# Earth-Moon system

I was just reading up some stuff about tides. Kind of figured this thingie out, hope my understanding is correct

The earth and moon both have ellipsoid orbits (Kepler Laws ;)) and have the orbits in such a fashion that for the earth’s orbit, the moon forms a focus and for the moon’s orbit the earth forms a focus. This is essentially because both the moon and the earth gravitationally attract each other which are contrary to what I previously believed that the earth had the moon revolving around its center and the earth spinning on its axis.
Since this is the case we will have on the far side of the earth, I.e the side not facing the moon, having tides because of centrifugal force and the lunar side having tides because of gravity of the moon, thus we have gravity of the moon and earth (assuming now that here centrifugal force and gravity is interchangeable, as in case of low velocities and distances) causing tides.
Here I come to pause now to regard to questions which come to my mind
1. Doesn’t this now become a binary system similar to the Pluto charon duplet?
2. Is the moon’s gravity large enough to affect the earth’s rotation? Would the earth have had an ellipsoid rotation had the moon not been there?

D H
Staff Emeritus
Any two bodies will orbit each other about their center of mass. When one is a lot more massive than the other (the Sun versus the Earth), it looks like only one is moving. Kepler's laws implicitly assume the Sun is stationary, which is only approximately true. The center of mass of the Sun and Jupiter is outside the Sun's surface, which is why the error in Kepler's laws is at its worst with Jupiter.

You don't need centrifugal force to explain orbits or tides. It is far better to explain both without invoking centrifugal force at all. Here is an easy way to think of it, without math. The side of the Earth facing the Moon is a bit closer to the Moon than is the Earth as a whole, so the water on the near side of the Earth accelerates a bit more toward the Moon than does the Earth as a whole. The result: A bulge on the near side. The side of the Earth away from the Moon is a bit further from the Moon than is the Earth as a whole, so the water on the near side of the Earth accelerates a bit less toward the Moon than does the Earth as a whole. The result: A bulge on the far side.

Ha thats fine,

my question was is the earth moon system a binary one by nature and also would the orbital velocity of earth change if we take the moon out of the picture?

The side of the Earth facing the Moon is a bit closer to the Moon than is the Earth as a whole, so the water on the near side of the Earth accelerates a bit more toward the Moon than does the Earth as a whole. The result: A bulge on the near side. The side of the Earth away from the Moon is a bit further from the Moon than is the Earth as a whole, so the water on the near side of the Earth accelerates a bit less toward the Moon than does the Earth as a whole. The result: A bulge on the far side.
Thanks, D.H. This is a good explanation of why we have two tides per day. There is a lot of energy disspiated by the tides. Does this energy come primarily from the rotational energy of the Earth about its axis, or from the Earth -moon binary system (does the moon get closer)?

Yes, that was a very good explanation DH. I've always thought of it that way myself so I'm glad to know that my reasoning is correct. The Earth and moon are in a state of constant acceleration toward each other (orbiting). So we observe the same difference in accelerations from the near side to the far side of the earth as we would if the two were not in orbit and simply on a crash course toward each other.

I thought that the tides were caused by centrifugal force too until recently. its easier to think in terms of the tides on the moon due to the earth. imagine that the moon wasnt rotating at all relative to the stars. the centrifugal force due to its motion around the earth would be the same at every point on its equator. but the gravity from the earth would be different at different points. hence tides.

the rotation of the moon only results in a uniform bulge everywhere on its equator and so is irrelevant.

Ha thats fine,

my question was is the earth moon system a binary one by nature and also would the orbital velocity of earth change if we take the moon out of the picture?
Your original post contained an error that seems to affect your reasoning for this question as well. The elliptical orbit of the Earth is around the Sun, not the Moon, i.e. the Sun is at one focus of the ellipse, not the Moon. The Moon would be at the focus of an elliptical orbit only for something orbiting it, like a satellite.

In fact, the approximation of an elliptical orbit for the Earth applies only if you think of the Sun and Earth as the only objects involved. As soon as you add the Moon into the picture, you have a three-body problem (Sun, Earth, & Moon), and elliptical orbits don't really apply.

So, technically, the Earth's orbit would change (hence, its velocity would as well) if the Moon weren't there, but its approximate elliptical orbit would not change, since that approximation ignores the Moon in the first place.

