Model-Independent Constraints on Possible Modifications of Newtonian Gravity

Abstract

New model-independent constraints on possible modifications of Newtonian gravity over solar-system distance scales are presented and their implications discussed. The constraints arise from the analysis of various planetary astrometric data sets. The results of the model-independent analysis are then applied to set limits on a variation in the 1/r 2 behavior of gravity, on possible Yukawa-type interactions with ranges of the order of planetary distance scales, and on a deviation from Newtonian gravity of the type discussed by Milgrom. PACS numbers: 04.80,+z, 04.90.+e, 96.35.Tf We present here the results of an analysis of highprecision solar-system data in which we test for an apparent variation of the effective value of /IQ=GMQ with distance, where G is the Newtonian constant of gravity and M© is the mass of the Sun. We also present new limits on an anomalous precession of the perihelia of Mercury and Mars, obtained by studying how closely the orbits of these planets complied with the predictions of general relativity. Both of these results are then interpreted in terms of constraints on a deviation of the law of gravity from Newton's 1/r 2 behavior, on possible Yukawa-type intermediate-range interactions, and on a modification of nonrelativistic gravitation of the type suggested by Milgrom.One of the consequences of a variation of /*© with distance is a modification of Kepler's third law:where T p is the period and a p is the physically measured semimajor axis of the orbit of planet p. Given a set of values for a p and T p > Eq. (l) can be used to determine jio(r). However, the period of a planet has historically been determined much more accurately than has the semimajor axis. For this reason the standard method of analysis of solar-system astrometric data 1 has been to define //© to have a particular (constant) value, jUo(r)=/io(tf®) = K: 2 , where K is Gauss's constant (0.017 20209895 AU 3/2 /day, where AU denotes the astronomical unit), and to derive a "semimajor axis parameter" viaThis procedure gives the semimajor axis relative to a standard orbit at 1 AU, and this is all that can be determined with period data alone. However, for several planets there are also range data available-either planetary radar or spacecraft tracking to a planetary orbiter, lander, or flyby. In these cases it is possible to measure a p directly (and to thereby determine the size of the AU in kilometers). If ju© is a function of distance, then the scale of the semimajor axes will be different for each planet, and we can combine Eqs. (1) and (2) to yield sU + ifr)-^o (flp) 1/3 (3)Thus, the signature for a variation of JIQ with distance is a disparity r\ p in the conversion from AU's to kilometers appropriate to each planet. We note that Eq. (3) assumes no particular functional form for p©(r), except that ji©(r) varies such that r\ p may be treated as a constant over the orbit of planet p.In addition to the prediction of a variation of p® from planet to planet, the various modifications of Newtonian gravity that have been sugg...

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