Yoshikazu Hashida and P L Palmer
In a previous paper we described an epicycle model for the perturbed motion of satellites under an axisymmetric
potential. In this paper we extend this analysis focusing on the tesseral harmonics in the potential. We restrict the problem to a near-circular orbit of which eccentricity is assumed to be
order of J2 – Earth’s second zonal harmonic – and introduce the analytical formulation
of rst-order perturbed epicycle orbit up to an arbitrary degree and order of tesseral
harmonics. Some periodic terms of interest due to tesseral terms are discussed. Explicit
coecients for these periodic terms are also given for second and third-degrees. We
have shown that the amplitude of the fourth-degree tesseral periodic perturbations can
become larger than that of the second-order tesserals for some specic orbits and the
conditions for this are addressed. We also present simulation results to establish the
accuracy of our epicycle modeling by comparing with numerically integrated orbits and
we obtain only sub-kilometers positional error after 5000 orbits propagation for a low
Earth near-circular orbit.
Ref: Hashida, Y. & Palmer, P.L., AIAA J Guidance, Control & Dynamics, 25, No 3, pp. 571-581, May 2002.