I really don't understand what you mean by all this, but there are a few points that seem to indicate a misconception or two.

First, a note: "rotation" generally refers to an object spinning about an axis through its center of mass, so the Earth rotates once every 24 hours. "Revolution" is what an object does in its orbit, i.e. the angular motion about a separate central body, so the Earth revolves in its orbit once every 356.25 days. The moon revolves in its orbit once every 28 days or so, and as it happens, it also rotates at that rate, which is causes the same side of the moon to face us at all times.
I thought that the tides were caused by centrifugal force too until recently.
I don't get what centrifugal force you are thinking about. The Moon's orbiting around the Earth does not cause any centrifugal force on the Earth - only the Earth's rotation can do that.
its easier to think in terms of the tides on the moon due to the earth. imagine that the moon wasnt rotating at all relative to the stars. the centrifugal force due to its motion around the earth would be the same at every point on its equator. but the gravity from the earth would be different at different points. hence tides.

the rotation of the moon only results in a uniform bulge everywhere on its equator and so is irrelevant.
What tides on the Moon? There's not a lot of water up there ....

There is no "uniform bulge everywhere on its equator" for the Moon; it is very nearly perfectly spherical. While the Earth is not perfectly spherical, the tides we're talking about are not uniform around the equator (as D H explained).

Maybe you're actually referring the ellipsoidal shape of the Earth, but that's not a tidal effect and has nothing to do with the Moon; it is in fact due to the Earth's rotation, so you could appeal to centrifugal forces to explain that.

the earth orbits the earth-moon center of mass.

the moon has tides whether it has water or not.

the equatorial bulge on the moon would be much smaller than the earths since it only rotates once per month and its radius is less than the earths.

and I know that the tides are not uniform everywhere on the equator. that was my point.

the earth orbits the earth-moon center of mass.
Quite true!
the moon has tides whether it has water or not.
Well, maybe we're arguing semantics, but I would say that the Moon experiences tidal forces. "Tides" generally refers to the changes in surface height of bodies of water, which are the result of tidal forces.

the equatorial bulge on the moon would be much smaller than the earths since it only rotates once per month and its radius is less than the earths.
True - and that explains the nearly spherical shape I mentioned. But this has nothing to do with tidal forces, right? It's a matter of the Moon's rotational motion and has nothing to do with the Earth, or the Moon's revolution about the Earth.
and I know that the tides are not uniform everywhere on the equator. that was my point.
I'm still missing your point ... so the "uniform bulge everywhere on its equator" referred to the Moon, then? Not much of a bulge, there ... and the tides that are not uniform everywhere (ref. above) - those are on the Earth? But they have nothing to do with the Moon's rotation, so ..... ??

This is what I'm still not getting:

"imagine that the moon wasnt rotating at all relative to the stars. the centrifugal force due to its motion around the earth would be the same at every point on its equator. but the gravity from the earth would be different at different points. hence tides."

How is the centrifugal force the same at every point on its equator? It should be greater on the far side than on the near side, right? Are you comparing the centrifugal force (linear in r) to the Earth's gravitational force (inverse square of r)? Is that the point? I'm just not following your line of reasoning; it could be correct, I just don't follow it.

you are picturing the moon as always facing the earth. which it does. but in my post I said to imagine that it wasnt rotating at all relative to the stars. in that case the centrifugal force due to its motion around the earth-moon center of mass will be the same at every point on its equator.

the moon has rock tides. (they're tiny)

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the moon has rock tides.
It does??!! I had never heard of that before! What causes their motion?

tidal forces

tidal forces
Ha ha!! Now you're messing with me!

Do you really mean that the variations in the Earth's gravity from one location to another on the Moon cause rocks to move across its surface?!! You'll have to provide some evidence for that before I'll believe it! I'll admit that I wish it were true - how cool would it be to see rocks sliding around on the Moon due to tidal effects?

Now, if you tell me that meteorites' trajectories are deflected in such a way as to create more debris on the nearest and farthest sides, then maybe I'll buy that. Maybe even that the trajectories of debris created by impact are affected in the same way ... but you'd still have to convince me that the effects are sufficient to cause a measurable difference.

no. rocks dont move across its surface. its surface moves up and down very slightly. just like ocean tides on earth only much much smaller.

