Talk:Tidal force

Why is the Weyl Tensor (or its simplification of differentiating Newton's force law equation) necessary?

Similar point: Some physicists, e.g., Richard Feynman in Lectures on Physics, vol 1, attribute the ocean bulge on the 'side' of the earth opposite the moon, to the centrifugal effect due to the rotation of the earth around the earth-moon center of mass. This seems to be a more cogent explanation than some mysterious 'cinching at the waist causes the the other parts to bulge' notion, especially where we are dealing with fluids rather than solids. Alternatively, a 'gravity warps the very fabric of space' argument may make some sense here.

Tidal forces causing the bulge on the other side

I'm surprised no one before Feynman seems to have suggested the obvious centrifugal force from the earth's orbit (one rotation per month) around the center of mass of the moon and the earth. Common geography texts and even encyclopedia britannica are missing this.

This centrifugal force is obviously most significant as it is what balances the gravitation pull from the moon. Without it the earth and moon would fall in on each other. I would think Newton took this into account in his 1686 paper?

It is the DIFFERENCE between this centrifugal force and the the moon's gravitational pull on any material object on the earth's surface that make up the tidal forces "ellipsoid" (similarly for the earth-sun "ellipsoid". From the average values that balance each other, the centrifugal force increases linearly with the distance from, and in a direction away from the earth-moon center of mass. The gravitational pull decreases as one over the square of the distance from the moon.

Centrifugal force not necessary

While convienient to ease explanation, centrifugal force (or rotation) is not necessary for tidal forces to occur. If the moon was falling "directly towards" earth, the tidal forces would also be felt. (Of course, as the two bodies come closer, tidal forces varies).

possible, but would the tidal effect on earh as is, be as strong without the centrifugical force? or am i missing the point here


Formula

(William M. Connolley 09:35, 27 Aug 2004 (UTC)) Having pondered this a bit, I don't think I believe the formula. Certainly the one on the page has a typo: its literally meaningless to have the formula immeadiately followed by "<< r". Also, dr is undefined. Check back to before it was TeX'd: a comma is now missing.

But also, I'm not sure the intended formula is accurate either. I think that if the outside grav field is:

a = GM/R^2

(a = acceleration; M mass of central body; R distance from) then the "tidal force" between the center and edge of a body radius r at diatance R is:

delta-a = GM ( 1/R^2 - 1/(R-r)^2)

which is then *approximately* equal to:

delta-a = GM ( 2/R^3 ) . r

if r << R (modulo a sign convention or two...).

A clear derivation can be found at fr:Discuter:Sphère de Hill.
Urhixidur 14:47, 2004 Aug 27 (UTC)

A look at the history shows an interesting migration in the formula over time, but it was never actually right; an extra factor of 2 got inserted early on. I rewrote most of the article, and I hope it's right now. Fpahl 21:24, 6 Oct 2004 (UTC)

I think the article needs to explain better why there is a force in two directions instead of simply adding together in one direction. --ShaunMacPherson 03:19, 17 Oct 2004 (UTC)

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