Handling of non-gravitational accelerations on a Callisto orbiter for orbit and gravity field determination

Introduction

The exploration of Callisto is part of the extensive interest in the icy moons characterization. As other missions will focus on Ganymede and Europa, mission proposals devoted to the exploration and characterization of Callisto are currently emerging [2][6]. Compared to the other Galilean moons, the outermost moon has kept the best-preserved records of the Jovian system formation, which makes it a candidate of choice to understand how the Jupiter system formed, and how it works.

Led by the National Space Science Center (NSSC), Chinese Academy of Science (CAS), the Gan De mission [2] aims to send an orbiter around Callisto in order to map its gravity and magnetic field, and to characterize its exosphere, surface and interior. Callisto’s degree of differentiation will also be investigated as well as the possible existence of an internal ocean, as Galileo measurements suggested.

Because the mission is at a very early planning stage, there is no definitive mission plan yet. In this context, we selected a small representative set of potential science orbits around Callisto. These orbits are tested under different assumptions in a detailed simulation environment, to analyse the orbit recovery as well as the recovery of Callisto gravity field and k₂ Love number using tracking data. The effect of non-gravitational forces exerting on the orbiter is carefully considered, especially the strategy to handle them through the whole estimation process.

Exploring different orbits

Flybys of Callisto from the JUICE and the Europa Clipper missions will already provide further information on this moon [4]. However, the global mapping of the outermost Galilean moon will be uniquely improved by means of an orbiter at a high inclination and a low altitude. A specific difficulty in the orbit design in the Jovian system is related to the orbit stability, which is highly impacted by the influence of Jupiter as a third body exerting strong perturbations on a Callisto orbiter.

Additionally, the occultations of the Sun by Callisto should be minimized to ensure a maximum solar illumination for power, which is critical this far from the Sun. This implies a minimum angle between the orbital plane w.r.t the direction of the Sun (β_Sun), which is larger the lower the orbit is. Depending on the position of the Earth at that time, this might have a direct impact on the angle between the orbital plane w.r.t the direction of the Earth (β_Earth), which is of importance for orbit determination and gravity field recovery using Doppler tracking data.

In this presentation, we selected various low Callisto orbits, which are suitable as science orbits for Gan De. These orbits have different altitudes, Earth beta angles, and injection date into orbit. Although several of them can be used sequentially, they are considered separately.

A detailed force model

The set of different reference orbits is propagated using the planetary extension of the Bernese Software (BSW) [3]. All the planets of the solar system, as well as the Galilean satellites, are considered as point masses. In the case of Jupiter, the zonal harmonics of the gravity field are also part of the force model. Because our knowledge of Callisto’s gravity field is restricted to the results of the Galileo mission (degree 2) [1], we have derived a synthetic gravity field as ground truth for our simulation. The scaled gravity field of the Earth’s Moon is used from degree 3 to 100. An artificial value of k₂ Love number is also adopted to provide a ground truth.

In order to rely on solar power this far from the Sun, the size of the solar panels is significant, which makes the effect of the solar and planetary radiation pressure on them essential to account for. However, the modelling of these forces can be challenging, particularly because of their dependency on the geometry and the optical properties of the probe. Even with a precise macro model, the optical properties of each plate can evolve with time. Several strategies are tested to handle these non-conservative forces, such as the use of pseudo-stochastics parameters and the possibility of an on-board accelerometer.

Orbit determination and gravity field recovery

Using a detailed noise model [5] and a realistic tracking station schedule, realistic Doppler tracking data (2-way Ka-band Doppler range rate) is simulated as measurements from the Deep Space Network. The non-gravitational accelerations in action during the orbit propagation are used to generate realistic accelerometer measurements. These observations are then used to reconstruct the orbit along with dynamical parameters in a global least-squares adjustment.

Within this closed-loop simulation, we investigate the impact of the non-gravitational accelerations and orbit geometry on the orbit determination and the recovery of the geodetic parameters. The focus of this presentation is on the quality of the retrieved gravity field parameters and tidal Love number k2.

Acknowledgements

This study has been funded with the support of the Swiss National Foundation (SNF).

References

[1] Anderson, J. D., et al. "Shape, mean radius, gravity field, and interior structure of Callisto." Icarus 153.1 (2001): 157-161.

[2] Blanc, Michel, et al. "Gan De: Science Objectives and Mission Scenarios for China's Mission to the Jupiter System." EGU General Assembly Conference Abstracts. 2020.

[3] Dach, R. et al. "Bernese GNSS software version 5.2." (2015).

[4] Di Benedetto, Mauro, et al. "Analysis of 3GM Callisto Gravity Experiment of the JUICE Mission." arXiv preprint arXiv:2101.03401 (2021).

[5] Iess, Luciano, et al. "Astra: Interdisciplinary study on enhancement of the end-to-end accuracy for spacecraft tracking techniques." Acta Astronautica 94.2 (2014): 699-707.

[6] Smith, David E., et al. "MAGIC, A Discovery Proposal to the Icy Moon Callisto." AGU Fall Meeting Abstracts. Vol. 2019. 2019.