Alternative theories being tested by Gravity probe B

However, three important, but unexpected, phenomena were discovered during the experiment that affected the accuracy of the results.

First, because each rotor is not exactly spherical, its principal axis rotates around its spin axis with a period of several hours, with a fixed angle between the two axes. This is the familiar “polhode” period of a spinning top and, in fact, the team used it as part of their analysis to calibrate the SQUID output. But the polhode period and angle of each rotor actually decreased monotonically with time, implying the presence of some damping mechanism, and this significantly complicated the calibration analysis. In addition, over the course of a day, each rotor was found to make occasional, seemingly random “jumps” in its orientation—some as large as 100 milliarcseconds. Some rotors displayed more frequent jumps than others. Without being able to continuously monitor the rotors’ orientation, Everitt and his team couldn’t fully exploit the calibrating effect of the stellar aberration in their analysis. Finally, during a planned 40-day, endof-mission calibration phase, the team discovered that when the spacecraft was deliberately pointed away from the guide star by a large angle, the misalignment induced much larger torques on the rotors than expected. From this, they inferred that even the very small misalignments that occurred during the science phase of the mission induced torques that were probably several hundred times larger than the designers had estimated.

What ensued during the data analysis phase was worthy of a detective novel. The critical clue came from the calibration tests. Here, they took advantage of residual trapped magnetic flux on the gyroscope. (The designers used superconducting lead shielding to suppress stray fields before they cooled the niobium coated gyroscopes, but no shielding is ever perfect.) This flux adds a periodic modulation to the SQUID output, which the team used to figure out the phase and polhode angle of each rotor throughout the mission. This helped them to figure out that interactions between random patches of electrostatic potential fixed to the surface of each rotor, and similar patches on the inner surface of its spherical housing, were causing the extraneous torques. In principle, the rolling spacecraft should have suppressed these effects, but they were larger than expected. The patch interactions also accounted for the “jumps”: they occurred whenever a gyro’s slowly decreasing polhode period crossed an integer multiple of the spacecraft roll period. What looked like a jump of the spin direction was actually a spiraling path—known to navigators as a loxodrome. The team was able to account for all these effects in a parameterized model.

The original goal of GP-B was to measure the frame-dragging precession with an accuracy of 1%, but the problems discovered over the course of the mission dashed the initial optimism that this was possible. Although Everitt and his team were able to model the effects of the patches, they had to pay the price of the increase in error that comes from using a model with so many parameters. The experiment uncertainty quoted in the final result—roughly 20% for frame dragging—is almost totally dominated by those errors. Nevertheless, after the model was applied to each rotor, all four gyros showed consistent relativistic precessions (Fig. 1, bottom). Gyro 2 was particularly “unlucky”—it had the largest uncertainties because it suffered the most resonant jumps.

But even attempting to use the diurnal and annual aberrations as the main calibration tools shows the experimenters did not plan on accounting for any solar system motion relative to the guide star – meaning they essentially used a static solar system model.

The core of 3C 454.3 provides a sufficiently stable reference with which to measure the proper motion of the Gravity Probe B guide star, IM Pegasi, relative to the distant universe.

Is it possible to explain in a simple way how to calculate the intensity of gravity effect detected by probe-b?
I mean, I know the formula F=GMm/r^2 for "standard" gravity, but how can I calculate the force generated by a rotating body?
I guess I need to know the distance of the test-body from the main-body, and the length of test-body (to calculate the force which makes it "rotate"), but which is the formula?

And can the Moon generate a similar force by rotating around the Earth? It's another kind of "mass current", I think.

jumpjack you may find this page from the GP-B website interesting: Spacetime & Spin.

There is no 'force' generated by a rotating body, but it warps and twists the space-time continuum, which introduces a rotation relative to the background continuum generated by a non-rotating body. The formulae for the geodetic and frame-dragging precessions are difficult to calculate but can be found in Misner, Thorne and Wheeler's book 'Gravitation' on page 1119 if you are interested.

I hope this helps,
Garth

The moon also has a geodetic precession, which showed up in the results from 25 years of laser ranging. NB, the formula for the geodetic effect in the picture posted above is now not the only formula for it, the other one gives almost identical numbers, so curvature is not the only interpretation that explains it.

The moon would have the same effect, anything orbiting it would change angle slightly over a long period of time, and over a longer period would rotate.

Oh God, why can't I explain my thought?!?
I'm talking about moon rotating AROUND earth, not around itself: would it cause any precession effect on earth surface?