Natural perturbations to produce heliotropic orbits on asteroid 2000 TW60

Heliotropic orbits are those in which the most distant point of the orbit, known as the apoapsis, remains, on average, oriented toward the Sun. When the apoapsis is directed opposite to the Sun, it is called an antiheliotropic orbit. This work examines the possibility of heliotropic orbits around the asteroid 34604 Vilhena (2000 TW60), considering perturbations caused by non-uniform distribution of mass, solar radiation pressure, and the gravitational influence of the Sun. Using the doubly averaged method, the disturbing potential applied to the Lagrange planetary equations is determined. With the doubly averaged method, quasi-heliotropic orbits are viable around the asteroid 2000 TW60. Furthermore, simulations of non-averaged dynamics were conducted, comparing the effects on the orbit both with and without shadow considerations. These findings have significant implications for understanding orbital dynamics around asteroid 2000 TW60 and may contribute to future space missions in the region.