[thedoc (OP)]

Judith Allport asked the Naked Scientists:
   
Can you please tell me why  when  a tide appears at the side of the earth due to the Moon's attraction another tide appears,  at the same time, on the opposite side?

What do you think?

[David Cooper]

The part of the Earth closest to the sun (including the water sitting on it) has a stronger gravitational pull on it than average, while the part of the Earth furthest from the sun has a weaker gravitational pull on it than the average, so the water nearest the sun is pulled up a bit towards the sun while the water furthest from the sun is not pulled towards the sun as strongly as the bulk of the Earth, so the rest of the Earth pulls sunwards away from it.

If you want to think about it another way, if there were two rocks sitting on the Earth with one on the point nearest the sun and the other on the point furthest from the sun, if the Earth then suddenly disappeared, two objects would fly on in different elliptical orbits with the inner object starting at aphelion for its orbit (meaning that it is at the furthest out part of its orbit, its speed being too low for it to be able to maintain the same course the Earth would have taken) and the outer object starting at perihelion for its orbit (meaning that it is at the closest in part of its orbit, its speed now being too high for it to continue on the path the Earth took).

The Earth's gravity is too strong for the water to escape, but in more extreme cases the difference in the strength of gravity can tear objects to pieces, as can be seen with some comets when they get too close to the sun, and black holes can strip almost anything apart.

There is much more to tides than two bumps on opposite sides of the Earth though, because continents get in the way and prevent the pattern form being so neat. In many places the tides are out by a full six hours, and this is because what we really see are oscillations in large bodies of water which resonate in time with the moon "passing overhead". In some places there are four tides a day instead of two, while in others there is only one tide a day because we are dealing with resonations rather than more simple pulls up and down.

[PmbPhy]

The part of the Earth closest to the sun (including the water sitting on it) has a stronger gravitational pull on it than average, while the part of the Earth furthest from the sun has a weaker gravitational pull on it than the average, so the water nearest the sun is pulled up a bit towards the sun while the water furthest from the sun is not pulled towards the sun as strongly as the bulk of the Earth, so the rest of the Earth pulls sunwards away from it.....

That's a beautiful explanation, David.

I'd like to add that what you just described are known as tidal forces. The mathematical object that's used to describe this is what is known in Newtonian gravity as a tidal force tensor. I derived a description of the tidal force tensor in non-relativistic mechanics here:
http://home.comcast.net/~peter.m.brown/mech/tidal_force_tensor.htm

In general relativity the effect is known as geodesic deviation which means that all the particles that make up the earth are trying to move along different geodesics, i.e. the geodesics deviate. For this reason its held that spacetime has an impact on spacetime itself. The mathematical object that describes geodesic deviation is the Riemann tensor also known as the tidal force tensor. This is obviously and over loading of the term tidal force tensor. However this is a common fact throughout math and physics. For example, there are three different meanings of momentum in physics, two from classical physics and one from quantum physics. The two from classical mechanics is the regular linear momentum that people are familiar with, i.e. p = mv and a similar one from relativity known as 4-momentum which is similar to 3-momentum but is defined for a 4-dimensional space.

The Riemann tensor is the 4-dimensional tensor which is the 4-dimensional version of the Newtonian today force tensor.

[Bored chemist]

The part of the Earth closest to the sun (including the water sitting on it) has a stronger gravitational pull on it than average, while the part of the Earth furthest from the sun has a weaker gravitational pull on it than the average, so the water nearest the sun is pulled up a bit towards the sun while the water furthest from the sun is not pulled towards the sun as strongly as the bulk of the Earth, so the rest of the Earth pulls sunwards away from it.

If you want to think about it another way, if there were two rocks sitting on the Earth with one on the point nearest the sun and the other on the point furthest from the sun, if the Earth then suddenly disappeared, two objects would fly on in different elliptical orbits with the inner object starting at aphelion for its orbit (meaning that it is at the furthest out part of its orbit, its speed being too low for it to be able to maintain the same course the Earth would have taken) and the outer object starting at perihelion for its orbit (meaning that it is at the closest in part of its orbit, its speed now being too high for it to continue on the path the Earth took).

The Earth's gravity is too strong for the water to escape, but in more extreme cases the difference in the strength of gravity can tear objects to pieces, as can be seen with some comets when they get too close to the sun, and black holes can strip almost anything apart.

There is much more to tides than two bumps on opposite sides of the Earth though, because continents get in the way and prevent the pattern form being so neat. In many places the tides are out by a full six hours, and this is because what we really see are oscillations in large bodies of water which resonate in time with the moon "passing overhead". In some places there are four tides a day instead of two, while in others there is only one tide a day because we are dealing with resonations rather than more simple pulls up and down.

A fine explanation in many ways, but given that the thread is about the Moon, and you only mentioned it once...

[David Cooper]

A fine explanation in many ways, but given that the thread is about the Moon, and you only mentioned it once...

Good point - I lost track of where I was taking it. That certainly applied more directly to the sun's influence on the tides which is outgunned by the pull from the moon, but in principle it's the same thing with the moon: anything on the side of the Earth nearest the moon will naturally try to follow an "orbit" round the moon which would take it closer to it while anything on the side furthest from the moon would try to follow an "orbit" which would take it further from it, though this is disguised by the relative lack of the moon's mass compared to the Earth's which results in the centre of mass of the two being inside the Earth. What I was trying to do with this description was push thing in the direction of an understanding that fits with Einstein's kind of gravity where there is no pulling force involved but where things simply follow geodesics instead. The first explanation I gave is more compatible with the idea of a pulling force.