The animation results from a set of coupled ordinary differential equations that are solved numerically using the fourth-order Runge-Kutta method.

Large spacetime curvature makes approximations used to calculate small precessions, like the precession of Mercury's orbit, inappropriate. Precession angles are calculated, after changes of variable that remove singularities at the endpoints of the integration interval, using Simpson's rule for numerical integration.

Speeds necessary to achieve given precession angles are calculated using the method of bisection. Each iteration of the bisection routine uses the Simpson's rule routine employed to calculate precession angles.

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