Harry Veeder wrote:
Consider the situation far from any planets or stars.
If the ball-bearing is initially at the centre of the shell it will remain
there. If it is initially off centre, the ball bearing and the shell will
move so as to minimize the distance between the point on the shell that was
initially closest to the ball bearing.
This is my prediction. It does not violate conservation of momentum,
but it is not based on Newton's or Einstein's conception of gravity.
I haven't worked it out, but I think a force going as 1/r^3 would have
that effect. Actually any rate of falloff faster than 1/r^2 should do
that, I think.
But ... the fact that Mercury's orbit precesses as it does is evidence
that "real" gravity around a spherically symmetric object doesn't
actually fall off as 1/r^2 (falls off a bit faster, IIRC), which makes
me wonder whether "real" gravity would also show that effect, albeit
weakly (my "proof" using the Ricci tensor notwithstanding ... among
other things I assumed a massless ball bearing, which is a little wrong).
Harry
