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Tidal Acceleration and planetary rotation 
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#1
Jun714, 08:09 AM

P: 8

I'm struggling to get my head around tidal acceleration. I get what is IS, I know how to calculate it, but what I'm not sure is how to apply it in a way that's meaningful to me.
So. If we took a stationary Earth (i.e. non rotating, tidelocked) and have the moon magically appear in orbit and applying the moon's ≈1.1e06N tidal acceleraton, how would I work out what effect that has on the rotation speed (and thus period) of the Earth? For, example, how would I calculate how long it would take for the Earth to become tidelocked to the moon (because that'd be the stable endpoint, yes?) Or how long a day would be some time period (say, 4 billion years) after the moon appeared? 


#2
Jun714, 09:35 AM

P: 561

Can you show how you derived that number for tidal acceleration?



#3
Jun714, 10:08 AM

P: 8

##a=GM\frac{d}{R^3}##
where a = tidal acceleration, G is the gravitational constant (6.67384e11), d is the diameter of the distorted body (in this case Earth, 2*6371000m), M is the mass of the distorting body (in this case the moon, 7.347E+22kg) and R is the distance between the two bodies (384399000m). (It is only a firstorder equation, as I understand, but sufficent to my purposes.) I calculated the numbers via spreadsheet, which gave me 1.09996E06N I also found this page, which gave consistent results (and in fact made me realise my spreadsheet have missed G being to the E11...!) (I could use the more complex equation on the linked page for greater accuracy  and may do later, but for the moment, firstorder is enough for me to get a handle on the numbers.) 


#4
Jun714, 10:36 AM

P: 486

Tidal Acceleration and planetary rotation



#5
Jun714, 10:46 AM

P: 8

I'm guessing there's no easy way to make an estimate of that without some significant mathamatical (or computer) modelling, is there? I'd ask if we know what the rate is for Earth, but I assume it would be different for a nonrotating Earth, yes? (During my reading around astrophysics these last few weeks, I saw something on tidal locking that said Earth would eventually become tidelocked to the moon, albeit on a timescale past the end of the life of the sun, which I why I thought it might be possible to estimate.) 


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