An epicycle system for planets
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.
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.
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