Research in Astronomy and Astrophysics Relativistic transformations between global and local velocities of an orbiter under IAU Resolutions ∗

Abstract Einstein’s general relativity (GR) has become an inevitable part of deep space missions. According to the International Astronomical Union (IAU) Resolutions which are built in the framework of GR, several time scales and reference systems are recommended to be used in the solar system for control, navigation and scientific op-eration of a spacecraft. Under the IAU Resolutions, we derive the transformations be-tween global and local velocities of an arbitrary orbiter. These transformations might be used in orbit determination with Doppler tracking and prediction of Doppler ob-servables for the spacecraft. Taking the YingHuo-1 Mission as a technical example of future Chinese Mars explorations, we evaluate the significance and contributions of various components in the transformations. The largest contribution of the relativistic parts in the transformations can reach the level of ∼ 5 × 10−5 m s−1. This suggests that, for such a spacecraft like we have assumed, if the accuracy of Doppler tracking is better than ∼ 5 × 10−5 m s−1 then the relativistic parts of the transformations of velocities will be required. Key words: reference systems — method: numerical — space vehicles — techniques: radial velocities