Assignment task: When one of the objects is a lot bigger than the other, we can ignore the mass of the smaller object in the expression. For example, if we think about the Sun and the Earth (as shown in the illustration above), M1 = MSun = 1 solar mass and M2 = MEarth = 10-6 = 0.000001 solar masses. There's not much difference between M1 = 1 and M1 + M2 = 1.000001 (the second mass is just a "drop in the bucket"), so we can just use M1 , reducing the expression to
a3 = M1 P2 (only when one of the masses is bigger than the other!)
Let's consider Pluto, which has a mass of MPluto 10-10 solar masses. The Pluto-Sun orbit has a semi-major axis of a = 39.48 AU. Let's find the orbital period of Pluto using the expression above!
Q1. Which expression would we want to use to calculate the orbital period of Pluto? Why can we ignore the mass M2?
Q2. Find the orbital period of Pluto.
Q3. In your lifetime, how many times has Pluto gone around the Sun?