[thedoc (OP)]

If the tides are caused by the gravity of the moon, why is there a high tide on the side of the Earth furthest from the moon as well as on the closest side?

Peter Conway

Asked by Peter Conway


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[Pmb]

The tidal force exerted on the earth causes a stretching effect on the earth. This causes the water to be pulled towards the moon on one side of the earth and pushed away from it on the other. This results in two bulges. As the earth turns each location on earth passes through the two bulges causing two tides.

[David Cooper]

Land barriers get in the way of that though and make it much more complicated, so it's really a case of oceans and seas sloshing around in resonance with the ideal pattern (for a landless globe that's all sea). The result is that in most places you get two high and low tides a day, though with times that vary from place to place far out of sync with the ideal case (when the two bumps would pass over), and in a few places there are four high and low tides a day instead of two, while in others there is only one high and low tide a day.

[Bored chemist]

pmb,
How does gravity push water away from the moon?

[A Davis]

I've never understood how there can be a high tide on each side of the earth, but I do know that the Sun also creates a tide some days they act in opposition and there's no tide at all. Never heard a satisfactory explanation.

[evan_au]

If you take a single large mass (say the Moon, which has a stronger tidal pull than the Sun due to its closer distance), the Moon's gravity effectively tugs on the center of Earth's mass, ie the center of the Earth follows an ideal elliptical orbit, and this point feels no tide.

• However, the point on Earth's surface closest to the Moon is closer than the center of the Earth, and feels a stronger pull than the center of the Earth, so water piles up higher there (a high tide).
  
• The point on Earth's surface farthest to the Moon is further away than the center of the Earth, and feels a weaker pull than the center of the Earth, so water piles up higher there (a high tide). Alternatively, it could be viewed as if centrifugal force "throws" the water outwards on the far side of the Earth.

Now, if you add a second mass (the Sun), which does not always line up with the Moon:

• When the Sun & Moon line up (Full Moon & New Moon), their tides add, leading to a very high tide.
  
• When the Sun & Moon are at 90 degrees apart in the sky (Half Moon), their tidal influences almost cancel, leading to a much reduced tidal range.
  
• At certain times of the year (near eclipses), the Sun, Moon & Earth line up in the same plane, and also when the Moon's elliptical orbit brings it particularly close to the Earth, the high tides are slightly higher than the monthly high tides - a "king tide".

[David Cooper]

That's close to it. If you think about every particle of the Earth trying to follow its own orbit round the sun, only a tiny proportion of them are going to be on the line of the orbit that the centre of the Earth follows. The rest want to do other things. The particles on the Earth nearest the sun are orbiting too slowly and want to behave as if they are at aphelion, so their natural course to follow would take them closer in towards the sun and away from the Earth (if the Earth's gravity wasn't holding them back). The particles on the opposite side of the Earth want to behave as if they are at perihelion, so their natural course to follow would be to take them further away from the sun and thereby away from the Earth too.

This same effect can rip comets apart, leaving a line of chunks like the Shoemaker-Levy remnants that slammed into Jupiter one after another.

[Pmb]

pmb,
How does gravity push water away from the moon?

That’s a great question. I may have interpreted this incorrectly. For the correct description see Newtonian Mechanics by A.P. French (1975) page 533. If you don’t have a copy of this textbook then you can download it from http://bookos-z1.org/book/2033048/a8c794

What I had in mind is different and it’s possible that I confused the two.

Consider a planet or radius R located at the origin of the (x, y, z) coordinate system.

At t = 0 let one object be released from rest at a location along the z-axis at a distance r1 > R. Let a object be released at the same time at a distance r2 > r1. Since r1 is closer to the center of the planet than r2 it will accelerate towards the center faster than r2. Therefore object 1 will accelerate away from object 2. An observer in freefall half way between them will see the objects accelerate away from him. This corresponds two the two particles being forced apart by inertial forces.

Calculation shows that the forces follow a 1/r^3 law. This is similar to how things are working on the earth in the gravitational field of the moon. The actual description is different and is described in French’s text. A good read but hard to understand in my opinion.

[bizerl]

I've always understood it as this:

On the near side of the Earth, the Moon's gravity is pulling the water away from the Earth so the bulge on the near side is the water that is being pulled towards the Moon more than the rest of the Earth.

