Assignment 6: Extra-Solar Planetary Systems and Kepler's 3rd Law of Planetary Motion

Due: in class on February 21, 2008

1. Visit the Marcy website, http://exoplanets.org/planets.shtml and find the orbital periods and sizes of the orbits of the planets for 55 Cnc (55 Cancri), the system with 5 planets (entries 87-91 in the table). Tabulate the orbital periods and orbital sizes for the planets.

2. Show that Kepler's 3rd Law of Planetary Motion holds for the planetary system chosen. To do so, express the orbital periods as multiples of the orbital period of the planet with the shortest period, and express the orbital sizes as multiples of the orbital size of the planet with the shortest orbital period, and then see if Kepler's 3rd Law of Planetary Motion in the form,

P² = a³

holds. Would Kepler's 3rd Law of Planetary Motion in the form above, P² = a³, have worked out if you had chosen to express P and a in terms of the properties of the Earth, that is, if you had measured the periods in years and the orbital sizes in astronomical units? Verify your answer.