calculating the distance of equal an opposite gravitational pull between the moon and earth

This problem has been annoying me for ages and I still haven't been
able to work it out. I am using the formula for universal garvitaional
force and I know it is a simultaneous equation but I can't get it to
work. Can anyone help.

Jason wrote:

This problem has been annoying me for ages and I still haven't been
able to work it out. I am using the formula for universal garvitaional
force and I know it is a simultaneous equation but I can't get it to
work. Can anyone help.

I know diddly about math, but I can tell you that there is a point where the
two gravitational pulls /plus the centrifugal force of the circular path/ (an
important consideration) balance out. It's called L-1 and is stationary wrt
Earth and moon. If this isn't something you already know about, plug "Lagrange
Points" into a search engine.

--


Regards,
Mike Combs
----------------------------------------------------------------------
We should ask, critically and with appeal to the numbers, whether the
best site for a growing advancing industrial society is Earth, the
Moon, Mars, some other planet, or somewhere else entirely.
Surprisingly, the answer will be inescapable - the best site is
"somewhere else entirely."

Gerard O'Neill - "The High Frontier"

JRS: In article , seen
in news:sci.space.tech, Jason posted at Fri,
10 Oct 2003 19:35:52 :-
This problem has been annoying me for ages and I still haven't been
able to work it out. I am using the formula for universal garvitaional
force and I know it is a simultaneous equation but I can't get it to
work. Can anyone help.

It need not be a simultaneous equation.

Let the Earth's mass be M, the moon's m, the separation R, and the
distance of the balance point from the moon be r.

Field balance is when Gm/r^2 = GM/(R-r)^2, i.e. Gm(R-r)^2 = GMr^2.

That is a simple quadratic. Since M/m ~ 81, to a first approximation
one can ignore r in (R-r) and get r = R/9.

If you want the Lagrange point L1, then the effects of rotation must be
included; see URL:http://www.merlyn.demon.co.uk/gravity3.htm#L15.

--
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