Orbits of One Body around Another

Joachim Köppen Kiel/Strasbourg/Illkirch April 2001 ... July 2016

- 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.