# Gravity Probe-B Completes Mission

Related Special and General Relativity News on Phys.org
Chronos
Gold Member
I suspect the good ship GPB will spring some tantalizing leaks in the less distant future.

Garth
Gold Member
Chronos said:
I suspect the good ship GPB will spring some tantalizing leaks in the less distant future.
Maybe not - we will have to wait and see.
Why does the data analysis take so long?

The GP-B consists fundamentally of four spinning gyroscopes and a telescope. Initially the spin axes of the four gyroscopes were electrically nudged into the same alignment parallel to the telescope axis pointed at a guide star, IM Pegasi.

Then, the spacecraft orbited the Earth some 5,000 times in a year leaving the four gyros to spin undisturbed—their spin axes influenced only by the relativistic warping and twisting of spacetime. Two specific precessions were looked for, an E-W 'frame dragging' gravitomagnetic precession caused by the Earth dragging space-time around with it as it rotated, and a much larger N-S geodetic precession caused by the 'vertical' 'leaning over' into the slope of space-time curvature caused by the Earth's mass.

On each orbit, the cumulative size and direction of the angle between the gyroscopes’ spin axes and the telescope were recorded. Over the course of a year, if GR is correct, an angle of 6.6 arcseconds (or 5.5 arcseconds if SCC is correct) should have opened up in the N-S plane of the spacecraft’s polar orbit, (geodetic effect), and an angle of 0.041 arcseconds (both in GR and SCC) should have opened up in the E-W direction of Earth’s rotation (Lense-Thirring effect).

A complex process of data reduction and analysis is required to obtain these gyro drift angles, which will take the GP-B science team more than a year to bring to completion.

The raw data is called Level 0 data. This 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 therefore 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.

A number of algorithmic processes will be run on the Level 1 data to extract around 500 data elements that will be used for science data analysis; this is Level 2 data.

If there were no noise or error in the gyro readouts, and if the exact calibrations of these readouts was known at the beginning of the experiment, then only two datapoints would be needed – a starting point for the gyroscope orientations and an ending point.

However, since the exact readout calibrations are determined as part of the experiment, collecting all of the data points in between will enable these unknown variables to be determined.
Furthermore, the electronic systems on-board the spacecraft do not read out angles. Rather, they read out voltages, and by the time these voltages were telemetered to Earth, they had 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 the size of the scale factors that accompany the science data to be determined. For example, the orbital and annual aberration of the starlight from IM Pegasi will be used to calibrate the gyro readout signals. As the telescope was 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 was introduced.

This will allow 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, the guide star IM Pegasi is both a radio source and it is visually bright enough to be tracked by the science telescope on-board the spacecraft. It has its own proper motion across the sky. Thus the angular displacements of the gyros have to be related to the telescope’s initial position, rather than its current position directed towards IM Pegasi.

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, a ”blind” component was added to the data analysis by insisting that the CfA withhold the proper motion data until the rest of the 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.

It will require much patience before the result is known to anybody, whatever that result might be.

Garth

Reference: "Gravity Probe B mission ends" Matters of Gravity No.26, Bob Kahn, Stanford University.

Last edited:
pervect
Staff Emeritus
I suspect that politics is also entering the picture here. Much like the Hubble, the people on the GP-IB want to be the first to examine the data for any possible surprises, without feeling that they have to "rush" hastily in order to avoid being scooped by a more ambitious and less careful researcher.

Aether
Gold Member
Garth said:
Over the course of a year, if GR is correct, an angle of 6.6 arcseconds (or 5.5 arcseconds if SCC is correct) should have opened up in the N-S plane of the spacecraft’s polar orbit, (geodetic effect), and an angle of 0.041 arcseconds (both in GR and SCC) should have opened up in the E-W direction of Earth’s rotation (Lense-Thirring effect).
Garth, When you say "if GR is correct" do you mean "if Schwarzschild's solution to Einstein's field equations is correct"? Does SCC differ from GR in the field equations, the line element, or both?

