The gravity of Mars is a natural phenomenon, due to the law of gravity, or gravitation, by which all things with mass around the planet Mars are brought towards it. It is weaker than Earth's gravity due to the planet's smaller mass. The average gravitational acceleration on Mars is 3.721 m/s2 (about 38% of the gravity of Earth), with a global variation range of ~0.059 m/s2.
In general, topography-controlled isostasy drives the short wavelength free-air gravity anomalies. At the same time, convective flow and finite strength of the mantle lead to long-wavelength planetary-scale free-air gravity anomalies over the entire planet. Variation in crustal thickness, magmatic and volcanic activities, impact-induced Moho-uplift, seasonal variation of polar ice caps, atmospheric mass variation and variation of porosity of the crust could also correlate to the lateral variations.
Over the years models consisting of an increasing but limited number of spherical harmonics have been produced. Maps produced have included free-air gravity anomaly, Bouguer gravity anomaly, and crustal thickness. In some areas of Mars there is a correlation between gravity anomalies and topography. Given the known topography, higher resolution gravity field can be inferred. Tidal deformation of Mars by the Sun or Phobos can be measured by its gravity. This reveals how stiff the interior is, and shows that the core is partially liquid. The study of surface gravity of Mars can therefore yield information about different features and provide beneficial information for future Mars landings.
Measurement
To understand the gravity of Mars, its gravitational field strength g and gravitational potential U are often measured. Simply, if Mars is assumed to be a static perfectly spherical body of radius RM, provided that there is only one satellite revolving around Mars in a circular orbit and such gravitation interaction is the only force acting in the system, the equation would be
where G is the universal constant of gravitation (commonly taken as G = 6.674 × 10−11 m3 kg−1 s−2),"CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2017-12-14. "2014 CODATA recommended values" M is the mass of Mars (most updated value: 6.41693 × 1023 kg),Jacobson, R. A. (2008). Ephemerides of the Martian Satellites—MAR080. JPL IOM 343R–08–006. m is the mass of the satellite, r is the distance between Mars and the satellite, and is the angular velocity of the satellite, which is also equivalent to (T is the orbiting period of the satellite).
Therefore, , where RM is the radius of Mars. With proper measurement, r, T, and RM are obtainable parameters from Earth.
However, as Mars is a generic, non-spherical planetary body and influenced by complex geological processes, more accurately, the gravitational potential is described with spherical harmonic functions, following convention in geodesy; see Geopotential model.
where are spherical coordinates of the test point. is longitude and is latitude. and are dimensionless harmonic coefficients of degree and order . is the Legendre polynomial of degree with and is the associated Legendre polynomial with . These are used to describe solutions of Laplace's equation. is the mean radius of the planet. The coefficient is sometimes written as . The lower the degree and order , the longer wavelength of anomaly it represents. In turn, long-wavelength gravity anomaly is influenced by global geophysical structures. The higher the degree and order , the shorter wavelength of anomaly it represents. For degree over 50, it has been shown that those variations have high correlation with the topography. Geophysical interpretation of surface features could further help deriving a more complete picture of the Martian gravity field, though misleading results could be produced. The oldest technique in determining the gravity of Mars is through Earth-based observation. Later with the arrival of uncrewed spacecraft, subsequent gravity models were developed from radio tracking data.
Earth-based observation Before the arrival of the Mariner 9 and Viking orbiter spacecraft at Mars, only an estimate of the Mars gravitational constant GM, i.e. the universal constant of gravitation times the mass of Mars, was available for deducing the properties of the Martian gravity field. GM could be obtained through observations of the motions of the natural satellites of Mars (Phobos and Deimos) and spacecraft flybys of Mars (Mariner 4 and Mariner 6).
Long term Earth-based observations of the motions of Phobos and Deimos provide physical parameters including semi-major axis, eccentricity, inclination angle to the Laplacian plane etc., which allow calculation of the ratio of solar mass to the mass of Mars, moment of inertia and coefficient of the gravitational potential of Mars, and give initial estimates of the gravity field of Mars.
Inferred from radio tracking data
Precise tracking of spacecraft is of prime importance for accurate gravity modeling, as gravity models are developed from observing tiny perturbation of spacecraft, i.e. small variation in velocity and altitude. The tracking is done basically by the antennae of the Deep Space Network (DSN), with one-way, two-way and three-way Doppler and range tracking applied. One-way tracking means the data is transmitted in one way to the DSN from the spacecraft, while two-way and three-way involve transmitting signals from Earth to the spacecraft (uplink), and thereafter transponded coherently back to the Earth (downlink). The difference between two-way and three-way tracking is, the former one has the same signal transmitter and receiver on Earth, while the latter one has the transmitter and receiver at different locations on Earth. The use of these three types of tracking data enhances the coverage and quality of the data, as one could fill in the data gap of another.
Doppler tracking is a common technique in tracking the spacecraft, utilizing radial velocity method, which involves detection of Doppler shifts. As the spacecraft moves away from us along line of sight, there would be redshift of signal, while for the reverse, there would be blueshift of signal. Such technique has also been applied for observation of the motion of exoplanets. While for the range tracking, it is done through measurement of round trip propagation time of the signal. Combination of Doppler shift and range observation promotes higher tracking accuracy of the spacecraft.
