Evaluation of the moments of the vertical distribution of the pericenter of a near-circular orbit

Mathematics – Probability

Scientific paper

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Circular Orbits, Satellite Orbits, Spacecraft Maneuvers, Vertical Distribution, Eccentric Orbits, Integral Equations, Orbit Perturbation, Probability Theory

Scientific paper

In space experiments, braking is used to guide a satellite into a lunar or planetary orbit. The errors in the parameters of the approach trajectory and the errors in the application of the braking impulse lead to a certain scatter of the satellite orbital parameters. A priori estimates of the probability characteristics of these parameters are usually obtained from linear relations. The problem of estimating, in a linear approximation, the vertical scatter of the pericenter of a near-circular orbit is examined, and is shown to require the determination of the eccentricity distribution. Analytical formulas for the initial moments of the eccentricity distribution are derived.

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