Hypothetical planet in the asteroid belt: An undergraduate exercise in celestial mechanics

We report results from numerical integrations of Solar System orbit for 100 mega years (Myr) from current epoch to the future with the integrator package EVORB. The model of the Solar System for asteroid belt region that previous researchers have proposed is reviewed in this paper. The previous results were very promising, up to more than 70% of the simulated cases have succeeded in removing terrestrial planets reside in the asteroid belt, region between the orbit of planet Mars and Jupiter. This is very close to the currently observed fact that massive objects no longer inhabit the asteroid belt region. We, therefore, simulated the presence of a massive object with a mass of the planet Mars at the current location of the dwarf planet Ceres (model02). The simulation results are compared with a Solar System model that excludes the presence of a hypothetical planet in the asteroid belt (model01). We found no significant difference in the orbital evolution of the Earth. At least for the next 100 Myr, Earth will remain a habitable planet. This computational laboratory activity provided an excellent case study for our upper-level undergraduate students in celestial mechanics course as their research project.