Orbit Simulation for the Determination of Relativistic and Solar-System Parameters for the ASTROD Space Mission

Abstract

ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) mission concept is to conduct high-precision measurement of relativistic effects,solar-system parameters and gravitational waves. In this paper, we first extend the stochastic model to simulate the determination of the masses of three big asteroids (Ceres, Vesta and Pallas). With one range observation per day for each spacecraft from 25 days to 800 days of the mission and ten range observations per day for each spacecraft from 800 days to 1050 days of the mission (when the apparent positions of the two spacecraft are close to the Sun), the accuracies of determining these parameters are 4.6*10**(-7) for gamma, 4.0*10**(-7) for beta, 1.2*10**(-8) for J2, and 6.4*10**(-5) M_Ceres, 7.6*10**(-4) M_Pallas, 8.1*10**(-5) M_Vesta for the mass determination of Ceres, Pallas and Vesta respectively. We then include in the simulation and determination the rate of change of the gravitational constant (G-dot), and an anomalous constant acceleration (aa) directed towards the Sun (Pioneer Anomaly). At the end of 1050 days of simulation, the accuracies of determining these two parameters are 9.5*10**(-15)/yr for G-dot/G and 2.0*10**(-16) m/s2 for a_a. The mass loss rate of the inner solar system is at the level of 1*10**(-13) M_Sun/yr. The accurate determinat-ion of Ġ/G will mean a need to simultaneously determine the mass loss rate. In other words, the mission gives a way to monitor the mass loss rate of the Sun if Ġ/G can be determined independently.