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

Figure 7-4. Normalized Telescope Signal vs Pointing Error7.3.1.1 Pointing Accuracy Requirements for Science Data AnalysisIn order to determine the direction of the spin axes of the Science Gyroscopes relative to distant space, theorientation of the GP-B space vehicle must be known accurately. The normalized telescope signal is used toprecisely determine the pointing error of the vehicle. The pointing error is subtracted from the gyroscope spinaxis direction, measured in the vehicle frame, to provide the spin axis orientation relative to the Guide Star.Therefore, the vehicle pointing error must be known at the same level of accuracy as the gyroscope spin axes.This can be accomplished when the normalized pointing signal is in the linear range.Also, the pointing error at the roll rate frequency must remain especially small. As we have already seen, anycross track control forces applied to the Science Gyroscopes at the roll rate frequency and cause the gyroscopesto precess or drift. Therefore, we require that the pointing error of the vehicle be especially small at the roll ratefrequency so that unwanted gyro suspension forces are not amplified.The attitude (pointing) control system requirements for science data analysis can be summarized as follows:• Vehicle pointing error must remain small enough so that the normalized telescope signal S N remains inthe linear range.• Pointing error at the roll rate frequency must be especially small so that gyroscope control forces at theroll rate frequency do not generate significant torques.7.3.1.2 Overall RMSFigure 7-5 below shows the individual pitch and yaw errors over the science mission. The data points arecalculated over each individual guide star valid period by taking the rms value of the attitude error, omitting theinitial data points (~2 minutes) corresponding to the time required to capture, and damp out accumulated gyrohold drift errors. The individual pitch and yaw pointing error standard deviations have ranged between 100-300milliarcseconds on the X-Axis and between 150-325 milliarcseconds on the Y-Axis. The corresponding estimateof the telescope noise during this time period using a method outlined by J. Turneaure, is approximately 150marcs per axis.Gravity Probe B — Post Flight Analysis • Final Report March 2007 177