An efficient algorithm of computation of the Earth's gravitational potential and its first order derivatives for solving artificial satellite problems.

An efficient algorithm is developed for computation of the Earth's gravitational potential and its first order derivatives when constructing artificial satellite orbits, including the polar ones. As compared with the well-known Cunningham's algorithm an application of simple normalizing factors for the associated Legendre functions and stable recurrence relations allow quadruple reducing of the calculation time. At the same time the required computer storage decreases considerably and the accuracy of results becomes one order higher, when the number of spherical harmonics is fixed. Application of this method permits practical utilization of geopotential models of high degrees and orders, when constructing satellite orbits with decimetre accuracy on computers of moderate efficiency.