Improved estimate of tidal dissipation within Mars from MOLA observations of the shadow of Phobos

Abstract

We report on new observations of the orbital position of Phobos, the innermost natural satellite of Mars, and show that these observations provide an improved estimate of the rate of tidal dissipation within Mars. The observations were made with the Mars Orbiter Laser Altimeter instrument on the Mars Global Surveyor spacecraft. The secular acceleration in along‐track orbital motion is conventionally expressed in terms of a quadratic term in mean orbital longitude, which yields s = (dn/dt)/2 = (136.7 ± 0.6) × 10−5 deg/yr2, where n is the mean motion. The corresponding fractional rate of change in orbital angular velocity is (dn/dt)/n = (6.631 ± 0.029) × 10−9/yr, the highest measured for any natural satellite in the solar system. The energy dissipation rate is (3.34 ± 0.01) MW. Because Phobos is so close to Mars, there are nonnegligible contributions to the tidal evolution from harmonic degrees 2, 3, and 4. However, the elastic tidal Love numbers are observationally constrained only at degree two. The observed acceleration is consistent with that for a homogeneous Maxwell viscoelastic model of Mars with effective viscosity of (8.7 ± 0.6) × 1014 Pa s.