3rd Kepler's law

[aphar]

I could never remember what was squared and what was cubed in the 3rd Kepler's law, I always had to derive it anew.

Now I finally have a mnemonic.

• Distance to the Moon is approximately 10 times the radius of the Geostationary orbit (which is just over the length of the equator)


• square root of 10 is just over 3


• 3 cubed is 27


• which is just under the lunar month (29.5 days)

So it's the semi-major axis cubed and period squared.

Comments

[brevi]

The centripetal acceleration is (v^2)/r and is proportional to the force which is 1/(r^2). Hence, assuming circular motion, (v^2)*r is the same for all planets of a given star.

[aphar]

right, that's what I used to do ...

[brevi]

I think it's easier to remember the principles than the relationships among the Earth's and the geostat radii and the distance to the Moon (cue in the joke about Einstein and Edison).

[aphar]

Yes, but I already remember both.