Orbit Estimation of Small Jovian Satellites

Abstract

The primary motivation for this work was the lack of open-source or clearly motivated studies describing the orbit estimation of natural satellites. The capability to accurately model the trajectory of the moons of Jupiter is crucial for properly understanding the evolution of the Jovian system and, by extension, the solar system. Considering the small Jovian moons remain relatively unknown, they will be the focus of this study. The goal of this project was to develop a framework for the full estimation process, based on the Tudat software library, starting from raw astrometric observations, to be made available publicly. The first step was designing a new data processing algorithm, capable of uniformising the observational data. These measurements are reported in a wide variety of formats, with differences in time format, time scale, orientation, and observation type, amongst others. The developed software was able to produce Tudat-compatible observations with limited user interaction. These processed measurements were then analyzed and validated, first by examining the mean residuals with respect to existing ephemerides to detect remaining biases in the data, before comparing the standard deviation of these residuals to those reported in their original publication, whenever available. Secondly, the estimation framework was set up. Based on the processed astrometric observations, the orbits of three minor Jovian satellites, Himalia, Elara, and Amalthea were estimated as case studies. Each of these posed its own set of challenges, but together they yield a good representation of the full range of outer moons. The SPICE kernel ephemerides were used to evaluate the quality of these orbital solutions. Estimating Himalia’s orbit proved the easiest, as it is the minor moon that is observed the most, in combination with its relatively slow dynamics. One problem was the fact that there was a remaining unmodeled bias in the oldest, i.e. pre-1960, observations due to errors in converting from old to new frames. Removing these observations and replacing them with simulated measurements with realistic residuals both proved to reduce the difference with respect to the SPICE benchmark to within the uncertainty level of this very benchmark. This proves that the framework allows to accurately estimate the ephemerides of Himalia, although no conclusions could be drawn on the exact contribution of the old observations. Elara’s orbit is in many ways similar to that of Himalia, as they are part of the same orbital group. However, a close approach with this more massive Himalia in 1949 had a significant impact on Elara’s trajectory. Therefore, estimating Elara’s orbit is not limited to its initial state. Instead, Himalia’s gravitational parameter is determined concurrently to optimize the solution. However, even when determining this gravitational parameter, it became apparent that the current dynamical model could not perfectly capture the dynamics at the close approach, due to the limited amount of data before the event, leading to an error of several hundred km. This is still well below the residual of the observations, however. Finally, Amalthea proved to be the most difficult body to get an accurate orbital solution for. Since Amalthea is an inner moon, as opposed to the outer moons Himalia and Elara, its angular velocity is over 500 times higher. This logically makes both timing and position errors significantly more impactful. Additionally, the very limited amount of data, which is constrained to just a few campaigns of several nights, further hamper accurate orbit determination. By limiting the step size of the update in the estimated initial state between iterations to a standard deviation of 100 km by defining the a-priori covariance, a stable solution, accurate to several 100 km could be found. A preliminary investigation of the contribution of simulated spacecraft data indicated that the few available spacecraft observations of Amalthea have a large impact, which warrants further studies. Thus, through determining and analyzing the orbit of these three case studies, the quality of the developed framework is ascertained. The solutions proved to lie within the uncertainty region of the ephemerides published in SPICE. Inaccuracies in the estimated orbit could always be linked to deficiencies in the input data, thus not taking away from the quality of the framework.