Frozen Orbit Design with the HP Prime

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A frozen orbit is characterized by the absence of long-term changes in orbital eccentricity and argument of perigee. This type of orbit maintains almost constant altitude over any particular point on a planet’s surface. The design of frozen orbits involves selecting the correct value of orbital eccentricity and argument of perigee, for a given semimajor axis and orbital inclination, which satisfies a system of nonlinear perturbation equations.

This HP Prime program determines the mean orbital eccentricity required for a frozen orbit. The user provides the mean semimajor axis and inclination and the program calculates the eccentricity using Brent’s method to solve the single constraining nonlinear equation. The program also calculates and displays the real roots of the frozen eccentricity cubic equation. The derivation of the governing equation can be found in the technical report, “Frozen Orbits in the J2 + J3 Problem”, by Krystyna Kiedron and Richard Cook, AAS 91-426, AAS/AIAA Astrodynamics Specialist Conference, Durango, Colorado, August 19-22, 1991.