Orbit propagation in irregular and uncertain gravity field using differential algebra

Uncertainty propagation has been addressed extensively in space missions around the Earth, but much less for missions around small solar system bodies. Small bodies usually have irregular and weak gravity and our knowledge of their gravity, rotation speed and surrounding space environment is largely uncertain. These characteristics make the orbit propagation around these small bodies a challenging task. Focusing on the uncertainty of the small body's gravity, this paper applies the differential algebra (DA) technique to study the orbit propagation problem, and addresses its efficiency for a given the required accuracy. Different from traditional studies that focus on the uncertainty of the initial state, this study assumes an exact initial state and studies the influences that gravity model uncertainties have on the orbit. Taking the asteroid Steins as an example, the accuracy and the efficiency of the DA approach are firstly validated by comparison with the traditional Monte Carlo method. Then, the effects of gravity uncertainties on different types of orbits (prograde, retrograde and polar) are studied. The retrograde motion is found to be more robust to the gravity uncertainty than the prograde ones. For near polar orbits, the impact of gravity uncertainty on orbital motion depends significantly on the initial position, and it reaches the maximum if the initial position is near the polar regions. Moreover, short-term effects are found to play an important role in orbit deviation as a result of the gravity uncertainty. These discoveries can help mission designers assess the posed risk and design appropriate mission orbits.