Relativistic transformation between y and TCG for Mars missions under IAU Resolutions

Considering the fact that the general theory of relativity has become an in- extricable part of deep space missions, we investigate the relativistic transformation between the proper time of an onboard clock τ and the Geocentric Coordinate Time （TCG） for Mars missions. By connecting τ with this local timescale associated with the Earth, we extend previous works which focus on the transformation between τ and the Barycentric Coordinate Time （TCB）. （TCB is the global coordinate time for the whole solar system.） For practical convenience, the relation between τ and TCG is recast to directly depend on quantities which can be read from ephemerides. We find that the difference between τ and TCG can reach the level of about 0.2 seconds in a year. To distinguish various sources in the transformation, we numerically calculate the contributions caused by the Sun, eight planets, three large asteroids and the space- craft. It is found that if the threshold of 1 microsecond is adopted, this transformation must include effects due to the Sun, Venus, the Moon, Mars, Jupiter, Saturn and the velocities of the spacecraft and Earth.