Gravity Probe B mission ends

Bob Kahn, Stanford University
On August 15, 2005, Gravity Probe B completed 352 days of science data collection and conducted a series of final instrument calibration tests before the liquid helium in the Dewar was exhausted around Labor Day. At that point, the main focus of GP-B shifted from mission operations to data analysis. The scientific analysis work will require over a year to complete, followed by up to six months of preparing and submitting scientific papers to major scientific journals. This process will culminate in the announcement and publication of the results, now anticipated to occur around April 2007. Thus it seems appropriate to provide an overview of what is involved in the GP-B data analysis process.

Recall that GP-B consists fundamentally of four spinning gyroscopes and a telescope. Conceptually the experimental procedure is simple: At the beginning of the experiment, we point the science telescope on-board the spacecraft at a guide star, IM Pegasi, and we electrically nudge the spin axes of the four gyroscopes into the same alignment parallel to the telescope axis. Then, over the course of a year, as the spacecraft orbits the Earth some 5,000 times while the Earth makes one complete orbit around the Sun, the four gyros spin undisturbed--their spin axes influenced only by the relativistic warping and twisting of spacetime. We keep the telescope pointed at the guide star using attitude control thrusters on the spacecraft, and each orbit, we record the cumulative size and direction of the angle between the gyroscopes' spin axes and the telescope. According to the predictions of Einstein's general theory of relativity, over the course of a year, an angle of 6.6 arcseconds should open up in the plane of the spacecraft's polar orbit, due to the warping of spacetime by the Earth (geodetic effect), and a smaller angle of 0.041 arcseconds should open up in the direction of Earth's rotation due to the Earth dragging its local spacetime around as it rotates (Lense-Thirring effect).

In reality, what goes on behind the scenes in order to obtain these gyro drift angles is a complex process of data reduction and analysis that will take the GP-B science team more than a year to bring to completion. We continuously collect data during all scheduled telemetry passes with ground stations and communications satellites, and this telemetered data is stored-in its raw, unaltered form-in a database at the GP-B Mission Operations Center at Stanford University. This raw data is called Level 0 data. The GP-B spacecraft is capable of tracking some 10,000 individual values, but we only capture about 1/5 of that data. The Level 0 data includes a myriad of status information on all spacecraft systems in addition to the science data, all packed together for efficient telemetry transmission. The first data reduction task is to extract all of the individual data components from the Level 0 data and store them in the database with mnemonic identifier tags. These tagged data elements are called Level 1 data. We then run a number of algorithmic processes on the Level 1 data to extract around 500 data elements that will be used for science data analysis; this is Level 2 data. While Level 2 data include information collected during each entire orbit, the science team generally only uses information collected during the portion of each orbit when the telescope is locked onto the guide star. We do not use for science any gyroscope or telescope data collected during that portion of each orbit when the spacecraft is behind the Earth, eclipsed from a direct view of the guide star.

If there were no noise or error in our gyro readouts, and if we had known the exact calibrations of these readouts at the beginning of the experiment, then we would only need two data points-a starting point for the gyroscope orientations and an ending point. However, since we are determining the exact readout calibrations as part of the experiment, collecting all of the data points in between enables us to determine these unknown variables.

Another important point is that the electronic systems on-board the spacecraft do not read out angles. Rather, they read out voltages, and by the time these voltages are telemetered to Earth, they have undergone many conversions and amplifications. Thus, in addition to the desired signals, the GP-B science data includes a certain amount of random noise, as well as various sources of interference. The random noise averages out over time and is not an issue. Some of what appears to be regular, periodic interference in the data is actually important calibrating signals that enable us to determine the size of the scale factors that accompany the science data. For example, the orbital and annual aberration of the starlight from IM Pegasi is used as a means of calibrating the gyro readout signals. As the telescope is continually reoriented to track the apparent position of the guide star, an artificial, but accurately calculable, periodically varying angle between the gyros and the readout devices is introduced. This allows the precise measurement of the voltage-to-angle scale factor. Measurement of this factor is optimized by a full year's worth of annual aberration data.

Finally, there is one more very important factor that must be addressed in calculating the final results of the GP-B experiment. We selected IM Pegasi, a star in our galaxy, as the guide star because it is both a radio source and it is visually bright enough to be tracked by the science telescope on-board the spacecraft. Like all stars in our galaxy, IM Pegasi moves relative to the solar system because of its local gravitational environment and because of galactic rotation. Thus, the GP-B science telescope is tracking a moving star, but the gyros are unaffected by the star's so called proper motion; their pointing reference is IM Pegasi's position at the beginning of the experiment. Thus, each orbit, we must subtract out the telescope's angle of displacement from its original guide star orientation so that the angular displacements of the gyros can be related to the telescope's initial position, rather than its current position. The motion of IM Pegasi with respect to a distant quasar has been measured with extreme precision over a number of years using Very Long Baseline Interferometry (VLBI) by a team at the Harvard-Smithsonian Center for Astrophysics (CfA) led by Irwin Shapiro, in collaboration with astrophysicist Norbert Bartel and others from York University in Canada and French astronomer Jean-Francois Lestrade. However, to ensure the integrity of the GP-B experiment, we added a "blind" component to the data analysis by insisting that the CfA withhold the proper motion data that will enable us to pinpoint the orbit-by-orbit position of IM Pegasi until the rest of our data analysis is complete. Therefore, the actual drift angles of the GP-B gyros, the quantities that are to be compared with the predictions of general relativity, will not be known until the very end of the data analysis process. For additional information about the GPB project, go to the website

Jorge Pullin 2005-10-05