Physics Commons^™

Computing Periods Of Nonlinear Hamiltonian Systems In The Two-Body Problem Of Celestial Mechanics, Maia Powell

Ursidae: The Undergraduate Research Journal at the University of Northern Colorado

The two-body problem in celestial mechanics models the gravitational relationship between two celestial bodies and predicts their corresponding orbital paths. Isaac Newton proposed a two-body problem that accurately modeled systems whose rotating mass exhibited a perfectly elliptical orbit. Albert Einstein’s theory of general relativity expanded the original two-body problem to include systems with irregular orbits. Einstein’s model, a nonlinear Hamiltonian system, produces solutions that are elliptic functions. Though we know that elliptic solutions exist, their complexity makes them inaccessible. Current research explores potential properties of such irregular systems represented by Einstein’s model in an effort to better understand and predict …