# An epicycle system for planets

##### Demonstration

Simple models to show epicyclic and retrograde motion from an Earth centred view.

#### Apparatus and materials

Ball, large (7.5 cm diameter approximately)

Ball, small (2.5 cm diameter approximately)

#### Health & Safety and Technical notes

In procedure b make sure that parts cannot fly off and hit observers.

A suitable turntable for part c can be obtained from ASCOL, catalogue number P16-1000.

#### Procedure

a Hold the larger ball stationary in front of you to represent the fixed 'Earth'. Hold the small ball in your outstretched arm so that you can sweep it in a large arc vertically around the 'Earth' as centre. At the same time make your outstretched hand turn quickly around the wrist so that the ‘planet’ turns in a small circle as it moves in its large orbit.

b You can use a small electric motor assembly to represent the ‘planet’ moving in its epicycle. Sweep the whole assembly in a large vertical arc about the fixed ‘Earth’ whilst the motor drives the ‘planet’ in its small circle.

c The electric motor assembly can be mounted on a rotating turntable. If the turntable is rotated slowly by hand whilst the sphere on the electric motor assembly rotates, you can observe the epicyclic motion. The motor may be tilted a little.

#### Teaching notes

This model still fixes the Earth at the centre of the star sphere. The radius of that circle acts as an arm to carry, at its end, a small circle (an epicyle). A radius of that small circle carries a planet round its circumference at a steady rate while the arm of the large circle revolves at a smaller steady speed.

In this epicycle system for Jupiter, arm EA rotates around the Earth once in 12 years, while arm AJ carries the planet J round once in 365 days. The two motions combine to give the pattern below.

This experiment was safety-checked in July 2007