## Practice with Calculations - Part I - Kepler's Third Law

The appendices at the back of your textbook have a lot of useful information, including reviews of simple problem solving. Read through them if you need to brush up on topics such as units or scientific notation.

These practice calculations should be completed before noon on Thursday February 8, 2018. More practice exercises will be posted soon after that. Be sure to aim for organization, accuracy, neatness, and clarity in your work.

1. Kepler's third law says that the value of a3 / P2 is the same for all objects orbiting the Sun. (a) What is the value of a3 / P2 for the Earth? (b) Use the Saturn data on page A-10 (Table E-2) at the back of your textbook to calculate a3 / P2 for that planet and show that your answer is the same number as the answer to part (a).

2. The signature below is that of Clyde Tombaugh, who discovered Pluto in 1930. If Pluto is, on average, 39.48 AU from the Sun, then how many years does Pluto need to orbit the Sun once, according to Kepler's third law? How does your answer compare to the period for Pluto given on page A-10 at the back of your textbook?

3. There are records of Comet Halley (shown below) going back thousands of years. If this object orbits the Sun once every 76 years, what is the average distance between the Sun and the comet?

4. Kepler's laws also hold for objects other than the planets orbiting the Sun and for units other than AU and years. Consider the three Galilean moons of Jupiter listed below. Verify Kepler's third law by calculating a3 / P2 for each object, using the data provided. Select any combination of units, but use the same ones for all calculations. Note that your values of a3 / P2 will not be the same as that of the Earth!

• Europa: a = 409,300 miles = 6.587 x 108 meters and P = 3.55 days = 306,700 sec
• Ganymede: a = 653,000 miles = 1.051 x 109 meters and P = 7.15 days = 617,760 sec
• Callisto: a = 1,149,000 miles = 1.848 x 109 meters and P = 16.69 days = 1,442,000 sec

• Pages maintained by Dr. Reggie Hudson
• Last changed: February 1, 2018