#TITLE_ALTERNATIVE# - PUSPITARINI (NIM: 10305002), LUCKY
Our solar system is a complex and fascinating dynamical system. One of among the examples is a phenomenon relating to a restricted three-body problem. If two bodies in the system is circular, coplanar orbits about their common centre of mass and the mass of the third body is too small to affect the motion of the other two bodies, the problem of the motion of the third body is called the circular-restricted-three-body problem. Phenomenon in our solar system that can be explained by the theory of restricted three-body problem is Earth's co-orbital asteroid, which the asteroid is in 1:1 mean motion resonance with Earth. Extensive studies of co-orbital asteroids have been done since the discovery of Jupiter's Trojans and then Janus-Epimetheus in Saturnian system. Nowadays, there are more than 1000 Trojans in the outer solar system. This leads to discoveries of co-orbital asteroids in the vicinities of terrestrial planets (Venus, Earth, and Mars). In the last decade, stabilities of co-orbital asteroids have become an important and interesting topic for investigation. In this Final Project, the motions and the stabilities co-orbital asteroids are explained by using the theory of restricted three-body problem. Data of Earth's co-orbital asteroids were obtained from the JPL-NASA Small-body Database in June 9th 2008, of which were selected with criteria of high accuracy orbit fit quality and orbit boundary of 1/100 AU from Earth. There were 21 asteroids that fulfill the criteria. Moreover, to understand the trend of their orbital stabilities, integrations of their orbital elements are done through 1000 years -forward and -backward from the epoch (MJD 54600 or May 14th 2008) by including other terrestrial planets and Jupiter as gravitational perturber bodies. The integrations were done by using the MERCURY packet program with Burlisch-Stoer method. The results of the first integration show that at least seven asteroids have coorbital motions. Investigations to more longer integration time of 50000 years -forward and -backward, show that almost all asteroids have co-orbital motions (about 90%), which qualitatively, showing different kinds of stabilities.