Earth horizon modeling and application to static Earth sensors on TRMM spacecraft

Data from Earth sensor assemblies (ESA's) often are used in the attitude determination (AD) for both spinning and Earth-pointing spacecraft. The ESA's on previous such spacecraft for which the ground-based AD operation was performed by the Flight Dynamics Division (FDD) used the Earth scanning method. AD on such spacecraft requires a model of the shape of the Earth disk as seen from the spacecraft. AD accuracy requirements often are too severe to permit Earth oblateness to be ignored when modeling disk shape. Section 2 of this paper reexamines and extends the methods for Earth disk shape modeling employed in AD work at FDD for the past decade. A new formulation, based on a more convenient Earth flatness parameter, is introduced, and the geometric concepts are examined in detail. It is shown that the Earth disk can be approximated as an ellipse in AD computations. Algorithms for introducing Earth oblateness into the AD process for spacecraft carrying scanning ESA's have been developed at FDD and implemented into the support systems. The Tropical Rainfall Measurement Mission (TRMM) will be the first spacecraft with AD operation performed at FDD that uses a different type of ESA - namely, a static one - containing four fixed detectors D(sub i) (i = 1 to 4). Section 3 of this paper considers the effect of Earth oblateness on AD accuracy for TRMM. This effect ideally will not induce AD errors on TRMM when data from all four D(sub i) are present. When data from only two or three D(sub i) are available, however, a spherical Earth approximation can introduce errors of 0.05 to 0.30 deg on TRMM. These oblateness-induced errors are eliminated by a new algorithm that uses the results of Section 2 to model the Earth disk as an ellipse.