earth-moon rotation

[Legion]

I was looking into the 'two tides' (why do we have two tides a day) question and came across the fact that we are a double planet, earth and moon rotating about a common centre, but how fast is this rotation?

[Chuck]

One month, apparently.

[Legion.]

Really, Why must this overall rotation be the same as the orbit of the moon?

[jadesmar]

I am not sure about "must" but, I presume that this is why the same side of the moon always faces the earth.

Instead of the reason that the moon has phases.

Or, that could be backward.

[Leptonn]

You are correct that the earth and moon are a two-body system, however, the centre-of-mass (about which both seen to rotate) is much closer to the earth than to the moon, so the moon pretty much follows a circular orbit around the earth.

As to the two tides, here is a picture:

It doesn't show exactly what I want, but never mind. Consider the moon being in the "full" position, and the earth rotating underneath it. Nearest the moon, the sea is "pulled" towards the moon with full intensity, while the middle of the earth is pulled with moderate intensity, and the opposite side is pulled with low intensity. Over the course of a day, we move from the side nearest the moon (high tides) to moonset (low tides) to the side opposite the moon (high tides) to the moonrise (low tides) and back to the start. However, the tides drag a little bit, so the tides aren't *quite* full at high moon.

Seems weird, but this is how it works.

Chuck is right... the moon goes around the earth in one month. I think it's actually 29.7 days or something like that.

The same side of the moon always faces the earth for the same reason that the tides drag a bit behind the moon. It's called merely "Tidal Forces". Eventually, the same side of the earth will always face the moon, too. The moon has phases because it goes around the earth and gets shined on by the sun from different angles.

[Legion]

I'm happy with the part about always seeing the same face of the moon, it's all synchronised after ages, but I'm not sure about the system rotation vs moon orbit vs earth rotation timings. I can't really picture it.

[Samadhi]

Yes the moon and the earth are orbitting around a common center. All orbitting bodies do this. In the case of huge differences in mass, like the Earth and the sun, the center of rotation is not significantly different from the center of the more massive body.

When two bodies orbit each other gravity produces a tidal force on each. Basically the part of the object closest to the center of mass is rotating slower than the part of the object furthest from the center of mass. This produces a stretching along the axis. This causes bulges on the sides closest to and furthest away from the center of mass.

All orbitting bodies tend to become tidally locked. But in the case of the larger of the two, there is generally some axial rotation (but tidal forces slow this down...our days are getting longer). In this case the "bulge" rotates around the surface of the object with the bulges on the inner and outer face. Since the Earth has fluid over most of it's surface this can be seen easily in the form of high and low tides.

[Dr. Borodog]

Everyone else has essentially already said anything interesting, but since I like to pontificate, I shall.

If you were to look down on the Earth from out in space, up above the north pole, you would see the earth rotating (relative to the fixed stars) counter-clockwise, once a day (the actual length of time in hours, minutes, and seconds depends on whether you are measuring your days by the sun or the stars, but the difference is small, only about 4 minutes in 24 hours). You would see the moon orbiting the Earth with the same sense of rotation (counter-clockwise) in one month (again, the exact length depending on how you go about keeping your time). The moon rotates once about its axis, in the same sense again, over the exact same period of time, so that the same face always faces towards the center of its orbit. Try it with a basketball or the like; the demonstration will really help you picture the situation.

Now tides are really cool. As Samadhi explained, tides are caused by "tidal forces," which aren't really forces at all; they are the differences between real forces. Because the force due to gravity is inversely proportional to the square of the distance between two masses, the gravitation force exerted on the surface of the Earth nearest to the moon is stronger than the force exerted on the Earth's center, which is stronger than the force exerted on the surface that is opposite the moon.

Now, to understand how tides arise, you must picture a bowl or glass of water, or a lake, or whatever. The surface of the water is flat (unless there are waves, but we don't care about that. The surface of the water will always be perpendicular to the lines of gravitational force. If it wasn't, it would "slide down the hill" until it was. This basically acts to minimize the gravitational potential energy of the water (it would take energy to maintain a "hill" of water, so all the water that the "hill" was made out of flows "off" the hill until there isn't one and the water is flat).

