Illustration of an elliptical orbit
Three methods of visualising elliptical orbits.
Apparatus and materials
Retort stand with rod and clamp, or tripod
Small steel ball approximately 5 mm diameter, or a marble
Large glass funnel at least 20 cm diameter
Steel ball approximately 3 mm diameter
Toy hoop or embroidery frame
Retort stand, rods, clamps, boss head
Alpha-particle scattering analogue apparatus
Health & Safety and Technical notes
For method b, stretch the rubber sheeting over the rigid horizontal circular frame and secure it tightly with tape. It should be stretched a little, equally in all directions.
Fix a vertical metal rod over the sheet so that it is pushing the sheet into a curved well, thus imitating, roughly, an inverse-square-force potential.
For method c, the apparatus is available from a number of suppliers (Philip Harris, Griffin Education, ASCOL), see Alpha particles scattering analogue (plastic hill and ramp).
a Firmly hold the glass funnel vertically and let the ball fall into it. Friction will affect the orbit and make it precess, but the motion around the funnel will be elliptic. Select a ball which will fall right through the funnel.
b Project the small steel ball across the sheet. By choosing suitable initial conditions the ball can be made to describe an oval like an ellipse with one focus on the axis of the well.
c Balance the plastic or aluminium hill upside down. Wood blocks can be used to hold it in position. Project the ball across the inverted hill so that it will orbit the centre. The elliptical path will be visible.
1 Method a is not a true representation of Kepler's Second Law. The ball starts in a circular orbit, but it gradually moves lower in the funnel because of friction and so the time for a circular orbit gets smaller. The orbit also precesses as a result of friction.
2 Method c uses a valley with a 1/r profile. This corresponds to a 1/r2 force of gravitational attraction and so will closely model the movement of a satellite around a larger mass.