Before I go and put the lecture onto this web page, I'll just give an outline on how to solve problems involving Kepler's 3rd Law.

Newton's version of Kepler's 3rd law: P²=[4 pi²/G (M₁+M₂)] a³ relates the period P and semimajor axis a of two objects in orbit--those two objects have masses M₁ and M₂

1. First, will you need to use Newton's version of Kepler's 3rd law? It's more complicated (involves pi and G) so avoid it if you can. You can just say P²=a³ if you can answer YES to the following three questions:
   • Is the object you're talking about in orbit around the Sun (a planet or comet or asteroid for example)?
   • Is the period P in units of years? If not, you can convert
   • Is the semimajor axis a in units of AU (astronomical units)? The conversion is that 150 million km is one AU
2. IF you are dealing with Kepler's form and not Newton's, and you met the 3 conditions in part 1), THEN you ca use the equation P²=a³.
   • If you KNOW the period P, and want to FIND OUT the semimajor axis a, then you can calculate P², and then take the cube root to find a. On a calculator, cube root is the same as raising a number to the 1/3 power, or 0.3333333 power.

   • If you KNOW the semimajor axis a and want to FIND OUT the period P, then first you calculate a³. Then you take the square root to find P.
3. IF you are dealing with Newton's form and not Kepler's, THEN you need to make sure that all your numbers are in the mks system of units.
   • The semimajor axis a should be in units of meters.
   • The period P should be in units of seconds.
   • The masses M₁ and M₂ should be in units of kg.
4. IF you are dealing with Newton's form and not Kepler's decide which variables you know (P, a, or M₁+M₂) and which you don't. Use algebra to solve the equation for the variable you don't know.
5. IF you are dealing with Newton's form, and one mass is much more than the other (say you are comparing the Sun and the Earth, or Jupiter and one of it's moons) then you should be able to ignore the lighter object.<