NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Global oceanic tides,
From: Trevor Kenchington
Date: 2003 Aug 24, 13:48 -0300
From: Trevor Kenchington
Date: 2003 Aug 24, 13:48 -0300
Eppo Kooi wrote: > My simple understanding is that the centres of gravities of both earth > and moon, disregarding the sun, should remain at unchanged distances. > Therefore, when the moon pulls the water mass to one side of the earth, > it has to be compensated such that the centre of gravity remains > unchanged. That can be obtained by having an equal displacement of water > on the opposite side of the earth. I do recall that that opposite mass > is not precisely of the same shape, due to land masses disturbing the > equilibrium. > I am sure there is a lot more to it, but the prime reason suffices for > most people, I guess. If it was a matter of "has to be compensated", we would have to suppose that every water droplet in the ocean acted in concert with one another and with the solid parts of the Earth. That just doesn't happen. To put it in fairly simple principles: Any moving object maintains its course and speed unless acted on by some force. That is one of Newton's laws but it is also the law that takes charge when you round your boat up into the wind and she carries her way past your mooring buoy and right into the boat on the next mooring to windward! Despite that basic principle, the Earth and Moon rotate around one another instead of flying off into space. (Actually, they both rotate around a common centre which lies 2430 nautical miles below the surface of the Earth.) They maintain this rotation because the force of gravity pulls them together. It acts as a "centripetal force". However, by another of Newton's laws, every action has an equal and opposite reaction. (Trying jumping from your small boat onto your yacht and you'll find that the little one moves away, leaving you to fall in the water between -- at least that is what I achieved one night. Newton's laws really do work.) In the case of a centripetal force, we call the opposite one the "centrifugal force". Try tying a knot in the end of a piece of rope and whirling it around your head. You will feel the centrifugal force pulling on your hand. The knot is pulled by the centripetal force which is equal and opposite to the centrifugal. So for the Earth/Moon system to remain in balance, gravity must pull the two bodies together, while a centrifugal force tries to whirl them apart. At the centres of mass of the two bodies, those forces are equal but opposite in direction. Now, the pull of gravity (as most of us learnt in high school) varies with the square of the distance between two objects. However, it turns out that the difference between the pull of gravity and the pull of the centrifugal force depends on the cube of the distance (as George has noted). So, although the side of the Earth towards the Moon is not a whole lot closer to it than is the side away (some 8,000 miles for the diameter of the Earth, versus some 500,000 to the Moon -- unless I have that number way off), the difference in the cubes of those distances is quite substantial. As a result, although the centripetal and centrifugal forces are exactly balanced at the centre of the Earth, the gravitational pull of the Moon exceeds the centrifugal force when the Moon is overhead (at your zenith), whereas the centrifugal exceeds the centripetal when the Moon is at your nadir. It turns out (through a bunch of math that I have never tried to understand) that those local, vertical forces are exactly equal, though opposite in direction. Those forces are, however, quite small. If you stood still on a hot, tropical night with the Moon directly overhead, the tidal effect would reduce your apparent weight by an amount equal to the weight of the bead of sweat that ran down your face and dripped off your nose. That much force wouldn't do anything much for the tides. However, when the Moon is 45 degrees off your zenith or your nadir, the imbalance between centrifugal and centripetal forces has a significant horizontal component. It is that sideways pull, sliding water across the surface rather than trying to lift it, which primarily drives the ocean tides. Again, if the Moon is 45 degrees off the zenith, water is pulled towards the geographic position of the Moon by centripetal forces exceeding centrifugal. If it is 45 degrees off the nadir, the excess centrifugal force pulls water towards the antipode of the Moon's geographic position. The forces are, once more, equal and opposite. And so we seen semi-diurnal tides. Eppo also mentioned land masses disturbing "equilibrium". That is a common misunderstanding or perhaps half truth. My above explanation deals with tide generating forces and, if the water were free to respond, it would produce Newtonian tides that looked like two watery hills, rotating around the globe once per lunar day (ignoring for now the effect of the solar tides). It has been clear for over 200 years, however, that no such hills would appear, even in the absence of land and with a uniformly-deep ocean. (The hills would act as waves and yet would be so long that they would progress as shallow-water waves, like tsunamis or like wind waves approaching a beach. Shallow water waves run at a speed set by water depth and the ocean just isn't deep enough for any wave to get around the world in 24 hours.) What really happens is that the tide generating forces excite natural oscillations in the ocean basins, with basins of different shapes and sizes oscillating at different frequencies. Hence we see such oddities as the tides at the Magdalen islands being very small and strictly diurnal when a hundred miles due south the Bay of Fundy has almost perfectly semi-diurnal tides with the greatest amplitude of any on the planet. The Gulf of St.Lawrence oscillates with one pattern, with a null point near its centre, where the Magdalen Islands lie, whereas the waters in the Bay of Fundy follow a quite different oscillation, even though the pull of the Moon on each of them is almost indistinguishable. So ... semi-diurnal tide generating forces predominate but not all tides are semi-diurnal. The forces pull the water towards a point directly under the Moon and towards the antipode of that point but high water does not necessarily happen when the Moon is on your meridian. The complications are due less to land masses as to the shapes and depths of the sea. Yes, as Eppo noted, when it is high water where you are, it won't necessarily be either high or as high on the opposite side of the planet. But then again, it won't necessarily be either high or as high a dozen miles down the coast either. Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus