# How does the gravitational force cause the motion of planets?

In antiquity the planets (the name comes from the fact that they seem to wander across the sky) were assumed to have circular orbits. In order to account for the observations, their motion was thought to involve circles attached to other circles. In between 1600 and 1605 Johannes Kepler (1571–1630) made careful studies of the observations of Mars made by Tycho Brahe (1546–1601). He found that a circular path required Tycho’s observations to be wrong by 2 minutes of arc (four times the apparent size of the moon), but he knew that Tycho’s work was better than that. After some 40 failed attempts he finally discovered that the orbit could be described as an ellipse. We now know an ellipse fits the orbits of all planets, comets, and other bodies about the sun, as well as satellites about planets. The shape of the orbit is called Kepler’s First Law.

An ellipse is not a circle, so the gravitational force of the sun is not always perpendicular to the motion. Therefore the planet’s speed changes as it moves around its orbit. Kepler’s Second Law says that in equal times planets sweep out equal areas. Thus if the planet is closer to the sun, it will move faster than it does when it is farther away.

Kepler’s Third Law was actually obtained in 1595 and was based primarily on philosophical and theological arguments. It stated that the relative sizes of the orbits of planets around the sun could be obtained by nesting the five Platonic solids: the cube, tetrahedron, dodecahedron, icosahedron, and octahedron. The planets’ orbits were in the spheres that circumscribed each solid. Today we state this law as the square of the period of the planet is proportional to the cube of the radius of the orbit. The proportionality constant depends on the mass of the object about which the orbit occurs and the universal gravitational constant. The law summarizes two of the properties of orbits of planets or satellites about a central star or planet.

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