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

Figure 14-11. Due to the motion of the Earth, the apparent position of a distant star viewed through a telescopediffers from its actual position—Bradley called this difference the aberration angle.From his observations of Gamma Draconis, Bradley knew that the maximum angle at which his telescope had tobe tilted was tiny—approximately 20 arc-seconds. Using this angle, and the velocity of the Earth moving aroundthe Sun, known in his day to be ~30 km/sec (~18.6 miles/sec), he calculated the speed of light to be about 10,000times faster than the orbital velocity of Earth or ~300,000 km/sec (~186,000 miles/sec).14.1.5.2 The Role of Stellar Aberration in the GP-B ExperimentYou can now see why the aberration of starlight played a role in the GP-B experiment. While constantlytracking the guide star, IM Pegasi, the telescope on-board the spacecraft was always in motion—both orbitingthe Earth once every 97.5 minutes and along with the Earth, the spacecraft and telescope have been orbiting theSun once a year. These motions result in two sources of aberration of the starlight from IM Pegasi. The first is anorbital aberration, which has a maximum angle of 5.1856 arcseconds, resulting from the spacecraft’s orbitalspeed of approximately 7 km/sec, relative to the speed of light. (In the case of orbital aberration, the relativitycorrection is insignificant.). The second is the now familiar annual aberration due to the Earth's orbital velocityaround the Sun, which when corrected for special relativity, amounts to an angle of 20.4958 arcseconds.In the GP-B experiment, the signals representing the precession in the gyroscope spin axes over time arerepresented by voltages that have undergone a number of conversions and amplifications by the time they aretelemetered to Earth. These conversions and amplifications imparted a scale factor of unknown size into thedata, and early on in the development of the GP-B experimental concept it was apparent that there needed to bea means of determining the size of this gyro scale factor in order to see the true relativity signal. Initially, itGravity Probe B — Post Flight Analysis • Final Report March 2007 411