We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network (DSN) tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k2 Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k2 solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k2 of 0.1697±0.0027 (3-!). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C30 and, for the first time, C50. Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C30 for ⇠1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics (l=60-80) than previous solutions

The NASA MESSENGER mission explored the innermost planet of the solar system and obtained a rich data set of range measurements for the determination of Mercury’s ephemeris. Here we use these precise data collected over 7 years to estimate parameters related to general relativity and the evolution of the Sun. These results confirm the validity of the strong equivalence principle with a significantly refined uncertainty of the Nordtvedt parameter η = (−6.6 ± 7.2) × 10⁻⁵. By assuming a metric theory of gravitation, we retrieved the post-Newtonian parameter β = 1 + (−1.6 ± 1.8) × 10⁻⁵ and the Sun’s gravitational oblateness, $${{J}}_{2 \odot }$$J 2 ⊙ = (2.246 ± 0.022) × 10⁻⁷. Finally, we obtain an estimate of the time variation of the Sun gravitational parameter, $$\dot{{G} {{M}}_ \odot} {\mathrm{/}}{{G}}{{M}}_ \odot$$G M ⊙ ° ∕ G M ⊙ = (−6.13 ± 1.47) × 10⁻¹⁴, which is consistent with the expected solar mass loss due to the solar wind and interior processes. This measurement allows us to constrain $$\left| {{\dot{ G}}} \right|{\mathrm{/}}{{G}}$$G ° ∕ G to be <4 × 10⁻¹⁴ per year.

Geodetic analysis of radio tracking measurements of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft while in orbit about Mercury has yielded new estimates for the planet's gravity field, tidal Love number, and pole coordinates. The derived right ascension (α = 281.0082° ± 0.0009°; all uncertainties are 3 standard deviations) and declination (δ = 61.4164° ± 0.0003°) of the spin pole place Mercury in the Cassini state. Confirmation of the equilibrium state with an estimated mean (whole planet) obliquity ϵ of 1.968 ± 0.027 arcmin enables the confident determination of the planet's normalized polar moment of inertia (0.333 ± 0.005), which indicates a high degree of internal differentiation. Internal structure models generated by a Markov Chain Monte Carlo process and consistent with the geodetic constraints possess a solid inner core with a radius (r_ic) between 0.3 and 0.7 that of the outer core (r_oc).

We have analyzed 3 years of radio tracking data from the MESSENGER spacecraft in orbit around Mercury and determined the gravity field, planetary orientation, and ephemeris of the innermost planet. With improvements in spatial coverage, force modeling, and data weighting, we refined an earlier global gravity field both in quality and resolution, and we present here a spherical harmonic solution to degree and order 50. In this field, termed HgM005, uncertainties in low‐degree coefficients are reduced by an order of magnitude relative to earlier global fields, and we obtained a preliminary value of the tidal Love number k₂ of 0.451 ± 0.014. We also estimated Mercury's pole position, and we obtained an obliquity value of 2.06 ± 0.16 arcmin, in good agreement with analysis of Earth‐based radar observations. From our updated rotation period (58.646146 ± 0.000011 days) and Mercury ephemeris, we verified experimentally the planet's 3:2 spin‐orbit resonance to greater accuracy than previously possible. We present a detailed analysis of the HgM005 covariance matrix, and we describe some near‐circular frozen orbits around Mercury that could be advantageous for future exploration.

Knowledge of the average density of the crust of a planet is important in determining its interior structure. The combination of high‐resolution gravity and topography data has yielded a low density for the Moon's crust, yet for other terrestrial planets the resolution of the gravity field models has hampered reasonable estimates. By using well‐chosen constraints derived from topography during gravity field model determination using satellite tracking data, we show that we can robustly and independently determine the average bulk crustal density directly from the tracking data, using the admittance between topography and imperfect gravity. We find a low average bulk crustal density for Mars, 2582 ± 209 kg m⁻³. This bulk crustal density is lower than that assumed until now. Densities for volcanic complexes are higher, consistent with earlier estimates, implying large lateral variations in crustal density. In addition, we find indications that the crustal density increases with depth.