where

denotes the radial distance from the Earth's center,

is the standard gravitational parameter,

is the equatorial radius,

are the zonal gravitational harmonic coefficients, and

are the Legendre polynomials. The

harmonic, known as the oblateness perturbation, is the dominant harmonic and causes significant precession of the near-Earth satellite orbits. The

perturbation affects the orbital elements right ascension of the ascending node

, inclination

, argument of the periapsis

, semi-major axis

, eccentricity

, and initial mean anomaly

in the following three ways: (1) short-period oscillations; (2) long-period oscillations; and (3) secular drift. For long-term investigation, the secular drift is of special importance and this is what this Demonstration studies. The effect of

on the mean orbit elements can be expressed by the following differential equations:

The differential equations were solved for 500 orbital periods (one orbital period for this orbit is 2.76445 hours). An orbit is synthesized from the orbital elements (which are continuous time functions) at the end of each orbital period and rendered on the screen. It can be seen that for the

inclined orbit, both the line of nodes and the periapsis regress, whereas for the orbit with the critical inclination, only the nodal line shows secular drift.

Reference: H. Schaub and J. L. Junkins,

*Analytical Mechanics of Space Systems*, Reston, VA: American Institute of Aeronautics and Astronautics, 2003.