Partial differentiations of vis-viva and Lambert equations

Mathematics

Scientific paper

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Astrodynamics, Euler-Lambert Equation, Kepler Laws, Orbit Calculation, Partial Differential Equations, Celestial Mechanics, Finite Difference Theory, Matrices (Mathematics), Vector Analysis

Scientific paper

The purpose of the paper is to determine the orbit of Keplerian motion from a given set of two geocentric position vectors, where one is a function of t and the other is a function of t plus a time interval, located on a rotating spherical earth model. Lambert's method is used to obtain explicit analytical expressions for an influence matrix of partial derivatives relating small changes in an input vector to a small change in the orbital velocity vector.

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