The tracking data would then be converted to develop global gravity models using the spherical harmonic equation displayed above. However, further elimination of the effects due to affect of solid tide, various relativistic effects due to the Sun, Jupiter and Saturn, non-conservative forces (e.g. angular momentum desaturations (AMD), atmospheric drag and solar radiation pressure) have to be done, otherwise, considerable errors result.
History
The latest gravity model for Mars is the Goddard Mars Model 3 (GMM-3), produced in 2016, with spherical harmonics solution up to degree and order 120. This model is developed from 16 years of radio tracking data from Mars Global Surveyor (MGS), Mars Odyssey and Mars Reconnaissance Orbiter (MRO), as well as the MOLA topography model and provides a global resolution of 115 km. A separate free-air gravity anomaly map, Bouguer gravity anomaly map and a map of crustal thickness were produced along with this model. Compared with MRO110C and other previous models, major improvement of the estimation of the gravity field comes from more careful modeling of the non-conservative forces applied to the spacecraft.
Gravity solutionsAuthorsYearDegree (m) and order (l) of the spherical harmonic solution [Surface resolution (km)]Data source –JP Gapcynski, RH Tolson and WH Michael Jr19776Tracking data of Mariner 9, Viking 1 and 2 spacecraftGeoide martienG Balmino, B Moynot and N Vales198218 [~600 km]Tracking data of Mariner 9, Viking 1 and 2 spacecraftGMM-1DE Smith, FJ Lerch, RS Nerem, MT Zuber, GB Patel, SK Fricke and FG Lemoine199350
[200–300 km]Tracking data of Mariner 9, Viking 1 and 2 spacecraftMars50cAS Konopliv, WL Sjogren199550Tracking data of Mariner 9, Viking 1 and 2 spacecraftGMM-2BFG Lemoine, DE Smith, DD Rowlands, MT Zuber, GA Neumann, DS Chinn, and DE Pavlis200180Tracking data of Mars Global Surveyor (MGS), and MOLA-derived topography data GGM1041CLemoine, F. G., 2009. Geosciences NASA PDS. FG Lemoine200190Tracking data of Mars Global Surveyor (MGS) and Mars Odyssey, and MOLA-derived topography dataMGS95JAS Konopliv, CF Yoder, EM Standish, DN Yuan, WL Sjogren200695 [~112 km]Tracking data of Mars Global Surveyor (MGS) and Mars Odyssey, and MOLA-derived topography data MGGM08AJC Marty, G Balmino, J Duron, P Rosenblatt, S Le Maistre, A Rivoldini, V Dehant, T. Van Hoolst200995 [~112 km]Tracking data of Mars Global Surveyor (MGS) and Mars Odyssey, and MOLA-derived topography dataMRO110B2AS Konopliv, SW Asmar, WM Folkner, Ö Karatekin, DC Nunes, SE Smrekar, CF Yoder, MT Zuber2011110Tracking data of Mars Global Surveyor (MGS), Mars Odyssey and Mars Reconnaissance Orbiter (MRO), and MOLA-derived topography dataMGM2011C Hirt, SJ Claessens, M Kuhn, WE Featherstone2012[3 km (equator) – 125 km]Gravity solution MRO110B2, and MOLA-derived topography dataGMM-3A Genova, S Goossens, FG Lemoine, E Mazarico, GA Neumann, DE Smith, MT Zuber2016120 [115 km]Mars Global Surveyor (MGS), Mars Odyssey and Mars Reconnaissance Orbiter (MRO) MGS (SPO-1, SPO-2, GCO, MAP) ODY (ODYT, ODYM) MRO (MROT, MROM) The techniques in tracking the spacecraft and geophysical interpretation of surface features can affect the resolution of the strength of gravity field. The better technique favors spherical harmonic solutions to higher degrees and orders. Independent analysis on Mariner 9 and Viking Orbiter tracking data yielded a degree and order of 6 spherical harmonic solution., Further combination of the two data sets, along with correlation of anomalies with volcanic features (positive anomaly) and deep-printed depression (negative anomaly) assisted by image data allows a degree and order of 18 spherical harmonic solution produced. Further use of spatial a priori constraint method, which had taken the topography into account in solving the Kaula power law constraint, had favored model of up to degree 50 spherical harmonic solution in global resolution (Goddard Mars Model-1, or GMM-1) then the subsequent models with higher completeness and degree and order up to 120 for the latest GMM-3.
Therefore, gravity models nowadays are not directly produced through transfer of the measured gravity data to any spatial information system because there is difficulty in producing model with sufficiently high resolution. Topography data obtained from the MOLA instrument aboard the Mars Global Surveyor thus becomes a useful tool in producing a more detailed short-scale gravity model, utilizing the gravity-topography correlation in short-wavelength. However, not all regions on Mars show such correlation, notably the northern lowland and the poles. Misleading results could be easily produced, which could lead to wrong geophysics interpretation.