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Modeling asteroid binary systems with the full two-body problem using surface integrals

In this thesis we have used the “surface integration” method to determine the motion of asteroids.

Alex Ho

Ph.d. candidate

Alex Ho will defend his PhD thesis Modeling asteroid binary systems with the full two-body problem using surface integrals.

Summary of thesis:

Asteroids are leftover pieces from the early formation of the solar system. In the solar system, the vast majority of the asteroids reside in the main asteroid belt, whose orbits are between Mars and Jupiter. Asteroids are also found beyond the orbits of Neptune, and some asteroids may leave the main asteroid belt and obtain Earth-crossing orbits, also known as near-Earth asteroids. Some asteroids have been observed to have a smaller asteroid orbiting around them, similar to how the Moon orbits the Earth. These types of asteroid systems are known as asteroid binaries, and it is estimated that they make up approximately 15% of the near-Earth asteroid population.

The most established theory to describe the formation of asteroid binaries, in the near-Earth asteroid population, is the mechanism called “rotational fission”. Rotational fission occurs when a rubble pile asteroid, which can be thought of as a collection of rocks loosely hanging together due to gravity, starts to throw off parts of its body when it spins fast enough. An analogy to this is someone falling off an office chair that spins too fast. When rotational fission occurs, the parts that are thrown off may fall into orbit around the parent body, thus forming an asteroid binary system.

Studying the motion of asteroid binaries allows us to better understand how they have evolved, which may provide better insight into the history of the solar system.  However, predicting the motion of asteroids is not trivial. This is because there are no exact mathematical solutions to calculate the dynamics of non-spherical bodies. Several approximations to this problem exist. However, these approximative methods often suffer from mathematical limitations, for example when two bodies are close to each other.

In this thesis we have used the “surface integration” method to determine the motion of asteroids. One advantage of this approach, compared to other approximative methods, is that the solution is valid when two asteroids are very close to each other. This is particularly useful in the early formation stages of asteroid binaries, as the two asteroids are very close to each other early on. We have used the advantage of this method to study the evolution of asteroid binaries formed by rotational fission and compared the simulation results with observed data.