Parallel computation of satellite orbit acceleration

We present a formulation of parallel computation of the satellite orbit acceleration due to non-spherical gravitational field. The key techniques are the vector computation of associated Legendre functions and the do-loop folding. These are easily implemented by a slight modification of existing programs and by embedding a few OpenMP directives. The formulation significantly speeds up the orbit integrations of low-altitude satellites. For example, that of GRACE under the influence of EGM2008, a 2190×2159 geopotential model runs around 4 times faster than the serial computation if conducted at a PC with a quad-core 8-thread processor.