# I How to calculate day length of a tidelocked double planet?

1. May 17, 2016

### AotrsCommander

Quick question: what's the calculation required for working out the day length (i.e. rotational period) of a double planet, where both planets are tidelocked to each other? Do just need to make adjustments to Kepler's Third?

I've got a spread sheet set up to allow me to calculate orbital periods via Kepler's Third, but I'm not sure what adjustments (if any) I need to make to the equation for double planets orbiting each other or whether this is even the right formula to use in this instance (i.e for rotational period of the two bodies.)

Currently set up for calcualtions as follows for orbital periods:

${T^2}=4π\frac{r^3}{G(M1+M2)}$

(Assuming circular orbits, because that's a good enough abstraction for what I'm doing.)

I am half-thinking that I don't need to do anything and that time for the rotatation period is equal to the orbital period, but I would appreciate a confirmation.

(Secondary question, more hypothetically, if they weren't tide-locked, what equation would you use?)

2. May 17, 2016

### DaveC426913

Of course. If the planets are tidally locked, their rotation periods are equal to their revolution period.

3. May 17, 2016

### AotrsCommander

Right, thanks. (It's been a few months since I last looked at the this, so I wasn't entirely sure.)