You can see now why we must have tides. The gravitational force due to the Earth always points straight downward. If that were the only force, we'd a spherical planet. But it isn't; the Earth is rotating, which creates an equatorial bulge all the way around, which we'll ignore, and we have tides. The force of gravity due to the moon is small, and always points towards the moon. But it is greatest nearest to the moon, and smallest on the far side from the moon. The vector sum of the Earth's gravitational force and the moon's gravitational force is then non-uniform around the surface of the Earth, and leads to an elliptical shape:



In this diagram, the Earth's surface is the solid circle, the Earth's gravitational force are the long black vectors, the moon's gravitational force are the shorter red vectors, with the moon located to the right. You can see the vector sum is non-circular. The oceans will follow this shape (not quite; they actually lag behind slightly because of the water's inertia, but that's neither here nor there).

Because the tides rotates once per month with the moon, and the Earth rotates once per day, we see the seas rise and fall not once but twice a day, because there are two "bulges" in the water's surface.

[Dr. Borodog]

Hmm. I just realized that diagram doesn't make a damn bit of sense given my explanation. That elliptical shape is most definitely not perpendicular to the net force vectors in the upper and lower limbs.

Must think . . .

[Doc Borodog]

Ah. Of course the force vectors aren't perpendicular to the ellipse at their heads; they are perpendicular to the surface at their tails.

Whew.

[Coyote]

Ah yes, of course. *nods knowingly* Force vectors at the tail, not the head...yes, yes, I see.

Ahahahaha!!! This is all way too heavy for me, but you said something earlier that got the clanking gears turning for a bit:

[Samadhi]

Nope. That's a closed system.

[Coyote]

Hmmm...okay, but even in a closed system the energy can be distributed in different ways. The spin of the planet versus the tendency of the water to seek its own level could be converted into heat.

[note:] I already know that you and Dr. Dawg have a way better grasp of physics than I'll ever have, and that I'm almost certainly wrong here. But what I want to know is why I'm wrong. Revealing the errors in our thinking is a time-honored method of learning, you know.
_________________
Hard work may pay off in the long run, but laziness pays off right now.

[extropalopakettle]

[Samadhi]

Well, thanks for grouping me in the dr's class, but with a doctorate, I think he'd probably out physics me any day. For example, I will probably mix up things like force and work in any explanation I give.

I'm trying to think of a good way to alleviate your trouble, and I'm not thinking of anything good.

The only thing I can think of is to explain why the tidal force acts as a brake. Moving all that water around takes force and that force acts in an opposite direction to the force of the rotation. Just like a brake on a car (except that's friction, but anyway). You can picture the brake on a car as pushing the wheel in the opposite direction that it's moving. This slows it down. All that water on the Earth is part of the whole system here, or the wheel. The tidal action is pushing that part of the Earth in a direction opposite our rotation. This slows the Earth down because that water is part of the Earth.

What you're talking about isn't rotational at all. It's all moving towards the center. To decrease the rotational energy you need to have a force that acts opposite to it.

And I can't think of anything else. My brain is tired, sorry.

[Samadhi]

And extro is right, I missed that bit. Rotation doesn't put anything up any hill. An object X meters from the center of mass has Y potential energy regardless of whether the body is spinning or not. A satelite in a geosynchronous orbit has the same potential energy as a satelite that's spinning around the Earth furiously, if it is at the same height.

[Dr. Borodog]

[Samadhi]

Torque was the force I was looking for.

[Doc Borodog]

I know what you mean, but torque is not a force.

[Samadhi]

See, I told you I'd mix up terms.

[Vinny]

Here's a theoreotical question,

what if the Earth has 2 moons, of the exact same mass, and they behave exactly the same except opposite of each other in location, e.g. on one side of the earth while the other one is on the other side.

Would we not have tides at all then?

And what if the Earth has 2 moons, of different size, and in some weird non-synchronize patterns.

Would that mean the end of life of Earth?

[Doc Borodog]

[extropalopakettle]

What if the Earth had two moons of the same size, in the same orbits, but going in opposite directions, and they were perfectly hard solid moons, like those steel balls on those click clack thingies:

Would that be weird or what? Would we still call it Earth, or would it be "the Click Clack Planet"?

[Mackay]

I think extro's post is one of my favourite ever.