In 1601 the German astronomer Johannes Kepler became director of the Prague Observatory....

In 1601 the German astronomer Johannes Kepler became director of the Prague Observatory. Kepler had been helping Tycho Brahe in collecting 13 years of observations on the relative motion of the planet Mars. By 1609 Kepler had formulated his first two laws:

i. Each planet moves on an ellipse with the sun at one focus.

ii. For each planet, the line from the sun to the planet sweeps out equal areas in equal times.

Kepler spent many years verifying these laws and formulating a third law, which relates the planets’ orbital periods and mean distances from the sun.

a. Plot the period time T versus the mean distance r using the following updated observational data.

b. Assuming a relationship of the form

T = Cr_a

determine the parameters C and a by plotting ln T versus ln r . Does the model seem reasonable? Try to formulate Kepler’s third law.