Principles of Astronomy is copyright protected, is the sole property of the author (Dr Jamie Love © 1997 - 2011) and is sold exclusively by Merlin Science. Any form of reproduction by any media is strictly forbidden.

The Moon's Motion

by Dr Jamie Love © 1997 - 2011

Many centuries ago, when the Ptolemaic model of the universe was considered correct, people believed that the everything revolved around the Earth. At least they got it right with respect to the Moon! The Moon is the Earth's satellite. By definition a satellite is a "secondary body orbiting a primary body". The Earth is a satellite of the Sun and the Moon is a satellite of the Earth. Much of astronomy has to do with the motion of one "body" around another so the word "satellite" is very important to understand and our satellite, the Moon, is a great way to learn about satellites and their motion.

The word "satellite" can also apply to an object placed into orbit around another object. In this century we have placed artificial satellites into orbit around the Earth, the Moon and several other planets.

The word "moon" has come to mean any natural satellite around a planet. Mars has two moons, Jupiter has at least 16 moons. Notice the small "m" in "moons". Those satellites are moons with a small "m", but our moon is called the "Moon". Some (although not all) astronomers understand that the Earth's moon is written as "Moon" when used as a proper noun. It's an easy mistake to make.

As you might imagine, the name or word "moon" has been around a long time and has been applied to satellites of other worlds. That is acceptable. Some folks, in order to highlight the idea that the "Moon" deserves a better name than simply "moon", will call our satellite "Luna". This is particularly true in conversations when it isn't always clear what M/moon you are talking about.

OK, the Moon revolves around the Earth. Right?

Right.
The Moon revolves around the Earth but that is a bit of an over simplification. Our Moon is a very large object. Indeed, the Earth-Moon "system" could be properly thought of as a "double planet system". No other pair in the Solar System are so close in size (except for Pluto's main satellite, Charon, but they are an unusual pair for a lot of other reasons that I will not discuss at this time). The Earth's diameter almost four times the diameter of the Moon. [The Earth's diameter is 12,700 kilometers and the Moon has a diameter of 3,400 kilometers. That's a difference of about four fold.]

The Earth is bigger so it is the "primary" body and the Moon is its satellite, but the Moon is a very big satellite! However, size can be deceiving because it is gravity that affects orbits.

All matter has mass and all mass attracts other masses by a force called gravity. The force of gravity depends upon the mass of the two objects and the distance between them. The Earth has a mass over 80 times that of the Moon, so the Earth is clearly the dominate partner. However, the Moon is still pretty massive, and pretty close too, so it is an oversimplification to say that the Moon goes around the Earth. In fact, the two bodies revolve around each other! The center of the Moon's orbit is not in the center of the Earth. The Earth and Moon revolve around a common point called the barycenter.

The barycenter is the center of mass of any system.
Imagine the barycenter as the point about which two people spin when they are dancing together. During some dances (square dancing, Scottish Highland dancing, etc.) it is common for both partners to grasp each other's hands and revolve in a circle. If you watch this spin carefully you will see that it is rarely centered - the larger partner is closest to the "spin barycenter" and determines where the smaller partner goes.

That is what happens with most satellites.

Where's the Earth-Moon barycenter?

It's in the Earth but not at its center.

Imagine a line drawn from the Earth's center to the Moon's center. The barycenter is along that line. The balancing of the two masses places it at all times within the Earth (below the Earth's surface), but never at its center.

The barycenter moves as the Moon revolves around the Earth.
Opps. That's not true. The Earth and the Moon revolve around the Earth-Moon barycenter!

Most folks are not familiar with the concept of a barycenter so it is "safe" (fair) to say that the "Moon revolves around the Earth" when in fact they both revolve around its barycenter which happens to be within the Earth. Indeed, it is such a well-accepted expression that I will use it ("the Moon revolves around the Earth") throughout the rest of our lessons. It isn't completely true but it is pretty close to true and it is easier to say that phrase than to explain it!

Why doesn't the Moon fall into the Earth?

Because the Moon is in orbit around the Earth. (Actually, around the Earth-Moon barycenter.)

What's an orbit?

Gee I wish you hadn't asked that!

There are two ways to understand orbits. One way (the best way - the correct way) is to learn how the effects of gravity, acceleration and velocity act together through a series of mathematical equations to produce a net effect that describes the position and motion of an object in orbit around another object. The other way is to simply imagine the final effect. I like that way because it's much easier.
[But, hey, don't think you're going to get away from this too easily. We'll return to orbits in June when I teach you Kepler's Laws. Don't worry. It's low on math and, unfortunately, will not give you the math you need to understand orbits. If you feel cheated, do a search using keywords like "gravitational formula". But finish this lesson first!]

