Misalignment and Resonance Torques and Their Treatment in the GP-B Data Analysis

Abstract

Classical torques acting on the GP-B gyroscopes decrease the accuracy in the measurement of the relativistic drift rate. Based on measurements made during the yearlong science data collection, tests done following the science data collection, and a theoretical analysis of potential torques, there are two dominant classical torques acting on the gyroscopes. The first torque, known as the misalignment torque, has a magnitude proportional to the misalignment between the gyroscope spin axis and the satellite roll axis and is aligned perpendicular to the plane containing these two vectors. The second torque, known as the resonance torque, mainly produces a permanent offset in the orientation of the gyroscope spin axis when a harmonic of the gyroscope polhode frequency is in the vicinity of the satellite roll frequency. These two torques have the same physical origin: an electrostatic interaction between the patch effect fields on the surfaces of the rotor and the housing. In the post-mission data analysis, the change in the gyroscope orientation due to both of these torques can be clearly separated from the relativistic drift rate.

The effects of patch-potentials on the gravity probe B gyroscopes

“…However, a misalignment torque and thus a disturbance drift, observed during the post-calibration phase of the experiment, was found to be substantially larger than that predicted. This misalignment torque was explained by Keiser et al 7 assuming that the gyro rotor and the gyro housing electrodes have surface potentials both on the order of 100 mV due to the patch effect. These surface potentials also explain other unexpected gyro behaviors.…”

“…7 During the mission the misalignment coefficient varied depending on the polhode angle. For gyro 3, for example, the roll-averaged drift rate was between 1.9 arc sec/yr and 6.9 arc sec/yr for the average misalignment of 10 arc sec.…”

Patch Effect in Cylindrical Geometry: The Step Accelerometer

“…The two significant Newtonian torques on GP-B gyroscopes, called a misalignment torque and a roll-polhode resonance torque, are caused by the PE. They are described in 7 where the observational evidence for these torques is presented, their physical origin is demonstrated and their theoretical expressions are derived, and some details of the data analysis methods for separating the relativistic gyroscope drift rate from the one caused by each torque are explained. Both torques resulted from the interaction of the PE potentials on the surfaces of the rotor and its housing.…”

Polhode Motion, Trapped Flux, and the GP-B Science Data Analysis

“…First of all, accurate polhode phase and angle values at any time of the mission are required for modeling both the scale factor variations and patch effect torques (Heifetz et al 2009;Keiser et al 2009), because all the torque coefficients are modulated by the polhode harmonics in the same fashion as the LF SQUID scale factor. In addition, TFM brings in an independent determination of those scale factor variations, which, first, allows for a separate determination of the LM scale factor and slowly varying D.C. part of the TF scale factor.…”