On the far side, the Moon's gravity is pulling the Earth away from the water, so the bulge on the far side of the Earth is the water that isn't attracted to the moon as much as the rest of the Earth.

Then there's the sun...

And probably quantum somewhere...  []

[bizerl]

• The point on Earth's surface farthest to the Moon is further away than the center of the Earth, and feels a weaker pull than the center of the Earth, so water piles up higher there (a high tide). Alternatively, it could be viewed as if centrifugal force "throws" the water outwards on the far side of the Earth.

I was lead to believe that "centrifugal" was a dirty word in physics?

[Pmb]

• The point on Earth's surface farthest to the Moon is further away than the center of the Earth, and feels a weaker pull than the center of the Earth, so water piles up higher there (a high tide). Alternatively, it could be viewed as if centrifugal force "throws" the water outwards on the far side of the Earth.

I was lead to believe that "centrifugal" was a dirty word in physics?

Not at all. It's very important. More so in general relativity then elsewhere.

The centrifugal force is what's called an inertial force defined as any force which is proportional to the mass of the body.

See http://home.comcast.net/~peter.m.brown/gr/inertial_force.htm

[A Davis]

I think I understand now, so if I drew a perfect elipse representing the earths orbit around the Sun there would be a monthly ripple on the orbit towards and away from the sun every two weeks, does this effect show up in any other measurement say the earths gravity or astronomical measurement.

[David Cooper]

There's nothing that happens every two weeks that isn't happening all the time. The part of the Earth furthest from the sun is being forced to orbit faster than the course it's following should allow, but its attached to the rest of the Earth and can't move about much. The water on top of it there can move more easily though, so it lifts off slightly, and that's why you get a bulge in the sea there. On the opposite side the opposite applies: the part of the Earth there is being forced to orbit more slowly than the course it's following should allow, so it wants to fall more towards the sun. Again it can't move much, but the water floating around on top of it can, so you get a bulge there too.

[A Davis]

It does happen all the time and the calculaton is extremely complicated, I've found ten variables in the calculation already there may be more. I was hoping that someone would answer the questions I posed, but I have answered one of them for myself after calculating the shift in the earths center of mass towards the moon.

[David Cooper]

It struck me last night that I'd only half switched my brain on when posting in this thread, due to pressure of time - I dash through here once a day to see what's new and am always in a hurry to get offline as quickly as possible. What I said before applies to the smaller component of the tide, that part caused by the sun, but I completely forgot to look at the larger component of the tides involving the moon.

The Earth and moon go round each other to some degree, but the point on the line between them which they actually go round is contained within the Earth because the Earth is so much more massive than the moon - it's an 8000 mile diameter vs. a 2000 mile diameter, so that's a ratio of 4:1, with the ratio for the volumes and the apx. masses being 64:1. That means that at the point of balance between them should be about 1/64 of the way from the centre of the Earth to the centre of the Moon, so that'll be 1/64 of 250,000 miles which works out at 3906 miles - that's about a hundred miles below the Earth's surface (beneath the point nearest to the moon). It's doubtless more complicated than that, so feel free to correct these figures if you have better ones.

Importantly though, the Earth must go round this point, even if it's more of a wobble around it rather than what would normally count as an orbit. Again though, the movement of the Earth in carrying out this wobble is perpendicular to the direction to the moon, so again the water on the side nearest the moon will not be moving fast enough to maintain this orbit and will try to follow a different path from the Earth as a whole, leading it to try to fall away slightly from the Earth, while the water on the far side will be moving too fast to maintain this orbit and will try to lift away outwards as a result.

I'm not convinced this explanation for either component of the tide is really any better than the one that says it's down to gravity pulling the water nearest the sun/moon more strongly towards it and pulling the Earth towards it more strongly than the water on the far side [I'll call this the second explanation] - it seems to me that they're just different ways of describing the same thing, with one of them (the second) being declared to be wrong when it may actually be equally correct. After all, if you started with just the moon and Earth in stationary positions about 250,000 miles apart and with neither of them rotating, the water on the Earth nearest to the moon would accelerate more quickly towards the moon and the water on the far side least quickly, so the same bulges would occur through the mechanism described by the second explanation. The first explanation may appear to apply better if you start them off in orbit around each other such that they stay roughly the same distance apart all the time, but it's really the same mechanism with a sideways movement component added in to confuse the issue, thereby leading to more complex explanations being brought in while the simplest explanation is then regarded as wrong, and yet the simplest explanation (the second one) looks as if it is still correct. So I think I've been misled by experts into rejecting it in the past, and now I'm putting it back at the top of my list for explanations of this phenomenon. It's still not the whole story, of course, because continents block the progress of these bumps of water and lead to the tides being completely out of time with these alignments in many locations as the oscillations work their way around seas and oceans, out by six hours in just as many places as it's on time, but the essential driving force which inputs energy into those oscillations will still be the simple one of the second expanation.