The Schwarzschild solution assumes that the spacetime surrounding a spherically symmetric gravitational field (of the Earth in this case) is empty, and that implies that the field is static. This is obviously not the case, but I'm not sure that the Gravity Probe-B experiment is sensitive enough to be affected by the difference. Were these assumptions of a static gravitational field embedded in empty spacetime used in calculating the geodetic effects for GR and SCC that you gave? Can you show both calculations, or provide a link if you have already done this somewhere else?

Garth
Gold Member
Aether said:
Garth, When you say "if GR is correct" do you mean "if Schwarzschild's solution to Einstein's field equations is correct"? Does SCC differ from GR in the field equations, the line element, or both?
The Schwarzschild solution assumes that the spacetime surrounding a spherically symmetric gravitational field (of the Earth in this case) is empty, and that implies that the field is static. This is obviously not the case, but I'm not sure that the Gravity Probe-B experiment is sensitive enough to be affected by the difference. Were these assumptions of a static gravitational field embedded in empty spacetime used in calculating the geodetic effects for GR and SCC that you gave? Can you show both calculations, or provide a link if you have already done this somewhere else?
Hi Aether!
First of course the whole purpose of spending \$700 Million on GP-B was to check whether GR made the correct predictions or not, it does not assume that it does as a forgone conclusion.

The predictions use the Parametrized Post Newtonian formalism which is a generalisation of the static spherically symmetric Schwarzschild solution; the frame-dragging Lense-Thirring or gravitomagnetic precession uses the stress term Ti0 and the geodetic precession parallel transports a vector around a closed orbit. General predictions are made by the PPN formalism and the GR predictions are obtained by slotting in $$\alpha=1, \beta=1$$ and $$\gamma=1$$ into the PPN expressions.

Why do you say the field is not static?

I must be careful in answering your question, I do not want to be accused of "peddling my own theory" and if you want to read it up, the latest published work is here. The SCC values PPN are: $$\alpha=1, \beta=1$$ and $$\gamma=1/3$$ but the value of G is 3/2 GNewtonian.

You will find the explanation there, or on the Threads in PF dedicated to SCC.

Garth

Last edited:
Aether
Gold Member
Garth said:
Why do you say the field is not static?
Because the universe is expanding/accelerating (e.g. the FLRW line element is not static). I used GRTensorII to calculate the Ricci tensor for a non-static cross between the FLRW and Schwarzschild line elements yesterday for example, and saw some new terms in there where $$\alpha$$ and $$\beta$$ are mixed up with the Hubble constant. Those terms are probably very small, but they aren't zero.

Garth said:
I must be careful in answering your question, I do not want to be accused of "peddling my own theory" and if you want to read it up, the latest published work is here. The SCC values PPN are: $$\alpha=1, \beta=1$$ and $$\gamma=1/3$$ but the value of G is 3/2 GNewtonian.
I will take a look at this paper.

Garth
Gold Member
Aether said:
Because the universe is expanding/accelerating (e.g. the FLRW line element is not static). I used GRTensorII to calculate the Ricci tensor for a non-static cross between the FLRW and Schwarzschild line elements yesterday for example, and saw some new terms in there where $$\alpha$$ and $$\beta$$ are mixed up with the Hubble constant. Those terms are probably very small, but they aren't zero.
That's very interesting - the question is:"If space is expanding what expands with it?"

The standard answer is only very large gravitationally unbound systems, but it is a bit unclear as to whether super-clusters of glaxies, clusters of galaxies or the galaxies themselves are included in this description. Generally galaxies are thought to be definitely bound - but that is all by the application of Newtonian theory.

In GR the field of a local gravitating body is given by the Schwarzschild solution and that is embedded asymptotically in flat non-expanding space-time. If you embed it instead in an expanding metric then the solution itself might be expected to expand with the universe, i.e. gravitational orbits should expand.

A clue that this could be happening might be the Pioneer anomaly interpreted properly.
I will take a look at this paper.
I will be glad to answer any questions and welcome constructive criticism.

Garth