DC cancellation as a method of generating a t~2-response and of solving the radial position error in a concentric free-falling two-sphere equivalence-principle experiment in a drag-free satellite

摘要

This paper presents a new method for doing a free-fall equivalence- principle (EP) experiment in a satellite at ambient temperature which solves two problems that have previously blocked this approach. By using large masses to change the gravity gradient at the proof masses, the orbit dynamics of a drag-free satellite may be changed in such a way that the experiment can mimic a freefall experiment in a constant gravitational field on the earth. An experiment using a sphere surrounded by a spherical shell both completely unsupported and free falling has previously been impractical because (1) it is not possible to distinguish between a small EP violation and a slight difference in the semi-major axes of the orbits of the two proof masses and (2) the position difference in the orbit due to an EP violation only grows as t whereas the largest disturbance grows as t ~(3/2). Furthermore, it has not been known how to independently measure the positions of a shell and a solid sphere with sufficient accuracy. The measurement problem can be solved by using a two-color trans-collimator (see the main text), and since the radial-position-error and t-response problems arise from the earth's gravity gradient and not from its gravity field, one solution is to modify the earth's gravity gradient with local masses fixed in the satellite. Since the gravity gradient at the surface of a sphere, for example, depends only on its density, the gravity gradients of laboratory masses and of the earth unlike their fields are of the same order of magnitude. In a drag-free satellite spinning perpendicular to the orbit plane, two fixed spherical masses whose connecting line parallels the satellite spin axis can generate a dc gravity gradient at test masses located between them which cancels the combined gravity gradient of the earth and differential centrifugal force. With perfect cancellation, the position-error problem vanishes and the response grows as t~2 along a line which always points toward the earth. In the practical case where the cancellation is not perfect, the t~2-response can hold for about 104 to 106 s (depending on the-cancellation accuracy), and the position error is also suppressed proportional to the accuracy of the cancellation. Experience with a prior drag-free satellite indicates that this cancellation may be accomplished with an accuracy of at least 10~(-2) and possibly 10 ~(-4) to 10~(-6), and this ameliorates the measurement problem sufficiently that equivalence-principle tests with accuracies from 10 ~(-19) to 10~(-23) g may be possible. t~2-response times between 10~5 and 10~6 s are equivalent to a very tall (0.1-10 AU) drop tower with an effective value of g equal to about 3.4 m s ~(-2) which is 3/7 of the value of g at the orbital altitude.