Solving for Keplers 3 laws

January 10,2012

• Using your Orbit of Mercury -------- you need to apply Kepler’s 3 laws of planetary motion…and write up in word your proof

• You need to prove :• 1- the orbit is an ellipse ---not a circle. • 2- that for equal periods of time planets

“sweep” out equal areas• 3 – that the square of the period of orbit(yrs)

is equal t o the cube of the semi major axis (AU’S). Remember 1 AU = 10 CM

Kepler's Three Laws can be used to describe the motion of the Planets:

1. Planets move in orbits that are ellipses 2. The planets move such that the line between the Sun

and the Planet sweeps out the same area in the same area in the same time no matter where in the orbit.

3. The square of the period of the orbit of a planet is proportional to the mean distance from the Sun cubed.

Law #1 Planets move in orbits that are ellipses

Examine your orbit of Mercury and prove the first law correct:

• Major axis = minor axis • Eccentricity = 0• 2 foci—a circle has 1 focus

Law #2

• The planets move such that the line between the Sun and the Planet sweeps out the same area in the same area in the same time no matter where in the orbit.

If CD and AB represent the same period of time then….

Area I = Area II

• LAW 2: A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time