The position of a Martian lander is affected by different aspects of Mars'
rotational motions: the nutations, the precession, the length-of-day variations
and the polar motion. These various motions have a different signature in a
Doppler observable between the Earth and a lander on Mars' surface. Knowing the
correlations between these signatures and the moments when these signatures are
not null during one day or on a longer timescale is important to identify
strategies that maximize the geophysical return of observations with a geodesy
experiment, in particular for the ones on-board the future NASA InSight or
ESA-Roscosmos ExoMars2020 missions.
We provide first-order formulations of the signature of the rotation
parameters in the Doppler and range observables. These expressions are
functions of the diurnal rotation of Mars, the lander position, the planet
radius and the rotation parameter. Additionally, the nutation signature in the
Doppler observable is proportional to the Earth declination with respect to
Mars.
For a lander on Mars close to the equator, the motions with the largest
signature in the Doppler observable are due to the length-of-day variations,
the precession rate and the rigid nutations. The polar motion and the liquid
core signatures have a much smaller amplitude. For a lander closer to the pole,
the polar motion signature is enhanced while the other signatures decrease.
We also numerically evaluate the amplitudes of the rotation parameters
signature in the Doppler observable for landers on other planets or moons.Comment: 30 pages 7 figures, In press PS
