This applet enables one to examine online a simplified model of how the planets orbit the Sun and how the 4 major moons of Jupiter, called the "Galilean Satellites" orbit Jupiter.

Choosing the first option, "Show scale", provides a listing of the orbiters and a scale drawing showing their distances from the central object. To view another means of scaling the solar system, click here.

Choosing the second option, "Show orbits", displays the objects orbiting with their periods as given by Kepler's second (harmonic) law.

In the Seventeenth century, a German mathematician, Johannes Kepler, used the positions of the planets, as compiled from historical records and observed by the great Danish astronomer, Tycho Brahe, to propose 3 rules describing the motions of the planets as they orbit the Sun. His third rule related the period of a planet that orbits the Sun to its semi-major axis as folows:

Period in years = square root((semimajor-axis in AU)**3)

Later, the great English scientist, Sir Isaac Newton, derived Kepler's rules governing planetary motion from the basic laws of mechanics that he proposed, consisting of 3 laws of motion and the law of Universal Gravitation. He recognized that he had to modify Kepler's rule to include the mass of the 2 objects. For the planets orbiting the Sun, this makes only a small change to Kepler's rules since the planets have masses which are much less than the Sun's mass. Were the planets orbiting a star with M solar masses, the relationship would be approximately:

Period in years = square root((semimajor-axis in AU)**3/M)

This law can also be applied to moons orbiting planets. For a moon which is much smaller in mass than the planet it orbits at a distance, d, measured in Mkm (millions of km):

Period in days = square root ( 120 x d**3 x mass of Earth/mass of planet )

For our Moon, d = 0.384, giving a period = 28 days. For the moons of Jupiter, which has a mass 318 times the mass of Earth,

Period in days = 6.7 x square root(d**3)