Asteroid gravity field estimation below the Brillouin sphere

Abstract

The history of space exploration shows a widespread interest in asteroids. These small bodies were visited by multiple spacecrafts made by different space organizations through time. The asteroids give us information about the history of the solar system, due to their unchanged state since the early beginning of the Solar System. In the future, these rocky bodies could provide resources for use on Earth or during human spaceflight. Besides these benefits, so-called near-Earth asteroids can be of danger by the possibility of collision. In the history of Earth, asteroid impacts had large consequences for life on Earth.

During missions towards asteroids, navigation is challenged by the gravity field of the asteroid. Asteroids are relatively small and often have a very irregular shape. The relatively small and irregular gravity field of the asteroid on the spacecraft, makes the acceleration difficult to predict. Therefore, gaining knowledge about this gravity field during the mission improves the safety of the spacecraft.

Gravity fields of celestial bodies often modeled and estimated using the spherical harmonics model. This model has the disadvantaged that its convergence is limited to the body's circumscribing sphere, called the Brillouin sphere. Because of their often irregular shape, this model is not suitable for orbits close to the asteroid, reaching inside this reference sphere.
To eliminate this problem, the alternative mascon (mass concentration) gravity model is implemented in an extended Kalman filter (EKF). This model distributes point-masses along the asteroid's body. The gravitational parameters of each defined mascon are estimated by the EKF using noisy position measurements.

To test the performance of the EKF, a spacecraft is simulated in an asteroid environment. For this simulator, the polyhedron gravity model using the 433 Eros shape model is defined as the real-world gravity field. This high-precision and non-diverging gravity field model assumes a constant density in the asteroid. The model is adjusted such that it also can include density differences inside the asteroid shape by dividing the surface shape model into numerous volume elements. Each element is assigned a density according to the smoothing Mátern Covariance function, which depends on the Euclidean distance between the elements.

The EKF is capable of handling asteroids with a heterogeneous density distribution with the same accuracy as for homogeneous asteroids. Its performance depended highly on the chosen mascon positions, as point masses can be highly correlated. The EKF can estimate the gravity field as accurate as the spherical harmonics degree 8 using noisy position measurements with 10 meter standard deviation.