Abstract
For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can’t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argu-ment of perigee and mean anomaly are set equal between two neighboring orbits to negate the separation over time due to the potential of the Earth and the third body effect. The expressions for the second order conditions that guaran-tee that the drift rates of two neighboring orbits are equal on the average are derived. To this end, the Hamiltonian was developed. The expressions for the non-vanishing time rate of change of canonical elements are obtained.
Highlights
Formation flying is a key technology enabling a number of missions which a single satellite cannot accomplish: from remote sensing to astronomy
The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived
The expressions for the time rate of change of the secular elements are obtained, second order conditions are established between the differences in momenta elements that guarantee that the drift rates of two neighboring orbits are equal on the average
Summary
Formation flying is a key technology enabling a number of missions which a single satellite cannot accomplish: from remote sensing to astronomy. Invariant Relative Orbits shows no drift between the spacecraft due to the perturbation even if in presence of a large disturbance. Schaub and Alfriend [1] presented a method to establish J2 invariant relative orbits for spacecraft formation flying applications. They designed relative orbit geometry using differences in mean orbit elements. Abd El-Salam et al [7] used the Hamiltonian framework to construct an analytical method to design invariant relative constellation orbits due to the zonal harmonics J2 ; J3 ; J4 up to the second order, assuming J2 being of order 1. The expressions for the time rate of change of the secular elements are obtained, second order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average
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