Gravity Probe B, the simplest data analysis ever

John Conklin

John W. Conklin is assistant professor in the University of Florida’s Department of Mechanical and Aerospace Engineering. Photo: Aurora M Agüero

What could be simpler than fitting a straight line to a set of data? The slope of the line is the science result for NASA’s Gravity Probe B experiment, a landmark satellite test of two predictions of general relativity. Prior to launch, the data analysis for GP-B was thought to be straight forward. After precise calibration of the measured data (not as easy as fitting a straight line), the resulting signal should change at a constant rate over time. Our goal was to measure this rate of change, hopefully with an accuracy of 1%.

In the fall of 2005, as the year-long science mission was concluding, the GP-B science team began producing plots of the science data collected from the Earth-orbiting probe.  The figure shows one such plot. The slope of the best-fit straight line to these data is the magnitude of the elusive frame dragging effect, the main science goal of Gravity Probe B. Fear began to set it in. Where was the straight line? Throughout this period, Francis Everitt, the GP-B principal investigator remained confident that the team would be able to resolve whatever issue was plaguing the signal. After checking and rechecking the data and its calibration, we were convinced that what we were seeing in these plots was actually what was happening on the satellite orbiting 640 km overhead.

Gravity Probe B Gyroscope 2 data

Gyroscope 2 East-West orientation, which contains the frame-dragging signal, plotted over the GP-B science mission.

Conceptually, the Gravity Probe B experiment is quite simple. You place a near-perfect gyroscope, fixed in its local inertial frame, in orbit about the Earth. You compare the orientation of this gyroscope with the orientation toward a Guide Star, using a telescope, which provides a reference for the distant inertial frame. Einstein’s theory predicts two measurable, constant rate precessions of the gyroscope: the geodetic precession due to the mass of the Earth and the frame dragging precession due to the rotation of the Earth. If you choose to place your gyroscope, and hence your satellite, in a polar orbit then these two precessions are orthogonal, allowing you to independently measure each effect. By April 2004, when the GP-B satellite was launched, the geodetic effect had been measured to several parts in 1000 by lunar laser ranging, but there were no such measurements of frame dragging.

The data analysis quickly turned from a data fitting exercise to detective work. No one believed that the erratic motion of the gyroscopes (we had four on board the satellite) was the work of general relativity. There must have been an unforeseen classical torque acting on the gyroscopes. A planned set of calibrations at the conclusion of the science mission provided the first clue. Part of this classical torque was proportional and orthogonal to the misalignment between the gyroscopes’ spin axis and the satellite’s roll axis, which was nominally aligned with the telescope. Other oddities included a gyroscope spin-down time constant that was only 10,000 years (it should have been more like 1 million years!), a slowly damping gyroscope polhode period, indicating that energy was being extracted from the rotors at phenomenal rate of 10–13 W (!), and the most peculiar of all were brief but rapid changes in the orientation of the gyroscopes that occurred every time a high harmonic of the gyroscope’s polhode frequency (1 / a few hours) coincided with the spacecraft’s roll frequency (1/77.5 seconds). These ‘jumps’ can be seen in the plot above.

The bulk of the five-year-long data analysis journey involved solving these mysteries by finding the underlying culprit. The ‘patch effect’, the single source of all of these oddities, quickly became a dirty word among the GP-B science team. The patch effect is a small spatial variation in the electric potential over the surface of a conductor (or superconductor in the case of the GP-B gyroscopes). A random distribution of ~50 mV patches on the gyroscope rotor interacting with similar patches on the rotor housing explained all of these strange observations, including the periodic jumps in gyroscope orientation, that when plotted as North-South versus East-West orientation of the gyroscope, formed a beautiful Cornu Spiral. We were convinced that we had solved the mystery once we saw that a simple electrostatic model, which included random electric patches, predicted Cornu Spiral motion every time a spacecraft roll / gyroscope polhode resonance occurred.

The actual GP-B data analysis, lasting only about one year, finally began in earnest once we had the true model for the gyroscope motion, which accounted for the patch effect. This model indeed consisted of the straight line precession predicted by Einstein, but superimposed on this straight line was the motion induced by the patch effect, unfortunately involving hundreds of additional fit parameters. Our simple pre-launch data analysis that could be run quickly in Matlab on a single desktop computer was converted into a sprawling code that took about a week to run on a 44-core computer cluster. In the end, a 20% estimate of the frame dragging effect, consistent with GR, resulted. This was not the 1% measurement that we were hoping for, but it is still one of the best and most convincing measurements of frame-dragging to date.

Read the Gravity Probe B focus issue in Classical and Quantum Gravity
Guest edited by C W F Everitt, B Muhlfelder and C M Will

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