Orbit of a planet around the Sun

In this example you can plot the orbit of a planet around the Sun. The settings you can choose are the initial distance from the sun, and the initial radial and angular velocities. You can also vary the power law for the attractive force between the planet and the Sun.

The equation of motion for a planet around a fixed sun (a reasonable approximation if the sun is much bigger than the planets) is

where n is the power law for the radial force. In classical gravity this is given as n=-2, the initial setting for the programme. Here we can investigate other possibilities.

Work through the following. Where you are expected to do some calculations do them, showing the working! try and confirm Kepler's laws in the way indicated, giving your estimates for the periods of at least 4 orbits. Bonus marks for an elliptical orbit (you will have to work out the semi-major axis).

Investigate the following:

Note: If nothing seems to happen try reloading the page.

Don't forget that it is not wise to allow your planet to hit the sun!

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Oliver Kerr 9/11/98