for example, by heat absorbed and reradiated from body surfaces and by outgassing, whereby solar energy and momentum is returned to space by volatile materials on and in the SV body. Indirect forces are of two kinds: predictable, such as the effects of Earthshine and SV heat flow; and anomalous, including outgassing and the so-called 7-bias force. Because none of the indirect effects, predictable or anomalous, were included in the early computer software devel- oped for GPS, many scientific GPS analysts have bypassed the modeling problem entirely and have determined SV accelerations directly as stochastic parameters to be estimated by tracking data.1'2 To attain highest accuracy, some such real-time estimation is nec- essary. Nevertheless, good a priori models are indispensable for three reasons: 1) many applications require not just precise fitting of orbits to tracking data already taken, but orbit prediction; 2) by us- ing a standard force model, workers more readily can intercompare ephemerides, which are calculated by many different agencies from data taken all over the world using different techniques; and 3) to filter real data accurately and reliably, one should know the statistics of the parameters measured—how fast they usually change, and how fast they can change—and this requires knowledge of the physics of the problem, and therefore, good a priori modeling. Our intention