Gravity of Mars

[2] 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.

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.

The tracking data would then be converted to develop global gravity models using the spherical harmonic equation displayed above.

[19] 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)[20] then the subsequent models with higher completeness and degree and order up to 120 for the latest GMM-3.

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.

[13] The later modifications of gravity model include taking other non-conservative forces acting on spacecraft into account, including atmospheric drag, solar radiation pressure, Mars reflected solar radiation pressure, Mars thermal emission, and spacecraft thrusting which despins or desaturates the angular moment wheels.

[14] In addition, Martian precession and third body attraction due to the Sun, Moon and planets, which could affect the spacecraft orbit, as well as relavistic effects on the measurements should also be corrected.

However, to interpret the crustal structure, further elimination of such gravitational effect is necessary so that the reduced gravity would only be the result of the core, mantle and crust below datum.

However, density of the material in building up the terrain would be the most important constraint in the calculation, which may vary laterally on the planet and is affected by porosity and geochemistry of the rock.

Volcanoes Olympus Mons and the Tharsis Montes produce the smallest positive free-air gravity anomalies in the solar system.

[5] Alba Patera, also a volcanic rise, north of the Tharsis Montes, however, produces negative Bouguer anomaly, though its extension is similar to that of Olympus Mons.

[27][6] Such setting has already been observed over the famous Syrtis major, which has been inferred to have an extinct magma chamber with 3300 kg m3 underlying the volcano, evident from positive Bouguer anomaly.

If they are, the positive anomalies may be due to uplift of Moho, crustal thinning and modification events by sedimentary and volcanic surface loads after impacting.

[5] In addition, certain portions of Coprates, Eos Chasma and Kasei Valles are also found to have positive Bouguer anomalies,[5] though they are topographic depressions.

[5] Early study of the geoid in the 1950s and 1960s has focused on the low-degree harmonics of the Earth's gravity field in order to understand its interior structure.

[4] It has been suggested that such long-wavelength anomalies on Earth could be contributed by the sources located in deep mantle and not in the crust, for example, caused by the density differences in driving the convection current,[4][28] which has been evolving with time.

The correlation between certain topography anomalies and long-wavelength gravity anomalies, for example, the mid-Atlantic ridge and Carlsberg ridge, which are topography high and gravity high on the ocean floor, thus became the argument for the convection current idea on Earth in the 1970s,[29][30] though such correlations are weak in the global picture.

Another possible explanation for the global scale anomalies is the finite strength of the mantle (in contrast to zero stress), which makes the gravity deviated from hydrostatic equilibrium.

[3] And the variations of density of the deep mantle could be the result of chemical inhomogeneities associated with continent separations,[3] and scars left on Earth after the torn away of the moon.

[4] The sublimation-condensation cycle of carbon dioxide on Mars between the atmosphere and cryosphere (polar ice cap) operates seasonally.

[31] However, current radio tracking data from MGS, ODY and MRO does not allow the effect of phase lag on the tides to be detected because it is too weak and needs more precise measurement on the perturbation of spacecraft in the future.

[35] Measurement of gravity field by different orbiters allows higher-resolution global Bouguer potential model to be produced.

[5] The undulation of the crust-mantle boundary, or the Moho surface, with mass of terrain corrected, should have resulted in varying residual anomaly.

[5] The Hellas and Argyre basins are observed to have crust thinner than 30 km,[5] which are the exceptionally thin area in the southern hemisphere.

[5] Utopia, an impact basin located in northern lowland, is filled by light and water-deposited sedimentary material and has slightly thickened crust at the center.

[5] While for Hellas, Argyre and Isidis basins, they have great Moho uplifted relief and exhibit annuli of diffuse thickened crust beyond the crustal rim.

[25] These have been suggested not caused by erosion and burial alone, as the adding of material into the basin would in fact increase the gravity strength rather than decrease it.

[9] For example, over the volcanic complexes, local density is expected to be as high as 3231 ± 95 kg m−3,[9] which matched the meteorite data and previous estimations.

[5][36][37] This has been set as the reference frame for developing the MOLA Mission Experiment Gridded Data Records (MEGDRs),[5][36] which is a global topography model.

The topography model is important in mapping the geomorphological features and understanding different kinds of processes on Mars.

Earth vs Mars vs Moon gravity at elevation
Rotating spherical harmonic, with for the vertical, and for the horizontal. For the Martian C 20 and C 30 , they vary with time because of the seasonal variation of mass of the polar ice caps through the annual sublimation-condensation cycle of carbon dioxide.
Scientists measured the perturbation of different spacecraft through Doppler and range tracking methods to develop different gravity models ever since the first arrival of the uncrewed space probe Mariner 9 in 1971. (Credit: NASA's Scientific Visualization Studio)
Three-way Doppler, with signal transmitter and receiver separated
Mars free-air gravity map produced along with the GMM-3 gravity solution [ 13 ] (Red: gravity high; Blue: gravity low) (Credit: NASA's Scientific Visualization Studio)
The crust-mantle boundary variation, intrusion, volcanism and topography can bring effect to the orbit of spacecraft, due to the higher density of mantle and volcanic material and lower density of the crust. (Not in scale) +ve: Positive anomaly; -ve: Negative anomaly
Mars Bouguer gravity map, produced along with GMM-3 gravity solution in 2016 [ 13 ] (Red: gravity high; Blue: gravity low) (Credit: NASA's Scientific Visualization Studio)
A sublimation-condensation cycle occurs on Mars which results in carbon dioxide exchange between the cryosphere and the atmosphere. In turn, there is exchange in mass between the two spheres, which gives seasonal variation of gravity. (Courtesy NASA/JPL-Caltech)
Histogram of percentage area against crustal thickness of Mars: 32 km and 58 km are the two major peaks of the histogram.
Comparison of topography , free-air gravity anomaly and crustal density map – Red: gravity high; Blue: gravity low
After the initial impact, high heat flux and high water content would have favored viscous relaxation to take place. The crust becomes more ductile. The basin topography of the craters is thus subjected to greater stress due to self-gravitation, which further drive crustal flow and decay of relief. However, this analysis may not work for giant impact craters such as Hellas , Utopia , Argyre and Isidis basins. [ 25 ]
The topography model MEDGRs was developed through range (distance) measurement done by MOLA 2 instrument and radio tracking data of the Mars Global Surveyor (MGS). [ 36 ] The highest point is located at the Olympus Mons while the deepest point is located within the Hellas Basin. [ 36 ] (Brown-Red: Topography high; Green-Blue: Topography low) (Credit: NASA/JPL-Caltech)