Keplerian orbit elements induced by precession, nutation and polar motion

Based on theoretical models of Precession, Nutation and Polar Motion (PNPM), as well as perturbed Gaussian equation of satellite motion, the influences of the PNPM on the Keplerian elements are studied. Theoretical derivation and analysis as well as numerical computations are carried out. The numerical results give the conclusion how to deal with the influence of PNPM on the Keplerian elements. The influence of the precession and nutation is one order lower than that of the disturbing force vector, and that of the polar motion is two order lower. Therefore, for the first order analytical orbit solution, the influences of PNPM are all the second order ones and therefore can be neglected. For the second order analytical orbit solution, only the first order disturbance needs to take the influence of the precession and nutation into account. Because only the Earth’s oblateness is the first order disturbance, only for J2 disturbance the influence of precession and nutation have to be taken into account. For orbits determination within a time span of less than three days, the variation of the precession and nutation is of the second order, therefore the influence of precession and nutation can be considered unchanged. The conclusion is guidance for analytic orbit determination.