Let's fantasize that the Earth changes in a non-rotating ball of water. And let's assume the only gravitational influences on it are those of the Sun and Moon.

What will happen to the form of the ball?

Will the form of the ball, for example, elongate (spaghettify) along the Earth-Moon axis (because of the tidal forces) while rotating in sync with the rotation of Moon around the CM of both? Because the direction of the developing elongation (if this happens, which I think will because there is no solid Earth to stop it) is rotating, the (much less strong) gravitational influence of the Sun on the rotating water will contribute to the elongation of the water as well as to a change in the form perpendicular to the elongation of the water.

So there are three contributions which will superimpose: 1) An elongation of the ball due to the tidal force between the Earth and the Moon an elongation.
2) An elongation due to the Sun's gravity if the long axis of the elongation is parallel to the line connecting the center of the elongation and the center of the Sun.
3) A broadening of the elongation, also caused by the Sun's gravitation, if the long axis of the elongation is perpendicular to the in 2) described line. If the elongation is between these two orientations there is a combined effect of elongation and broadening.

So is it fair to conclude: the ball of water elongates only along the line that connects the middle points of the Earth and the Moon until the water hits the Moon's surface after which the elongation rate fastens (because of the increase of the mass of the Moon). The thickness of the "spaghetti" decreases until the moment the last water falls on the Moon? A little bit (because of the relative weakness of the Sun's gravity) of the elongation is caused by the Sun. Also, the elongation broadens a tiny bit (when the elongation is tangent to the Earth's orbit in a maximum way and also when the elongation finds itself in a different orientation (but then the broadening becomes less, and the elongation bigger), so a kind of long slab (a little bit broader than high) will hit the surface of the Earth when taking the influence of the Sun in account. The Sun's influence is negligible compared to the Moon's influence so the ball transforms (by good approximation) as I wrote at the beginning of this Alinea.

So is my conclusion fair or am I missing something here?


marked as duplicate by sammy gerbil, John Rennie, Kyle Kanos, user191954, Jon Custer Nov 26 '18 at 15:17

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