Atmospheric contribution to the dissipation of the gravitational tide of Phobos on Mars

Details Atmospheric contribution to the dissipation of the gravitational tide of Phobos on Mars Atmospheric contribution to the dissipation of the gravitational tide of Phobos on Mars

May 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agusm.p41b..07t&link_type=abstract

American Geophysical Union, Fall Meeting 2007, abstract #P41B-07

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1221 Lunar And Planetary Geodesy And Gravity (5417, 5450, 5714, 5744, 6019, 6250), 1240 Satellite Geodesy: Results (6929, 7215, 7230, 7240), 1243 Space Geodetic Surveys

Scientific paper

Observations made with the MOLA instrument on the Mars Global Surveyor spacecraft (Zuber et al, 1992, Smith et al, 2001) provide improved estimates on the orbit position of Phobos, the innermost natural satellite of Mars. These estimates in turn provide an improved estimate of the rate of tidal dissipation of the Mars-Phobos system, corresponding to a rate of secular orbit angular velocity of 6.631+/-0.029 * 10-9 /year. This is equivalent to an energy dissipation rate of 3.34+/-0.01 MW. Assuming all dissipation is in the interior of the planet in the form of solid-body tides, the bulk interior viscosity of Mars, treated as a homogeneous Maxwell solid, was estimated to be 8.7*1014 Pa.s. (Zuber, 2005). Here we consider another potential source of energy dissipation--dissipation in the Martian atmosphere in the form of atmospheric tides. We apply the classical theory of atmospheric tides (Chapman and Lindzen, 1970) to a steady-state atmosphere perturbed periodically by the gravitational potential of Phobos. Using vertical temperature profiles from Viking descenders, we calculate steady-state perturbations to the basic state. This perturbation takes the form of gravity waves, which can either propagate vertically (if 4κ H/hn <1) or are damped (4κ Hhn>1), where H is the scale height and hn is the equivalent depth. We find that almost all of Phobos's gravitational forcing is projected onto the first symmetric Hough mode which has an equivalent depth of about 57 km; however, we find this mode is trapped, and propagation for an isothermal atmosphere only occurs for modes of order n≥6. Therefore, no significant dissipation occurs through the vertical propagation of energy and subsequent breaking of the tidal wave as the wave amplifies with height. Alternatively, from the energy stored in the first trapped mode we estimate that the time scale required for the dissipative mechanisms to account for the total dissipation of the tides is of order 102 s. This time scale is unrealistically short, since it would contradict observations of propagating thermal tides in the Martian atmosphere. We therefore conclude that energy dissipation in the atmosphere is of sufficiently small order to be neglected.

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