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 :\frac{GMm}{r^2}=mr\omega^2, where
G is the
universal constant of gravitation (commonly taken as
G = 6.674 × 10−11 m3 kg−1 s−2),
M is the mass of Mars (most updated value: 6.41693 × 1023 kg),
m is the mass of the satellite,
r is the distance between Mars and the satellite, and \omega is the
angular velocity of the satellite, which is also equivalent to \frac{2\pi}{T} (
T is the orbiting period of the satellite). Therefore, g = \frac{GM}{R_M^2}=\frac{r^3\omega^2}{R_M^2}=\frac{4r^3\pi^2}{T^2R_M^2}, 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. :U(r, \lambda,\psi)= -\frac{GM}{r} \left(1+ \sum_{\ell=2}^{\ell=L} \left ( \frac{R}{r} \right )^\ell \left( C_{\ell 0} P_\ell^0(\sin\psi) + \sum_{m=1}^{+\ell} (C_{\ell m}\cos m\lambda+S_{\ell m}\sin m\lambda)P_\ell^m(\sin \psi) \right) \right), where r,\psi,\lambda are spherical coordinates of the test point. 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). 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. 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). 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 ==