CGC2 Ephemeris Framework

Ephemeris is necessary for mission orbit design. For non-astrodynamical missions, an existing ephemeris like JPL DE 405 and 406 can be used for this purpose. For astrodynamical missions, one needs to have a working ephemeris flexible enough that one can do orbit simulation for mission design, and orbit determination and astrodynamical-parameter fitting during actual mission. In real-time with the astrodynamical mission, the working ephemeris is continuously improved. After the mission the working ephemeris would be better than all previously existing ephemeris at least for certain parts of the ephemeris. For the ASTROD orbit design and simulation, we have worked out CGC 1 and CGC 2 ephemeris framework. Here we describe how CGC 2 ephemeris framework is built (CGC: Center for Gravitation and Cosmology). In the CGC 2 framework, we include the Sun, nine planets, the Moon and 3 big asteroids in a mutually interacting evolution with the solar field to the post-Newtonian order. Solar quadrupole moment and Earth's quadrupole moment are also included. We include additional 489 asteroids with diameter larger than 65 km in the calculation of the perturbation of orbits of nine planets, the sun, the moon and the 3 big asteroids. To simplify calculation, the heliocentric orbits of these 489 asteroids are determined by the Kepler elements. At each calculation step, the Newtonian perturbation forces are calculated and added to the equations of motion of the 14 celestial bodies. For more accurate calculation of the positions and velocities of the Earth and the Moon, the quadrupole moment effect of Earth is added to the equations of motion of the Earth and the Moon. We use the Runge-Kutta 4 th order algorithm to solve the differential equations of essential celestial bodies with the stepsize 0.01 days. The initial time is 0:00 2005/06/10 (JD 2453531.5) with the initial positions and velocities of 11 celestial bodies taken from JPL DE405 ephemeris; those of the three big asteroids are calculated from MPO98 (1997). This is the CGC 2 ephemeris framework and computing algorithm. The computing program (in C++) is open to public. A comparison of CGC 2 with DE 405 for the range, latitude and longitude of Mercury and Mars in the Earth-Moon mass-center equatorial coordinate frame for 1200 days after the initial time shows that the deviations from DE 405 are below 0.5 km in range, 0.3 mas in latitude and 1.2 mas in longitude.