Astrophysics Research - Orbital Simulation

Research Experience for Undergraduates (REU)
University of Wisconsin at Milwaukee, summer 2002
Alethea Bair, University of Illinois, Urbana-Champaign
Alan Wiseman, University of Wisconsin, Milwaukee

Project Summary

Understanding the orbits of bodies around an extremely massive object, such as a black hole, is a fundamental problem in astrophysics. Depending on the conditions such as mass and spin of the black hole, and position and velocity of the orbiting body, a wide variety of orbits can be observed.

This project serves as a visual teaching tool for students learning the differences between Newtonian, Schwarzschild and Kerr approximations to particle orbits. It also includes an approximation to a 'radiation reaction' force.

Numerical integration of the equations of motion was tested for accuracy by calculating conservation of energy, angular momentum, and the 'Carter' constant. The orbiting body is assumed to be a 'test particle'; that is a particle without mass

Sample Orbits

Newtonian: If the force of gravity is assumed to be inversely proportional to distance, then orbits are eliptical.

Schwarzschild: However, the bending of space from massive objects causes a phenomena known as "procession of the perihelion". The perihelion is the major axis of an eliptical orbit, which 'precesses' meaning the axis rotates slightly with each successive orbit.

Schwarzschild: If the ellipse of the orbit is very long, then when the particle gets close to the black hole the precession is very strong. The 'glory effect' is a name for an orbit in which the particle is pulled in, spun very rapidly around the black hole at close range, and then spun out at a distance again.

Kerr: If the black hole is rapidly spinning, this also warps space, so that the particle is dragged in the direction of the spin. The following pictures show an example of this when the particle has a large velocity perpendicular to the spin direction. The first image is a side view, the second a top view.

Kerr: If the initial particle velocity isn't strong enough, the particle will be pulled in to the black hole.

Kerr: Finally, a phenomena exists called the "Lense-Thirring" effect. In this case, if the particle has a large velocity in the direction of the spin, and a small velocity perpindicular, it can oscillate vertically as it spins rapidly around the black hole.