## Practice with Calculations - Part II - Kepler and Newton

Review the class, webpage, and textbook materials related to the work of Newton and Kepler, and then do the four exercises shown here. Try to comlete your work by 12:30 PM on Tuesday September 22, 2015 (before class). Aim for organization, accuracy, neatness, and clarity. Be sure to show your work (the various steps) if you would like credit on exams and so on for similar exercises. The information in the bonepile below may be useful.

• G = 6.67 x 10-11 m3 / (kg sec2)
• In general, (a3 / P2) = G(m1 + m2) / (4 π2).
• If "a" is in AU and "P" is in years then we usually write just (a3 / P2) = 1 solar mass.
1. Consider Ganymede, Jupiter's largest moon. Ganymede orbits Jupiter in 6.18 x 105 sec with a semi-major axis ("a") of about 1.05 x 109 meters. Use Kepler's third law, as revised by Newton, to calculate Jupiter's mass from this information.

2. The signature shown here is of James Christy, who discovered Charon, the largest satellite of Pluto. If Charon and Pluto are, on average, 1.90 x 107 meters apart and require 5.52 x 105 sec to orbit one another, then what is the combined mass of Pluto and Charon in kilograms?

3. Sirius and its stellar companion are separated by about 20 AU and orbit one another with a period of about 50 years. What is the combined mass of these two stars?

4. The star Procyon has a small stellar companion. These two objects are separated by about 15 AU and orbit one another with a period of about 41 years. What is the combined mass of these two stars? [Data from p. 450 of Burnham's Celestial Handbook.]

• Pages maintained by Dr. Reggie Hudson
• Last changed: September 19, 2015