Abstract: This talk is on dynamics of solar system, we show strong evidences that an alien planet once invaded our solar system. There is a long unsolved mystery concerning a group of asteroids called Jupiter Trojans. Mathematically, there are two symmetric relative equilibrium points for the Sun-Jupiter system, L4 and L5. However, there is a large difference in numbers of observed asteroids: L4 has 60% more than L5. We theorized that this asymmetry is caused by an invasion of alien planet, we computed the necessary parameters for the invading alien planet to cause such an asymmetry. It is quite amazing and surprising to us that these exact parameters perfectly solved another mystery in solar system. The Hildas are a group of a few thousands of asteroids locked in a 3-2 resonance with Jupiter. The very strange thing is that none of the Hildas has small eccentricity. The invading alien planet explains this and perfectly matches with the observations.
This is a joint work with Jian Li, Nanjing University.