[evan_au]

While force of gravity follows an inverse square law with distance, the tidal force follows an inverse cube law with distance (being the difference of two points on an inverse square law curve).

This results in the Moon producing a higher tide than the Sun, due to its closer distance.
This is despite the fact that the Sun exerts a much stronger gravitational force on the Earth than the Moon does.

[David Cooper]

Thanks - that's a good link. It also agrees that the simplest explanation in this case is indeed the right one.

[thedoc (OP)]

We discussed this question on our  show



Dominic - Tides certainly are caused by the gravity of the moon which is always pulling the Earth very gently towards the moon. Now, the side of the Earth which is faced directly towards the moon is slightly closer to the moon from the middle of the earth. That means it feels a slightly stronger pull because gravity decreases with distance from the moon. And so, that's being pulled more strongly towards the moon and so, you can understand why you get a high tide there. Water is being pulled there more strongly towards the moon.



Now, on the far side, the pull towards the moon is weaker than anywhere else on the Earth, just because it’s further away from the moon. And that means the moon is pulling down on that water on the far side less strongly than elsewhere. And so, it rises up away from the moon in the opposite direction from the moon to form this second high tide. So, you've got two, one on either opposite side of the Earth.



Chris - As the planet turns, it’s turning through both of those bulges of water, so you get high tide number 1, then it takes 12 hours to get round to the other side which is half a rotation, half a day, and there's the second bulge, second high tide.



Dominic - Exactly, so. Those two bulges stay in the same place in space more or less on the line through the Earth to the moon, and the Earth is rotating once every 24 hours, so we move through one of those two bulges every 12 hours as you say.



Chris - And just very briefly, Dominic, the difference between a spring and a neap tide. How does that happen and why?



Dominic - The sun also produces tides. They're about half the strength of the lunar tides. So, that's another signal on top of the lunar tides and sometimes the sun and moon tides coincide and sometimes they don't. They coincide at full moon and new moon, and then you have tides which can be 30%, 40% higher than at other times of the month when the moon and the sun are ninety degrees apart in the sky when you have what are called neap tides which are much lower.



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[Colmik]

Evan-au said "the center of the Earth follows an ideal elliptical orbit", but that's not quite true.  The Earth and moon are tied together into a system by gravity, and it is the centre of mass of that system that goes around the sun in a smooth orbit.  Well, if you want to be sniffy about it, there are lots of other influences on this system, and the highest tides of all occur when the Earth, Sun, and all planets are in a line - but that doesn't happen often.  However, ignoring these lesser influences and concentrating on the Earth-moon system, it is the centre of mass of the system that orbits the sun, not the centre of the Earth.  I believe that the centre of mass of the system is, in fact, inside the Earth, but not at its centre.  If the moon is directly over the UK, then the UK is closer to the centre of mass of the Earth-moon than New Zealand is, and whether "centrifugal" is a dirty word or not, it is helpful to think of water close to New Zealand as being thrown out by centrifugal force.

Think of a Scotsman throwing the hammer in the highland games - he is twirling around with the hammer (an iron ball on a chain) being thrown out in front of him, but he is also leaning backward to counter-balance it - and his kilt is being thrown out behind him.  The hammer is one tide, and his kilt is the other.

Incidentally, as every yachtsman knows, the Spring Tides occur about 3 days after new moon and full moon - not on the day itself.

[Bill]

Chris and Dominic seem to be saying the high tides are close to the moon and opposite the moon.  That way of thinking of it is just wrong.  If it were true, then high tides would occur simultaneously along lines of longitude, but in fact they don't.  Have a look at this: http://www.seafriends.org.nz/oceano/tides.htm