GP-B Post-Flight Analysis—Final Report - Gravity Probe B - Stanford ...

At launch, GP-B’s inclination was just 5x10 -5 degrees away from the desired inclination, which corresponds toonly about 6 m of error assuming a planned 60-day Initial Orbit Checkout (IOC). This small error eliminatedthe need to carry out orbit trim maneuvers. Even without trimming, the average orbit plane errors over the lifeof the science mission are expected to remain under 0.020 degrees - well within requirements.GP-B operations also required accurate orbit determination (OD) in order to establish the GP-B position andvelocity to within 25 m and 7.5 cm/sec RMS throughout the mission. GPS observations available at 10-secondintervals were processed using the commercial Microcosm orbit determination program in daily 30-hour batchfits to satisfy those requirements.4.4.1 The GP-B Mission Orbit DesignThe GP-B altitude was planned to be approximately 650 km, based on launch weight considerations and a desireto be above the region in which atmospheric drag could overpower the Helium thrusting that maintains themission’s drag-free status. The specific mean semi-major axis was finally chosen to be about 10 km lower, at7018.0 km, in order to be between two repeat ground track resonances that would have complicated the IOCtrimming process. In addition, it was desired that the orbit be nearly circular in order to minimize dragfluctuations around the orbit. The target mean eccentricity and argument of perigee were chosen to be 0.00134and 90 degrees, the stable (“frozen”) values at GP-B mission altitude.The orbit plane was to have its descending node remain near the right ascension of the guide star, so that thespacecraft axis would remain nearly in the orbit plane to minimize gyroscopic torques. That implied a nearpolar orbit to minimize nodal precession and, after HR 8703 was chosen as the guide star, it implied a launchthat was timed to place the right ascension of the orbit’s descending node near 343 degrees.The specific inclination and nodal values for the GP-B orbit plane were derived from the requirement that:“[The] final target orbit shall be chosen such that the predicted angle between the line-of-sight to guidestar and the orbit plane, averaged over an interval longer that 10 months and less than 14 monthsstarting 2 months after launch, is less than 0.025 degrees.”The specified angle in the preceding requirement, commonly known as η (eta), is illustrated in Figure 4-5below. The η-angle is significant because of its relationship to gyroscopic torque. Outside disturbances likegyroscopic torque must be kept to a minimum to improve the accuracy of measurements obtained by the GP-Bscience experiment. Since gyro torque is proportional to the distance between the gyroscope and the orbit plane,gyro torque is also proportional to η. The science requirement that η be < 0.025 degrees when averaged over aninterval of 10 – 14 months, allows the effects of gyro torque on precession rate to nearly cancel.Mathematically, the angle η is obtained from the following equation:sin η = cos i sin δ* + sin i cos δ* sin(Ω - Ω*)η ≈ (90°- i) sin δ* - (Ω - Ω*+180°) cos δ*where δ* and Ω* are declination and right ascension of the guide star, corrected for aberration and propermotion and expressed in true-of-date coordinates. Errors in η-average arise from errors in the histories of theorbit’s inclination and right ascension of ascending node (i and Ω) during the mission, after the end of IOC.The key issue here is that there can be no corrective thrusting after the drag-free mission begins, so the orbitparameters at the end of IOC must be established very accurately. In particular, the inclination then must becorrect to within about ±0.00020 degrees, a value much more precise than needed for most missions. In order toobtain that inclination accuracy, the mission profile allowed for almost continuous cross-track thrusting(“trimming”) during the nominal 60-day IOC, using low-thrust Helium venting to remove the inclinationerrors made by the launch vehicle at insertion.Gravity Probe B — Post Flight Analysis • Final Report March 2007 111