Why doesn't the moon leave earth's orbit?

Sorry for interrupting but i am having trouble with this inverse square law and units.

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The gravitational pull of the sun on the moon is slightly more than twice the earth's pull on the moon(Newton's gravitational Law).
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If i use the inverse square law for earth/moon i get:
(4000/240000) * 32 ft/sec acceleration = 0.53 ft/sec acc.

And for sun/moon i get:
(425000/93000000) * 896 ft/sec acceleration = 4 ft/sec acc.

this is a lot more than twice the earths pull - how?

a beginner - cheers

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[kingdavid]
If i use the inverse square law for earth/moon i get:
(4000/240000) * 32 ft/sec acceleration = 0.53 ft/sec acc.

And for sun/moon i get:
(425000/93000000) * 896 ft/sec acceleration = 4 ft/sec acc.

this is a lot more than twice the earths pull - how?
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It is called the inverse SQUARE law because you have to use the SQUARE of the ratio of the two radii, not the ratio itself.

____(4000/240000)^2 * 32 = 0.0088
(425000/93000000)^2 * 896 = 0.0187
_________________^
(note exponent added to your equations)

As you can see Sol's pull actually is about twice that of Earth's.

You may also notice that I've removed all units from these equations, rather than using the correct units as I normally do. I did this to focus your attention on the reason you got the wrong answer. (There is a coincidental similarity between the numerical problem and the units problem that might cause further confusion.)

We can work on getting the units right later, if you are interested.

Regards,
LB

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It is called the inverse SQUARE law because you have to use the SQUARE of the ratio of the two radii, not the ratio itself.
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Excellent! Thanks very much for pointing this out to me - its been baffling me for a long time and yet its been right in front of me the whole time.

This also answers a lot of other questions I have been wanting to ask to do with moons that should not have an atmosphere but clearly do.

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We can work on getting the units right later, if you are interested.
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I would appreciate this. My maths is ok but when it comes to complex formulae and strange symbols, you will have to be patient with me as I only have a college teaching in this area and the rest I have taught myself.

P.S. Please forgive my delayed responses as I can only gain access to the internet via public library.

Cheers

David