Earth-Mars trajectories with lunar gravity assist study using the self-adaptive Levenberg-Marquardt Algorithm - Rosa, Flávio Daniel Dias (2019)
As the interest in interplanetary missions is rising, new trajectories and methods should be studied and analyzed to decrease the costs and increase the capacity of transporting scientific instruments and payload to Mars. In this work, a numerical study of interplanetary trajectories between Earth and Mars is performed, using the Moon to carry out a lunar gravity assist manoeuvre, with the objective of decreasing the launch energy for the interplanetary transfer and analyze the use of the self-adaptive Levenberg-Marquardt algorithm as a differential corrector for space mission design. The obtained results are compared with the values of the direct transfer achieved with the same methods and with the estimated values for the next interplanetary transfer Windows between Earth and Mars. The results are obtained with the astrodynamics two body problem simplistic model and verified and validated with the open source NASA’s software GMAT for a more realistic approach. The self-adaptive Levenberg-Marquardt algorithm developed for this work in the programming language Python 3.6 is tested and used as a differential corrector to obtain the trajectories for the two-body problem. The results demonstrate that the self-adaptive Levenberg-Marquardt algorithm is adequate to design space missions, a lunar gravity assist can be executed in all situations studied and only in a few cases is not viable. Of the four launch windows analyzed only in one situation the lunar gravity assist does not diminish the launch energy. The results show that the energy needed to perform future Mars missions or missions to other Solar System bodies can be reduced and consequently the payload mass can be increased. The possible introduction of a new calculation method for space mission design is also shown due to the observed results.