Chandramouli, Harini2020-10-262020-10-262020-08https://hdl.handle.net/11299/216900University of Minnesota Ph.D. dissertation. 2020. Major: Mathematics. Advisor: Richard McGehee. 1 computer file (PDF); xiii, 98 pages.The details of the way in which the Earth orbits the Sun can have profound effects on Earth’s climate. Elements such as the Earth’s tilt or how tight the orbit is can affect temperature distribution or glacial formation. One event that could lead to such changes is if a star passes near our solar system close enough to disturb Earth’s orbit. Over the Earth's 4.5 billion year history, many stars could have approached the Solar System. Disturbances that are forced due to such an event could have effects on the orbit of planets in the Solar System. Even small changes to the orbits of the planets can have large effects on the climate a planet experiences as they could disrupt the Milankovitch cycles. These effects would be visible in the Earth's sediment core data, which can be used to help model the Earth's position as it orbits the Sun. This work focuses on modeling the effects of a star passing within the Solar System on the eccentricity, semi-major axis, and argument of the periapsis. The changes to the Earth's climate due to the changes on those orbital elements are also considered. Here the focus is on what the system would look like if the star were to pass within Kuiper Belt and the Oort Cloud. Passage within the Kuiper Belt has can change the equilibrium temperature of the Earth up to $2^\circ$ C without even taking into consideration the interactions of the planets with each other on the climate. The position of a planet as the star passes has an effect on the system, giving different results for different initial conditions. This position is seen to lead to dramatic differences between the orbital elements for various solutions.enCelestial mechanicsDynamical systemsGeological recordMilankovitch cyclesOrbital elementsThesis or Dissertation