Let's do some order of magnitude and scaling exercises related to the 2 body nd problem! ot bhas t i yeoar arbit what isthe sma ofa 1 year orbi boutnr how about an o star? 2. consider the planet found around proxima centauri that has been described as near or in the "habitable zone". in the hz, the temperature of the planet should allow for liquid water. for our purposes, let's say this means that the flux it receives is comparable to that received by earth from the sun. the proxima centauri planet has a period of 11.2 days, and proxima centauri has a mass of mpc0.12mo. (a) compare the gravitational force that the pc planet feels to that felt by earth? (b) if the flux received is in fact pc comparable to that on earth, how must stellar luminosity scale with mass to reproduce this result? 3. we've extended our study of orbits to two bodies. when is it a good idea to use the two body formulation (i. e. the reduced mass / total mass) vs the 1 body formulation? come up with a criterion to decide whether a given system requires the use of the two body formulation. your criterion should depend on the properties of the objects and the orbit.