![]() ![]() is the radial distance from the center of attraction to the spacecraft increases as fuel is burned is the initial distance is the final and maximal distance.is time in the given interval, which is called the horizon.The blue curve is the orbital transfer trajectory, while the red and green curves are the initial lower circular orbit and the final upper circular orbit. Here is a sketch of a solution to the problem with some notation. The orbit transfer trajectory is coplanar with the two circular orbits and the center of attraction.Īll these assumptions are stated in.The spacecraft moves to the largest possible circular orbit around the center of attraction.The spacecraft moves with a constant thrust from a rocket engine operating in the time interval. ![]() Initially the spacecraft moves in a circular trajectory around the center of attraction.There is a unique center of attraction.The Orbit Transfer Problemįor the orbit transfer problem, assume that: The Earth-Mars orbit transfer problem is timely, given the successful flight and smooth landing of the American Curiosity rover on Mars. This article is divided into five sections: the orbit transfer problem, equations of motion, the optimal control problem, necessary conditions for the Mayer problem, and a dynamic approach to the maximal orbit transfer problem using Mathematica ’s built-in Manipulate function. Finally, assume normalized values for all constants and variables. Also assume that there is only one center of attraction at the common center of the two circular orbits. Assume that a spacecraft is in a circular orbit and consider the problem of finding the largest possible circular orbit to which the spacecraft can be transferred with constant thrust during a set time, so that the variable parameter is the thrust-direction angle.
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