What?? Why up and down? Wave motion?

The variations in the tides on the Earth are due to the difference between the Moon's orbital period and the Earth's rotational period (as well as the Solar year), but since the Moon's orbital and rotational periods are the same, shouldn't these effects have settled out into a steady state long ago?

ah. you are right. you caught me sleeping. the moon always faces the earth so doesnt have tides like the earth does.

it does shift back and forth slightly and that does cause moonquakes but that is pretty negligible. (its pretty substantial on IO though)

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ah. you are right. you caught me sleeping. the moon always faces the earth so doesnt have tides like the earth does.

it does shift back and forth slightly and that does cause moonquakes but that is pretty negligible.
Ah, yes - the oscillation that causes the face we see to vary around the edges slightly - that one I've heard of ...

A great surf of Moon rocks crashing about on its surface ... sadly, no - and we are all the poorer for it.

D H
Staff Emeritus
Google solid body tides, or earth tides.

They aren't tiny. They are about 30% of the height ocean tides (Hint: The Earth's K2 Love number is 0.3).

Both the Earth tides and ocean tides affect a satellite's orbit. Even though Earth tides are smaller in magnitude than the ocean tides, the affect of the Earth tides dominate over the affect of the ocean tides vehicles. The reason is simple: The Earth tides affect the entire Earth. The ocean tides, just a very thin layer on the surface of the Earth.

Well, darn my sox! I never knew that ...

granpa said:
ah. you are right. you caught me sleeping. the moon always faces the earth so doesnt have tides like the earth does.
No, the moon doesn't have tides like the Earth but it is/was affected by the Earths tidal forces. That's the reason for the moons bulge.
http://physics.fortlewis.edu/astronomy/astronomy%20today/chaisson/AT308/HTML/AT30803.HTM [Broken]

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The variations in the tides on the Earth are due to the difference between the Moon's orbital period and the Earth's rotational period (as well as the Solar year), but since the Moon's orbital and rotational periods are the same, shouldn't these effects have settled out into a steady state long ago?
Correct. The Moon cannot have tides, because the same side always faces the Earth. Maybe it has a "bump" (a stationary rock tide). But it is reasonable to expect that in the beginning, it had spin. The dissipative nature of Moon tides (rock tides?) probably stopped the Moon's rotation relative to Earth. If the Moon originally spun on its axis once per Earth day, how long would it take to stop spinning?

that would depend on how close it was to the earth and probably on how thick its crust was at that time.

30%. wow.

BobG
Homework Helper
I was just reading up some stuff about tides. Kind of figured this thingie out, hope my understanding is correct

The earth and moon both have ellipsoid orbits (Kepler Laws ;)) and have the orbits in such a fashion that for the earth’s orbit, the moon forms a focus and for the moon’s orbit the earth forms a focus. This is essentially because both the moon and the earth gravitationally attract each other which are contrary to what I previously believed that the earth had the moon revolving around its center and the earth spinning on its axis.
Since this is the case we will have on the far side of the earth, I.e the side not facing the moon, having tides because of centrifugal force and the lunar side having tides because of gravity of the moon, thus we have gravity of the moon and earth (assuming now that here centrifugal force and gravity is interchangeable, as in case of low velocities and distances) causing tides.
Here I come to pause now to regard to questions which come to my mind
1. Doesn’t this now become a binary system similar to the Pluto charon duplet?
2. Is the moon’s gravity large enough to affect the earth’s rotation? Would the earth have had an ellipsoid rotation had the moon not been there?

1. has been answered. Yes, the Earth-Moon is a binary system orbiting the combined center of mass, meaning the Earth has to have a slight wobble in its spin (the same is true for stars, which was originally how planets around other stars were discovered).

2. Yes, the Moon's gravity is large enough to affect the Earth's rotation. It constantly slows the Earth's rotation and will continue to do so until only one side of the Earth faces the Moon. The slowing is due to the ocean floor dragging the tides out from under the Moon as the Earth rotates. The peak of the tide always winds up leading the Moon, slowing the Earth and speeding up the Moon (which means the Moon is constantly drifting further away from the Earth).

Essentially should this not mean that the orbit of the earth around the sun also changes in nature, if the moon does affect the orbit i am fairly sure there would be a change in the nature of earth's orbit