# [geocentrism] Tides

• From: Regner Trampedach <art@xxxxxxxxxxxxxx>
• To: geocentrism@xxxxxxxxxxxxx
• Date: Wed, 07 May 2008 15:18:40 +1000
 There has been a couple of references to tides, lately, and much confusion on the subject. I'll do what I can to clear it up a bit. Please take the time to read the whole post before commenting. The force of gravity moves objects The Moon and the Earth orbit each other due to their gravitational interaction. It can be shown that you can simplify this problem:    Every single bit of the Moon interacting gravitationally with every single    bit of the Earth. is exactly equivalent to    All the mass of the Moon being located at the centre-of-mass of the Moon,    and all the mass of the Earth being located at the centre-of-mass of the    Earth. From such an analysis we find that the two objects will orbit their common centre-of-mass in elliptical orbits. Tidal forces deform objects But the Earth and the Moon are extended objects so what effect does that have?  Well, the Moon is still close enough to the Earth, that the gravity from the Moon will change over the diameter of the Earth:     Moon                                Near     Centre     Far                                         side    of Earth    side       O                               <-------- <-------  <------   Okay, if we now subtract the part that actually moves the Earth, that is we subtract   <------- which is the same as adding ------->  to all three vectors (arrows) above, and we get the tidal forces:     Moon                                Near     Centre     Far                                         side    of Earth    side       O                                  <-         |        -> So looking at the Moon-Earth system from the outside we see that the Moon-side of Earth experience a larger gravitational pull from the Moon than the centre of the Earth, and the opposite side of Earth experience experience even less gravitational pull from the Moon. Seeing it from the Earth point of view, we have a Moon-ward force on the Moon-side of Earth and an opposite force on the opposite side of Earth. This is what causes the tidal bulge, and this is why there are (approximately) two high- and two low-tides a day. The oceans, being a liquid, obviously responds much stronger than the bedrock, but the Earth's crust is flexing too, as has been measured. The Earth rotates under this tidal bulge, which makes it a dynamical phenomenon.   The gravitational force is proportional to  1/r²  where r is the distance between the Earth and the Moon. The tidal force is the difference in gravitational force over a certain distance, which means it can be expressed as the r-derivative of the gravitational force. The tidal force is therefore proportional to  1/r³. That means the tidal force falls off more rapidly with distance than the gravitational force. This is the reason that the gravitational force of the Sun dominates the orbit of the Earth, but the Moon's tidal forces on Earth are larger than the Sun's.   The Sun also contributes a significant tide (about half that of the Moon) and when the two are aligned at new Moon or full Moon, we get more powerful tides called spring tides. At either half Moon we get neap tides. The ellipticity (eccentricity) of the Moon-Earth and the Sun-Earth orbits also causes variations in the strength of tides on Earth.   The Moon experience (about 22 times) stronger tides from the Earth because of the Earth/Moon mass ratio of 81 and the size ratio of 3.7. The Lunar tide from the Sun is 3.7 times weaker than here on Earth, due to the 3.7 times smaller diameter of the Moon. The tides would of course be exactly the same in a geocentric Universe. Allen's concerns in the "Acceleration thread" To account for tidal influences, the centre-of-mass of the test-mass of the accelerometer, should coincide with the centre-of-mass of the free- falling laboratory. Tides would have NO effect on such a set-up. But then the tidal effects on such a lab are very small in the first place: Less than a billionth per meter of the gravitational force keeping the lab AND the test-mass in orbit. That's all for now (sorry for such a long post), and I hope it clarified a few things.           - Regner