As the Moon falls towards the Earth, under the influence of gravity, the Moon's orbital velocity (actually its "tangential velocity") causes the Moon to fall off center to the Earth. While the Moon falls (say, 1000 kilometers) towards the Earth, the sideways motion of the Moon (several thousand kilometers) during that time it is falling, changes the Moon's position with respect to the Earth's surface such that the surface of the Earth is now (1000 kilometers) further away.
[Wow! What a mouth full. Read that again - with and without the stuff in parentheses.]
The combined effect of the Moon's sideways motion along with its falling means the Moon is ALWAYS falling towards the Earth but NEVER HITS it! It's in "free fall", because it is falling freely, but never hits its "target". For every meter that the Moon falls towards the Earth, the Earth's surface curves a meter away due to the motion of the Moon.
Notice that the Earth isn't moving out of the way of the falling Moon. (In fact, the Earth's orbit causes the Earth to move slightly forward, in the same direction of the Moon but that motion isn't as much as that of the Moon so it has little effect and can be ignored.) Instead, the Moon is missing its target because the Moon's orbital velocity pushes it off center from the Earth. The overall effect is that the Moon falls towards the Earth at the same rate that the Earth's surface curves away from it.

This diagram (which illustrates this idea using "vectors", a more scientifically rigorous way to think about it) might help you to understand what an orbit really is. The view is from "above", looking down on the Earth's (north) pole. Notice how the effects of gravity and velocity create the orbit.

All orbits, not just the Moon's orbit, behave this way so it's a good idea to understand this important idea.

It takes 27.3 days for the Moon to circle the Earth. (Actually it takes 27.3 days for the Moon to circle the barycenter! ) That means the Moon will move westward through the sky at a rate of 13.2 degrees each night. [That's a full 360 degree circle divided by 27.3 days to give 13.2 degrees of motion each night.] Don't confuse that with the nightly motion of the stars caused by the Earth's rotation. What I mean is that the Moon will move through the starfield 13.2 degrees eastward each night. [That's a "fist and several fingers" if you are using the measuring method I taught you last month.] No other (natural) object moves through the starfield so quickly.

The Moon's orbital period is exactly equal to its rotational period. That means the Moon turns to face the Earth as it revolves around us so we see only one side of the Moon from Earth. Again, this behaviour is similar to that found in dancing.

Yeah, but dance partners hold each other that way. What causes the Moon to face the Earth?

Tidal friction!
To understand tidal friction it helps to first understand tides. Tides are caused by the Moon's gravitational forces working on the Earth and its oceans.

This diagram shows a cross-section of the Earth (in light grey) and its ocean (in dark blue). Understand that this diagram is a simplification of the Earth because it doesn't show the continents, but I'm sure you get the picture. The water in the oceans is attracted by the Moon's gravity and bulges (upwards) towards the Moon. That causes a high tide to occur on the side facing the Moon.

What causes the other high tide on the other side?

Gravity (again).

As the Moon pulls on the water it is also pulling on the Earth. The Moon's gravity pulls the Earth away from the water on the Earth's far side! The net effect is that the water is higher on the side opposite the Moon. (This effect is actually caused by inertia - it just depends on how you want to explain it.) The highest of the two tides is the one facing the Moon because the water is closer on that side and therefore the effect of the Moon's gravity is stronger.

So, the highest tide occurs when the Moon is directly overhead.

Ah, well it would be if not for two complications.
First, the tidal "bulge" cannot keep up with the Earth's rotation. Our oceans are relatively shallow and water has a lot of momentum (when moving) and a lot of inertia (when not moving). Together, this causes the high tide to be delayed by about a quarter of the Earth's rotation. That means the tide is highest when the Moon is on the horizon. That's when you would expect the lowest tides!
Second, local coastline geography can affect the local tides. If the water has to travel around a large island, peninsula or other bit of land, it will be delayed.

By the way, the low tides fit between the high tides. They occur because they are at the positions of the ocean least affected by the Moon's gravity, due to their positions at right angles to that of the Moon's pull. Off course, the two complications noted above for high tides also affect low tides.

Once you understand the local tidal effects along your coastline, assuming you have a coastline, you can keep time to the tides by knowing that they will progress at the same rate as the Moon. If the highest tide today was at 10AM, there will be another, slightly lower, high tide 12 hours later - at 10PM. (Actually, that's not true. Read the rest of this paragraph to understand why the high tides are slightly more than 12 hours apart.) The two low tides will occur half way between the high tides (roughly). Tomorrow, the highest tide will occur later because the Moon has moved a small amount ahead of the Earth's rotation. Remember, each day the Moon moves 13.2 degrees ahead of us. That means the highest tide will be advanced by about 0.88 hours. [I got that by dividing the Moon's relative motion of 13.2 degrees by 360 degrees to get 0.03666 of a day. That means the Moon is ahead of the Earth's rotation by 0.03666 of a day and multiplying that by 24 hours (in a day) I get 0.88 hours.]. Each tide, high or low, will be advanced by 0.88 hours from the previous day because of the Moon's motion.

Some students get confused here so let me explain it again. When I say the Moon (and tide) has advanced by 0.88 hours I mean that the Moon has moved that much farther ahead in its orbit. That means it will take an additional 0.88 hours for the Earth to rotate to the new alignment so the tide will be 0.88 hours later. So each day the the tide is about an hour late. There are two problems whenever I teach this subject. 1 - The advancing of the Moon means the tides are later each day. (24 hours plus the 0.88 hours) 2 - There are four tides a day (two lows and two highs) but when I speak of a tide returning I am talking about one (or the other) specific tide. Today's 9:00AM high tide will return tomorrow at 9:53AM (24 hours plus 0.88 x 60 minutes = 24 hours and 52.8 minutes). But before that high tide there will be another high tide in half that time which is in 12.44 hours. That would be at 21:26 (9:26PM). Half way between those high tides will be a low tide. This low tide occurs 6.44 hours (half of 12.88 hours = 12 hours and 26.4 minutes) after the high tide so at 15:13 (3:13PM). The next low tide will be 12.44 hours later at 3:39AM.

OK, fine. But I want to learn astronomy not oceanography! What's this have to do with the Moon always facing us?

Oh, yeah right.

All astronomers should understand tides because they cause tidal friction and that's what causes the Moon to face us. The ocean tides are an obvious effect of the Moon's gravity but the Moon causes "land tides" to occur too. As the Moon passes overhead the Earth rises towards it by several centimeters and then drops down again as the Moon moves on. (Actually, as the Earth rotates.) Don't confuse this with the tug of the Moon that causes the Earth to move towards it, producing the lower high tide opposite the Moon. What I am talking about here is the actual distortion of the Earth's solid "rock" due to the Moon's gravity! These land tides are not noticeable because the shifting they cause is very slight, very slow, and the rock returns to the same position as the Earth rotates. It has no overall effect on the Earth's position or shape.

Land tides occur on every object in the Solar System (if it has "land"). They cause friction and affect the orientation of many satellites. Here's how.

Both the primary and secondary bodies in a pair can be affected by land tides caused by its partner. Long ago, when the Moon used to have a more rapid rotation, it experienced land tides caused by the gravitational pull of the Earth. Because the Earth is so big, the Moon experienced a great deal of land tide and the regular "land bugle" produced by the land tide caused tremendous friction with the Moon's own rocks. It was like applying brakes to the Moon's rotation! This caused the rotation of the Moon to slow down and after a long period of time (millions of years) the rotation became so slow that one side always faced the Earth.
That way there is no longer a "moving land tide" on the Moon. Now that the Moon is always positioned with one side to us, it is no longer tugged around by the Earth as the Moon orbits us. The Moon has reached a "comfortable" position (tidally speaking).

This is true of our Moon and of many other moons. The secondary partner is "despun" (as we like to say) by the tidal friction caused by its primary partner. When a body has despun its partner it is said to have "captured" its partner's rotation and we describe the partner's rotation as synchronous with that of the primary body. Many moons in the Solar System have been despun, their rotation captured by their larger partner, so they have a synchronous rotation. A despun moon shows only one side, one face, to its primary partner.

Tidal friction is an important "shaper" of the interaction between a pair of worlds. Not only does it cause a body to be despun, but it also changes the orbital period and its orbital distance. That's because of a complexity involving the "conservation of angular momentum". This is an important part of the physics of astronomy but I think we've gone deep enough.
According to calculations, we know that long ago the Moon was closer to the Earth and the Earth rotated more quickly than it does today. Tidal friction has despun the Moon, moved it further from the Earth and has also slowed the Earth's spin!

Tidal friction is still at work today and it's moving the Moon away from us at a rate of a few centimeters each year. Meanwhile, the land tides on the Earth caused by the Moon, are slowly braking the Earth's rotation, slowing us down. Many billions of years from now the Moon will have captured the Earth's rotation! So someday in the far, far future the Earth and Moon will be much further apart and face each other. At that time they will be like two proper dancers face-to-face. The Earth will have a "moon side" from which the Moon will always be seen and a "star side" from which you could never see the Moon, only the stars. (Cool, Huh? )

But let's concentrate on the current situation.

Because the Moon's rotation has been captured by the Earth, one side always faces towards the Earth and (of course) that means one side always faces away from the Earth. The side facing us is called either the "near side" or more rarely the "Earth side" because it is the side nearest us and the side from which you could see the Earth if you were on the Moon. The opposite side is called either the "far side" or more rarely the "star side" of the Moon because that side is furthest from us and if you were there (on the star side of the Moon) you could never see Earth, only stars.
It is unfortunate that the phrase "the dark side" is often used to describe the far side of the Moon because it isn't any darker than the Earth side. The Moon undergoes one rotation as it completes each orbit around the Earth and as it does so it undergoes one complete "Moon day". Therefore the side facing way from us, the star side, experiences just as much sunlight as the Earth side. Perhaps it was named "darkside" because it cannot be seen from here and was thus a mysterious place. Indeed, until 1959, when the Russians sent Lunik 3 around the Moon, we had no idea what lay on the "dark side" of the Moon.

OK, the dark side isn't really dark so I'll call it the star side or far side of the Moon, but how does the Sun fit into all of this?

That's a very important question because it's "how the Sun fits into all of this" that causes the phases of the moon.
In our next lesson I will teach you how the geometry (positions) of the Sun, Earth and Moon cause the phases of the Moon.

Principles of Astronomy is copyright protected, is the sole property of the author (Dr Jamie Love © 1997 - 2011) and is sold exclusively by Merlin Science. Any form of reproduction by any media is strictly forbidden.