User talk:Mukinduri

Your request for explanation about Tides
Hallo, Mukinduri, thanks for your recent edit of 'Tide', and your request for an explanation of the reason why the Moon causes (practically) equal outward tidal forces both on the side of the Earth facing the Moon and also on the opposite side.

At the moment, I am trying to put the pieces of the explanation together in a way that's going to be clear, without using too many words.

Some of the pieces of explanation are already around, but scattered and maybe not as clear as they could be.

While I'm still at work on it, you might be interested to look at some of the pieces.

In a nutshell:
 * The water on the Moon side of the Earth is closer to the Moon than the center of the Earth is. It gets pulled harder towards the Moon than the Moon's pull on the Earth. Net result, an outward tidal force on the water away from the Earth and towards the Moon.
 * The water on the side of the Earth farthest from the Moon is farther from the Moon than the center of the Earth is. It gets pulled less hard towards the Moon than the Moon's pull on the Earth. Net result, an outward tidal force on the water away from the Earth and away from the Moon (or you could look at it as the Earth getting pulled harder towards the Moon because it's closer, and away from the water on that side).

[1] John Wahr, "Earth Tides", Global Earth Physics, A Handbook of Physical Constants, AGU Reference Shelf, 1, pp. 40-46, 1995 (should normally be available at but they seem to be offline at present, hopefully it's temporary and not a case of a new address). On page 40 he says "The tidal acceleration is the part of the lunisolar gravitational acceleration that causes the ... earth tides. Its value at a point P" (which can be anywhere on the Earth's surface)  "is defined as the [total gravitational acceleration at P] minus [the acceleration of the Earth's center-of-mass]." Then in Figure 1b on page 41 he shows pictorially the result of this difference, and it comes out as two practically equal outward forces, both on the side towards the Moon and on the opposite side.

There's a similar definition in page 509 here, "The tidal force is the difference between the forces exerted by the [disturbing] planet on the two [other] bodies".

There must be plenty of other examples but those are two that I found.

Tidal force shows the result in a clear diagram rather like Fig. 1b in 'Wahr' (although the accompanying words in the wkp article do not seem wonderfully clear to me).

[2] The remaining questions include
 * a Why is it all about the difference of accelerative forces?
 * b Why is it about the Earth's centre of mass?
 * c How does it come out to be two outward forces, one on each side?

For an answer to question a, you might have a look at Lunar theory. Although this is about the Moon, the principles are the same, if you consider the Moon as just another movable object subject to a tidal force and disturbed in its motion relative to the Earth, as it is.

For an answer to question b, you might try two explanations why the center of attraction to or by a sphere is always to or by the center of mass:
 * A modern explanation using calculus is given at.
 * Newton's original explanation (1729 translation) using geometry is given at (the diagrams are on an unnumbered page after page 268).

(By the way, in a non-rotating frame of reference with a bunch of gravitating bodies, there are no centrifugal forces, only centripetal forces! On the rotating Earth, the outward 'centrifugal force' on the oceans is the same all the way round. In the mutual motions of the Earth and Moon, the forces are accounted for by their gravitational attractions via their centers, there are no 'extra' forces.)

For an answer to question c, the maths is actually not that hard:


 * The attractive gravitational acceleration towards the Moon of an object at distance D is Gm/D^2.
 * If the center of the Earth is at distance R from the Moon, and the radius of the Earth is r, then the acceleration towards the Moon of the center of the Earth is Gm/R^2, the acceleration of an object on the side facing the Moon is Gm/(R-r)^2, and the acceleration of an object on the other side away from the Moon is Gm/(R+r)^2.


 * So taking the necessary differences, the tidal perturbation (+ is towards the Moon) of the object on the side facing is


 * Gm/(R-r)^2 - Gm/R^2


 * and the the tidal perturbation (again + is towards the Moon) of the object on the remote side is


 * Gm/(R+r)^2 - Gm/R^2


 * You'll find that to order 1/R^3 these differences are equal and opposite, both 2Gmr/R^3, sign + for the object on the side facing, sign - on the side opposite, which means outward from the earth in each case.

I hope this helps. Comments are welcome. With good wishes, Terry0051 (talk) 00:47, 7 September 2009 (UTC)