# Kepler's Second Law on ice

##### Demonstration

Demonstrating the law using air or carbon dioxide pucks – or an ice rink.

Air table

Air or CO2 puck

Light spring

Rope

#### Health & Safety

Take care when handling the glass plate.

If taking a class off site, follow your employer's procedures for off-site educational visits.

#### Procedure

a Tether the puck to the air table using a light spring.

b Project the puck across the surface so that it orbits the tether point. The elliptical path can be observed.

Alternatively, if the class is taken to an ice rink, a heavy student, representing the Sun, should be positioned firmly in the centre of the rink, holding a rope, the other end of which is held by another, lighter, student, who skates around the first. As the first student pulls the rope in, the second, the orbiting planet, will speed up.

#### Teaching notes

1 The change in speed as the puck orbits can be clearly seen and the areas traced out in equal times mapped out.

2 When the 'arm' from the Sun to an orbiting planet is long, the planet's speed is slower and the arm is short, the planet's speed is faster.

3 Starting with Mars, Kepler discovered that the orbital path of each planet is an ellipse with the Sun at one focus. The line from the Sun to any planet sweeps out equal areas in equal times. All the sectors shown have equal areas; the planetary orbits are much closer to circles in shape than in this figure. This is Kepler's Second Law.

4 If you mark the position of a planet once a month on its elliptical orbit, and draw radii from the Sun to those points, the areas of sectors between those radii are all equal. This demonstrates Kepler’s Second Law.

5 Later, Newton showed that Kepler's Second Law can be explained by a central gravitational force (directed towards the Sun) which goes as 1/r2, where r is the planet's average radius of orbit.