Asteroid perturbations and the possible determination of asteroid masses through the ASTROD space mission

ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) Mission Concept uses drag-free spacecraft in solar orbits to combine high-precision measurement of relativistic effects, measurement of solar angular momentum via Lense-Thirring effect, improvement in the measurement of Ġ and the detection of low-frequency gravitational waves in a single mission. As a simple implementation, two spacecraft in separable solar orbits are considered. These drag-free spacecraft will experience gravitational perturbations of the asteroids. This will limit the accuracy of the Ġ measurement, and the accuracy of determining the orbit elements and secular relativistic effects. However, from these perturbations, the masses of larger asteroids can also be determined. In this preliminary analysis, we use the present mass estimation of Ceres, Pallas and Vesta to calculate the perturbations of the spacecraft.