A Simple Leapfrog Integration Scheme to Find Optimal Interplanetary Trajectories Public Deposited



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  • The calculation of interplanetary trajectories is a numeric problem which requires a high degree of precision for the results to be accurate. A computer program was written for this project which uses leapfrog integration combined with Newton’s method of iterative root finding to find ideal interplanetary trajectories. Reasonable initial conditions are found by assuming a Hohmann transfer between two orbits. The program accounts for the gravitational influence of all planets in the solar system and seeks a solution which favors the least amount of energy for the transfer. Newton’s method of iterative root finding converges exponentially, and leapfrog integration allows for large timesteps which causes the program to find solutions quickly and efficiently. The program can be used to calculate the ideal trajectory between any two planets in the solar system (including our moon). Additionally, a user can input the absolute initial position and velocity of a craft to model more complicated orbits or trajectories which do not originate on a planet.
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Last modified: 03/13/2018

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