Orbits of One Body around Another
Joachim Köppen Kiel/Strasbourg/Illkirch April 2001 ... July 2016

Some brief explanations

• This simulation shows the orbit of a body in an attractive radial potential, such as the gravitational field of a massive body.
• The force exponent specifies the potential: -2 for gravity or an attractive electrostatic field, +1 for the harmonic oscillator
• One gives the initial conditions, and clicks start. Then the trajectory for the time interval is shown, with the blue box denoting the start position and direction
• Clicking more shows the subsequent trajectory ...
• The time step determines the computational accuracy. Choosing it too large results in inaccurate, perhaps interesting but wrong results. Choosing it too small gives reliable results, but for reasons of computational economy only a short part of the orbit can be shown ...
• In a gravitational field (exponent = -2) the orbit shows a precession, i.e. the major axis of the orbit turns around the centre. This is a purely computational effect, since the precession rate depends on the chosen time step.
• But for exponents different from -2 the orbit shows a genuine precession, as the precession rate does not change when a sufficiently small time step is chosen.
• For exponents equal to -3 or smaller, the orbits get unstable. Even the circular orbit is difficult to keep on its track, with very small time steps.
• There are only two cases where the orbit has no true precession: exponent = -2 and +1.