The Solar Test of the Equivalence Principle

Abstract

The Earth, Mars, Sun, Jupiter system allows for a sensitive test of the strong equivalence principle (SEP) which is qualitatively different from that provided by Lunar Laser Ranging. Using analytic and numerical methods we demonstrate that Earth-Mars ranging can provide a useful estimate of the SEP parameter $\eta$. Two estimates of the predicted accuracy are derived and quoted, one based on conventional covariance analysis, and another (called ``modified worst case'' analysis) which assumes that systematic errors dominate the experiment. If future Mars missions provide ranging measurements with an accuracy of $\sigma$ meters, after ten years of ranging the expected accuracy for the SEP parameter $\eta$ will be of order $(1-12)\times 10^{-4}\sigma$. These ranging measurements will also provide the most accurate determination of the mass of Jupiter, independent of the SEP effect test.Comment: 10 pages; LaTeX; three figures upon reques

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“…2 ) ⊙ ∼ −3.52 × 10 −6 [75,88]. Because gravitational self-energy is proportional to m 2 i and also because of the extreme weakness of gravity, the typical values for the ratio (E/mc 2 ) are ∼ 10 −25 for bodies of laboratory sizes.…”

“…Furthermore, the equality of gravitational and inertial masses implies that different neutral massive test bodies will have the same free fall acceleration in an external gravitational field, and therefore in freely falling inertial frames the external gravitational field appears only in the form of a tidal interaction. Apart from these tidal corrections, freely falling bodies behave as if external gravity was absent [75].…”

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“…1 in (Jaekel 2005), reproduced thanks to a courtesy of J. Coy, E. Fischbach, R. Hellings, C. Talmadge and E.M. Standish. It shows that the Yukawa term is excluded with a high accuracy at ranges tested in lunar laser ranging (Williams 1996) and tracking of martian probes (Anderson 1996). At the same time, it also makes it clear that windows remain open for large corrections (α > 1) at short ranges as well as long ranges.…”

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