To calculate orbits in the applet, we first assume some analytic
gravitational potential for the galaxy. The potential used is the
general logarithmic potential:
In this potential, rc represents a "core radius" and q
represents the flattening of the potential on the y axis. For example,
rc = 0 gives the singular logarithmic potential, and q = 1 gives a round
potential. Smaller values of q give more flattened potentials. In
models where the central black hole is turned on, there is an
additional acceleration provided by a black hole of mass M = 0.01 and
gravitational softening epsilon = 0.01.
We calculate the gravitational acceleration from:
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We integrate orbits using a 4th order Runge-Kutta integrator. Because
the RK timestep gets smaller when the potential gradient gets larger,
it takes more calculation time to follow the orbit when the star is
close to the center of the galaxy (particularly in the singular model,
or a model with a black hole). Because of this increase in computing
time, the star appears to slow down when it passes through the center.
Realize that this is only due to the longer computing time; in reality,
the star actually speeds up when it passes near the center, since the
accelerations are large.
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