Orbital evolution of the BepiColombo Mercury Planetary Orbiter (MPO) in the gravity field of Mercury

Kurzfassung

This bachelor thesis analyses the influence of Mercurys gravity field on the orbit of the Mercury Planetary Orbiter (MPO) which is the part of the European-Japanese mission BepiColombo launched in October 2018. The gravity field of Mercury was determined from radio tracking data of the NASAs spacecraft MESSENGER which was orbiting the planet until 2015. Due to the highly eccentric orbit of MESSENGER, the calculated gravitational harmonic coefficients are afflicted with uncertainties. Therefore, the orbital evolution of MPO is predictable but with some inaccuracy. For this reason, different plausible gravity fields were generated using a Monte Carlo Method. The generation of the random gravity fields was performed using the gravitational coefficients up to degree and order of 100 and their uncertainties, which were determined by MESSENGER. For that, a function, based on Gaussian distribution, was used. This function was implemented in a numerical orbit integrator developed by DLR, Berlin. Furthermore, scale factors 1, 3, 5 and 10 were used for generating the gravity fields. Before performing the simulations for orbital prediction of MPO, the boundary conditions were determined. The number of the simulations was set to 10,000 per scale factor, the degree and order of the gravity field was limited to 50. The time frame of the mission was set to 2 Earth years, which covers the nominal and the extended mission phases. The distribution of some important harmonic coefficients was checked and the impact of the gravitational and non-gravitational forces affecting the motion of MPO was determined. As expected, the main accelerations are caused by the gravity field of Mercury, followed by the gravity force of the Sun. The third and fourth disturbing forces are the solar radiation pressure and indirect radiation pressure. The smallest perturbations are caused by the remaining solar system bodies. The simulations of the orbital evolution of MPO were performed using the generated gravity fields of Mercury with the scale factors 1, 3, 5 and 10. The results of the simulations were analyzed and compared with each other. The evolution of the orbit of MPO is expressed in the orbital elements. The analysis is mainly focused on the periherm as the minimal distance to the surface of Mercury is critical for the mission. The results show that the geopotential of Mercury causes an increase in the eccentricity and a decrease in the periherm altitude. The semi-major axis and the inclination have a periodic character but remain almost constant. The longitude of ascending node decreases slowly with periodic fluctuations. The argument of periapsis falls almost linear. The standard deviations, as well as the difference between the minimal and maximal values get larger with a growing scale factor and over time. The values of the elements are still in an acceptable range after the first year. The change in the periherm after 2 years could already be considered as critical in some cases for the scale factor 1 because the periherm falls below critical value of 200 km. Moreover, the likelihood that the periherm is below 200 km after 2 years increases with the rising scale factor. Furthermore, there is a possibility that the satellite collides with the planet in the simulations for the scale factor 5 and 10. The influence of the harmonic coefficients J2, J3 and J$ on the longitude of ascending node, argument of periapsis and the eccentricity was investigated analytically which allows for an estimation of the effect of these coefficients, assuming the linear tendency. In addition, the influence of the gravity of the Sun was investigated. The results show that the Sun has positive effect on the evolution of the periherm after 2 years. Taking into account Mercurys gravity field, the gravity of the Sun, radiation pressure and the solar system bodies, the results of the simulations are very similar to the case with the consideration of the geopotential of Mercury and of the Sun. Thus, the orbital evolution of MPO in mainly affected by the gravity of Mercury and the Sun.