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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...

The solar tidal deformation of Mars, measured by its k 2 potential Love number, has been obtained from an analysis of Mars Global Surveyor radio tracking. The observed k 2 of 0.153 ± 0.017 is large enough to rule out a solid iron core and so indicates that at least the outer part of the core is liquid. The inferred core radius is between 1520 and 1840 kilometers and is independent of many interior properties, although partial melt of the mantle is one factor that could reduce core size. Ice-cap mass changes can be deduced from the seasonal variations in air pressure and the odd gravity harmonic J 3 , given knowledge of cap mass distribution with latitude. The south cap seasonal mass change is about 30 to 40% larger than that of the north cap.

Doppler and range measurements to the Mars Pathfinder lander made using its radio communications system have been combined with similar measurements from the Viking landers to estimate improved values of the precession of Mars' pole of rotation and the variation in Mars' rotation rate. The observed precession of -7576 Ϯ 35 milliarc seconds of angle per year implies a dense core and constrains possible models of interior composition. The estimated annual variation in rotation is in good agreement with a model of seasonal mass exchange of carbon dioxide between the atmosphere and ice caps.Little is known about the interior of Mars. From telescopic observations and spacecraft missions, the mass and radius of Mars have been determined and hence its mean density. Because Mars is significantly asymmetric, its polar moment of inertia C cannot be inferred from the gravity field. Determination of the polar moment of inertia yields information on the distribution of mass within the planet, such as whether the planet has a dense core surrounded by a lighter mantle. Analysis of radio tracking measurements from the Viking landers has determined the normalized polar moment of inertia C/MR 2 , where M is the mass of Mars and R is its mean radius, to be 0.355 Ϯ 0.015 (1). However, the uncertainty in this estimate is not small enough to determine with certainty that Mars has a dense core or to distinguish between interior models ranging from an Earth-like composition to iron-enriched compositions characteristic of the meteorites thought to originate from Mars (2).The Mars Pathfinder mission has provided an opportunity to improve our knowledge of Mars' polar moment of inertia and hence our knowledge of Mars' interior. As with the Viking landers, the Pathfinder radio system used for communication with Earth was also used to measure the distance (from the signal travel time) and changes in distance (from the Doppler frequency shift of the signal) between Earth and Mars. These measurements provided information on the changing orbits of Earth and Mars and on the rotation of Mars (3). Of particular interest is the martian rotational information: secular precession and periodic nutation of the spin axis, seasonal and tidal variations in the rotation rate, and Chandler-like wobble of Mars' figure axis relative to the spin axis. These quantities can be used to constrain models of the interior of Mars and estimate the annual mass exchange between the atmosphere and the polar ice caps.The precession is driven by the gravitational torque of the sun acting on Mars' oblate figure and is proportional to (C -(A ϩ B)/2)/C where C Ͼ B Ͼ A are the principal moments of inertia of Mars. The factor C -(A ϩ B)/2 ϭ J 2 MR 2 is already known with high accuracy from detection of Mars' gravity field with the use of Viking orbiter and other tracking data (4). Accurate measurement of the precession is needed to determine the polar moment of inertia. Knowledge of the moment of inertia, combined with measurements of Mars' mass, size, shape, and low-order grav...

Observations of the icy Galilean satellites, conducted during 1987-1991 with the Arccibo 13-cm system and the Goldstone 3.5-cm system, yield significant improvements in our knowledge of the satellites' radar properties. Hardly any wavelength dependence is seen for either the total power radar albedo •T or the circular polarization ratio bt c . For Europa, Ganymede, and Callisto our 13-cm estimates of mean values and rms dispersions are •T = 2.60 + 0.22, 1.39 + 0.14, and 0.69 + 0.06; and bl.c = 1.53 + 0.03, 1.43 + 0.06, and 1.17 + 0.04. Radar albedo features arc seen on each satellite. Evidence for btc featurcs is lacking, except for indications of a weak hemispheric asymmetry for Callisto. That intersatellite and intrasatellite fractional variations in albedo greatly exceed variations in bl.c is consistent with prcdictions of coherent backscatter theory and implies that albedo might be a crude indicator of relative silicate abundance. The satellites' albedo distributions overlap. The most prominent radar featurcs are tentatively identified with Galileo Regio and the Valhalla basin. Estimates of echo Doppler frcquencies show Callisto to be lagging its ephemeris by 200 + 50 km. INTRODUCTIONThe radar echoes from Europa, Ganymede, and Callisto are extraordinary. It has been known for 15 years that these objects' radar reflectivities dwarf values reported for comets, the Moon, the inner planets, and nonmetallic asteroids. When the radar transmission is circularly polarized, the icy satellites return echoes with the incident handedness preserved, in contrast with the behavior of other targets. At the principal Arecibo wavelength of 13 cm, the circular polarization ratio Rc, of echo power in the same sense of circular polarization as transmitted (the SC sense) to that in the opposite (OC) sense, exceeds unity for each of the icy Galilean satellites but is only ~0.1 for the Moon and less than 0.4 for most other planetary radar targets. The linear polarization ratio (gL = OL/SL) is about one half for all three satellites, again considerably larger than for other targets. The satellites' 13-cm radar albedos increase from Callism to Ganymede to Europa, whose OC radar reflectivity is the same as that of a metal sphere. Observations of Ganymede at Goldstone in 1977 [Goldstein and Green, 1980] indicated that this object's exotic radar behavior is preserved at 3.5 cm. (Articles reporting radar observations of the satellites are listed in Table 1.) Most efforts to understand the satellites' radar signatures have focused on the search for an electromagnetic scattering mechanism capable of yielding strong echoes with Ix c greater than unity. The 1978-1989 literature suggested that the satellites' signatures might be understood as being due to Eshleman, 1986a] and/or mode-decoupled, multiple, total-internal reflection [Goldstein and Green, 1980; Eshleman, 1986b] from subsurface variations in refractive index. Ostro and Shoemaker [1990] approached the problem from a geologic perspective and outlined explanations for the satellites' ...