Originally posted by ThinkingHuman
It says that the elongation is due, not to gravity by itself, but to the difference between gravity and centrifugal force. Those two forces are equal
in size at the center but their amounts are, at the closest and furthest points, different from each other - but in opposite directions. Therefore the
This makes sense but even the line you pointed out does not address what I said, that the earth is not subject to centrifugal force with regards to
the Moon. Only the Moon is subject to centrifugal force relative to earth because it is in earth's orbit.
Earth should not experience elongation, at least not because of a difference between gravity and centrifugal forces.
TH: I haven't had time to sit down and compose a lengthy response, between near 16 hour shifts at work and feeling like warmed over dog poo due to
this bronchitis (at least I gave it to the military staff - take that! Sounds like a TB ward in the hangar now).
Since I haven't, here's the short form answer: I think I see it from your viewpoint - you see the Earth as being motionless and the Moon falling
around it, so there ought not be centripetal force acting on the Earth. (centrifugal forces are illusory)
However, that's not true, exactly. Another thought experiment. Say you have two bodies. One very very massive, say a star, and one comparatively
small, say Mercury. From an outside viewpoint, Mercury seems to go around the Sun and the Sun seems to sit there. Now, replay it with two bodies of
the same size. What orbits what? Does one sit still and the other go around it? Which is still and which moves? What chooses that?
The truth is, that's not what happens. In any two body orbital system, BOTH orbit each other
. There is a "still place" that they both orbit
about, the location of that is somewhere on a radial line between the two centers of mass. Celestial mechanics calls this the "barycenter". In the
Earth-Moon system, the barycenter of orbit is not the center of the Earth, it's somewhere between, but due to the mass difference, it's still
somewhere inside the Earth, IIRC.
nice link with pictures and math
BTW, this is how astronomers "detect planets" around distant stars. They can't resolve them directly with a telescope, but you can spot the stars
orbiting around their barycenters as the planets go around. The star is actually moving back and forth a bit as it orbits a point inside itself. This
motion causes very tiny Doppler shifts in the spectrum of the star. If you analyze this with some neat math tricks (Fourier, primarily) you can pick
out the various influences on the star's motion, and through magic, you can pick out how many planets and about what size they are.
18-1-2013 by Bedlam because: (no reason given)