# Homework Help: Moon's evolution backward in time

1. Sep 11, 2012

### buzz3

1. The problem statement, all variables and given/known data
Extrapolate the evolution of the Moon's orbit backwards in time. Use conservation of angular momentum for the Earth-Moon system to derive a variant of eq. 1. You may neglect solar tides in your calculations, but comment qualitatively on their effects. Assume that kt1/Q1 has remained constant and use the data on fossil bivalve shells to determine the value of the constant. state your result in the form a2(t), where a2 is in units of earth radii and t is in Gyr before present. As tidal evolution was much more rapid when the bodies were closer, your result should imply that the Moon was quite close to the Earth substantially less than 4 Gyrs ago. This was considered a major problem until it was realized that a substantial fraction of the tidal dissipation in Earth today results from sloshing of waters in shallow seas, and that kt1/Q1 could have been much less in the past when Earth's continents were configured differently.

2. Relevant equations
eq. 1 (see attachment 'modeleq'):

t_impact = (2/39)*(m1/m2)*(Q1/kt1)*(a2^(13/2){0} -1)/n1

other potentially useful equations (see attchment 'extraeq'):
(2.18) is an angular momentum equation
(2.44a) is the rate that tides transport angular momentum between planetary rotation and satellite orbits
(2.44b) is the expansion/contraction rate of low-eccentricity orbit of satellite

sign(x) = 1 if x >0 and = -1 if x <0

3. The attempt at a solution

I don't even know where to begin really... I'm guessing something like 2.44b would need to be integrated wrt time??? If so, how is the sign function treated??

Solar tides - I assume they would have constructive/destructive periodic effects...?

Bivalve shell fossils... I don't know where that came from, I've found nothing in the text about this...

I'm at a loss, any help is appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

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• ###### extraeq.jpg
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