C[omp]ute

From: "andrew cooke" <andrew@...>

Date: Thu, 26 Jan 2006 12:16:33 -0300 (CLST)

My take on this question - http://ask.metafilter.com/mefi/31481

In very simple terms, only the mass "inside where you are" generates
gravity.  If you go deep into the earth, gravity would change just as you
would expect for a planet of the size that corresponded to having a
surface where you were (assuming the earth were solid etc).

So going down 1000 miles you'd feel a gravity similar to an "earth" that
had a radius 1000 miles smaller.

Now it seems to me that what the question is asking is - what happens if
we move some of the earth's mass to outside the moon, and everything else
stays the same?

If so, then the answer is probably obvious - the moon would behave as it
would if the earth had a smaller mass (the mass left in the new, smaller
planet).

Exactly what would this behaviour be?

First of all, it would continue to orbit the sun.

Second, relative to the earth, I think (and I'm guesing - I'd need to do
the maths, or at least think harder, to be sure, and I'm in a hurry) that
the orbital period would increase (more time between full moons) and the
average earth-moon distance would increase.

Exactly how the earth-moon distance would increase depends on the way the
weight is lost.  If it were lost rapidly then the moon would end up in an
eliptical orbit, with the closest point being the same as now.  If it were
lost gradually, I suspect you'd keep a circular orbit.

An intereesting consequence of the changing period is that the moon would
not necessarily continue to spin so that we always see the same side of
the moon.  Again, this probably depends on the rate of loss of mass.  If
mass were lost very slowly from the earth tidal interactions might keep
the moon "facing us".

However, something that makes me think I may be wrong above.  I'd also
expect the earth's orbit around the sun to change, with years becoming
longer and the earth-sun distance increasing.  That's from the same
arguments (potential energy decreases, kinetic stays the same) as I used
to think about the moon/earth relationship.

Now that sounds OK.  But I *also* thought that various (? at least one?)
asteroid belts coresponded to the positions of old, "broken" planets. 
This seems to be inconsistent with the argument above.

So something seems incorrect.

Andrew