U3AOS2 Topic 3: Orbital Motion

This chapter is basically the same as circular motion but with just a few extra things. First off we have the acceleration formula in the forms

$a = \frac{v^2}{r} = \frac{4\pi^2r}{T}$

T is the time it takes for 1 orbit.

Then similarly, the velocity equations are

$v = \frac{2\pi r}{T} = \sqrt{\frac{GM}{r}}$

The universal formula to solve for all variables in a orbital motion problem is described below. Since everything has to be balanced this relationship will hold true for all questions you will have.

$4\pi^2 r^3 = GMT^2$

If you have difficulty rearranging questions, it might be best to practice or write down the following forms for each variable.

A key relationship to remember is that if

$r \uparrow then T \uparrow but v \downarrow$

Most importantly, MASS DOES NOT AFFECT RADIUS OR PERIOD!!

Key Concept:

'zero gravity' is called free fall. It's when there is 0 normal force. This is because the ship and the astronaut are being accelerated at the same rate.