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Trajectory
This problem is especially complex because force is continually added to the system. Because conservation of energy does not apply, there is no closedform analytical solution to the spiral trajectory. With a few assumptions, however, the trajectory can be modeled. There are multiple approaches to the problem. This report follows the approach suggested by MIT Aero/Astro Professor Richard Battin. We assume the following: that acceleration due to thrust from the engines is constant and in the direction perpendicular to the direction of motion, and that perturbations due to the influence of the Van Allen radiation belts are negligible.
Definitions of Variables = thrust acceleration =velocity of initial circular orbit around a large mass (either Earth or Mars or the Sun) = initial radius of orbit =
Calculations Orbit of Earth: = = Orbit around the sun: = = = = = semimajor axis = m = Orbit around Mars: = =
= Total time as a function of thrust acceleration: = References: Battin, Richard H. An Introduction to the Mathematics and Methods of Astrodynamics. New York: American Institute of Aeronautics and Astronautics, 1987.

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© 2000 Massachusetts Institute of Technology
Comments and questions to mission2004students@mit.edu Last updated: 10 December, 2000 