Equilibrium points and stability around Psyche

The asteroid Psyche is highlighted in the literature for being one of the largest ever observed,
located in the main asteroid belt, with a diameter of approximately 232 km. Classified as type
M, it is speculated based on radar observations, that it is an exposed core of a primitive planet,
composed mainly of iron-nickel. Although it was initially believed to have a high density,
reaching values of 7.6 g/cm3, recent studies indicate lower values. Given such uncertainty, we
sought not to use a specific density, but to explore this range of possible densities for Psyche.
For each case, we compute the gravitational potential employing the polyhedral method, in
which the irregular shape of the object is represented using several tetrahedra, maintaining a
constant density. From this potential, we determine the equilibrium points and their linear
stabilities, looking for possible changes in behaviour according to the density. Since linear
stability influences the time particles can remain close to the equilibrium point, we integrate
orbits around Psyche and analyze the number and lifetime of particles that survive and collide
with the asteroid. The concentrated mass method (MASCONS) was employed and we also took
into account the radiation pressure. This analysis is essential to assist in missions that aim to
orbit the asteroid to collect information, such as the Psyche Mission launched by NASA in
2023, which stands out for its objective of exploring a metallic object for the first time,
unraveling the uncertainties surrounding this asteroid.