Effect of Initial Tangential Velocity on Simulated Earth-to-Mars Transfer Trajectories

Abstract

This study investigated the impact of varying the initial tangential velocity of a spacecraft on its trajectory and the minimum approach distance to Mars, within a fixed alignment of the planets. A two-dimensional heliocentric model was designed and constructed using Python with the NumPy and Matplotlib libraries. In this model, the Sun was considered stationary, and Earth, Mars, and the simulated spacecraft all moved within the same two-dimensional orbital plane. The simulation integrated the equations of motion and calculated the spacecraft’s distance to Mars over a period of 300 days, using a 28.125 s timestep (1/128 hour) for the main sweep. The initial tangential velocity increment, varied from 0 to 5,000 m/s, was the only independent variable in the simulation. The results showed that a greater initial tangential velocity increment did not always reduce the distance to Mars. Among the 16 tested increments, 2,900 m/s produced the smallest closest-approach distance, approximately 1.42 × 108 m at approximately day 224.65. This result applies to the fixed alignment and numerical settings tested and does not imply rendezvous or capture. An arrival in the orbital region of Mars was not sufficient to ensure an encounter, as the spacecraft and Mars had to be present in the same place at the same time. While the range of the simulation did not include fuel consumption, trajectory corrections, inclination of the orbit, and orbital capture at Mars, it was able to show the effect of tangential velocity on the trajectory and the closest approach distance.