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Andrew Blaikie

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2013

The // body problem (slash-slash) is the study of the gravitational interaction between 2 extended line masses. The topic of this thesis is the study of the planar // body problem, where the universe is restricted to a plane. The analysis is performed using completely classical methods. The potential and kinetic energies are derived in the center of mass frame using polar coordinates. The Euler-Lagrange equations are then used to write down the equations of motion. Geometric vectors are used to radically simplify the equations.

The equations of motion are shown to reduce to the planar /. body problem and the Newtonian 2 body problem in the appropriate limits. Three classes of periodic orbits are solved exactly and one class is believed to be stable. The Runge-Kutta-Fehlberg method is used to find numerical solutions for a given set of initial conditions using 64 digit precision. We describe a robust numerical mechanism to detect collisions before they occur. A GUI application automates the numerical processes.

Retrograde spin was observed to stabilize orbits while prograde spin destabilized orbits. Escape not possible in the Newtonian 2 body problem was observed in the planar // body problem. Using parameter space plots we found that the gravity gradient orbit generates a valley of stability around its theoretical curve.