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

7.3 ATC PerformanceData gathered from the GP-B space vehicle throughout the mission shows that the ATC system is performedwell. The back up drag-free control mode, which minimizes gyro control effort, is used as the translation controlmode throughout the Science Mission phase. Drag-free operations have proven to reduce control forces appliedto the gyroscopes by a factor of 10 and generates a cross track control force on the order of a mere nanonewtonat the roll rate frequency. Also, the attitude control system has proven to maintain the pointing of the GP-BScience Telescope to within a few hundred milliarcseconds of the Guide Star IM Pegasi. More importantly, theScience Telescope signal is kept in the linear range roughly 95% of the time while the Guide Star is not eclipsedby the Earth. Finally, the roll rate component of the attitude error signal has generally been at or below 10milliarcseconds rms while the notch filter on the rate path error is enabled.7.3.1 Pitch/Yaw PointingAt the start of the science phase of the Gravity Probe B mission, the Science Telescope and gyroscope spin axesare aligned with the Guide Star IM Pegasi. Over the course of the Science Mission, the GP-B Science Telescoperemains precisely pointed at the Guide Star.If the predictions based on Eintsein’s theory are correct, the gyroscopes’ spin axes should slowly drift away fromtheir initial Guide Star alignment, in both the space vehicle’s orbital plane, due to the curvature of localspacetime, and perpendicular to the orbital plane, due to the frame-dragging effect. These relativistic effects inthe vicinity of a small planet like the Earth are barely noticeable. For example, the spin axis deflection due to theframe-dragging effect corresponds to the width of a human hair as seen from 100 mile away. In order to detectsuch minute deflections in the gyroscopes’ spin axes, the GP-B Science Telescope must remain pointed at theGuide Star with equivalent accuracy.The Guide Star pointing error is computed using the Science Telescope signals. The telescope measures theGuide Star position in the x and y orthogonal directions independently. The GP-B Science Telescope focuses thestarlight in the “lightbox” at the telescope’s front end. Figure 7-3 is a general schematic of the Science Telescopecomponents. Light from the Guide Star enters the telescope and is separated into two signals with a beamsplitter. One signal is used to measure the Guide Star position in the x direction, and the other is used tomeasure the Guide Star position in the y direction. In each direction, the Guide Star’s image is sliced into twohalf disks which are directed to hit opposite ends of a tiny sensor. The sensors convert each half signal intovoltages S + and an S – corresponding to each half disk image. The difference between these two signals is then ameasurement of how well the Guide Star image is centered on the roof prism, and hence provides the ATCsystem with attitude (pointing) error during Guide Star Valid periods. A Guide Star Valid period refers to theperiod of time when the view from the GP-B space vehicle to the Guide Star IM Pegasi is not blocked by theEarth.Gravity Probe B — Post Flight Analysis • Final Report March 2007 175