Re: Question on a Universal Gravitation problem

[Ken Caviness <caviness@SOUTHERN.EDU>]

"Paul O. Johnson" wrote:

> The point is much nearer to the moon.
>
> poj
>
> ----- Original Message -----
> From: "J. Manor" <jmanor@REMC4.K12.MI.US>
> To: <PHYS-L@lists.nau.edu>
> Sent: Tuesday, April 23, 2002 12:15 PM
> Subject: Question on a Universal Gravitation problem
>
> > Can you help me explain this:
> >
> > Somewhere between the earth and moon, gravity on a space pad would
> > cancel.  Is this location nearer the earth or the moon?
> >
> > Thank You,
> > JoAnn Flejszar


There is a place on a straight line between the earth and the moon where the
gravitational force on any object due to the moon is equal and opposite to
that due to the earth.  We can use Newton's "law" of universal gravitation, F
= G m1 m2 / r^2 and let the distance from the object to the earth be "d_earth"
and to the moon be "d_moon":

  F_due_to_earth = G m_obj m_earth / (d_earth)^2
  F_due_to_moon  = G m_obj m_moon / (d_moon)^2

Setting these equal to one another we find that

  m_earth / (d_earth)^2  = m_moon / (d_moon)^2

and so

  (d_moon)^2 / (d_earth)^2  = m_moon / m_earth =(approximately) 1/81

So

  d_moon/d_earth =(approximately) square root of (1/81) = 1/9

So the point to put the object is 1/10 of the way from the moon to the earth.
Then its distance to the earth is 9 times greater than its distance to the
moon.  The earth-moon distance is about a quarter of a million miles
(250,000), so you should be about 25,000 miles away from the moon.  Very
roughly speaking.


But keep in mind that gravity is not "cancelled".  An object which stayed at
this position is still caught in earth's gravitational field and would be
orbiting the earth, as the moon does.  Also it is in the gravitational well of
the sun and of the galaxy, etc., etc.

Cheers,
Ken