# Period of the Earth a long time ago

1. Apr 16, 2009

### Ai52487963

1. The problem statement, all variables and given/known data
Find the period of the Earth 540,000,000 years ago.

2. Relevant equations
$$\frac{dL}{dt} = -2/5 MR^2 \frac{2 \pi}{P^2} \frac{dP}{dT} = -2/5 MR^2 \frac{2 \pi}{P^2_{t}} \left(\frac{dP}{dT}\right)_t \par \left(\frac{dP}{dT}\right)_t = .0016 sec / century \par P_t = 24 hours$$

3. The attempt at a solution

$$\frac{dP}{P^2} = \left(\frac{dP}{dT}\right)_t \frac{1}{P^2} dt \par \left(\frac{dP}{dT}\right)_t \frac{1}{P^2_t} \Rightarrow \alpha \par \int^{then}_{now}\frac{dP}{P^2} = \alpha \int^{then}_{now} dt \par \Rightarrow -\frac{1}{P_{then}} + \frac{1}{P_{now}} = \alpha t_then \par P_{then} = \frac{1}{\frac{1}{P_{now}} - \alpha t_{then}}$$

The period I get for the Earth 540 million years ago, for some reason, is 1.11 days. It should be .90 (or, the inverse of my answer). Is my math ok? My units all check out, but my period is longer, not shorter.