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5.23 The Earth-Moon System

We think of ourselves as living on a single planet, but in reality, we live in a system of two worlds. Our sister world, the Moon, is easily visible in our sky, and we can see its daily effects on ocean tides. The relationship between the two bodies was first appreciated in 1968, when humans started to explore the other half of our system.


Earth's Moon. Click here for original source URL



The Moon affects the Earth in several observable ways. Consider the monthly movement of the Moon around our planet - we see the phases of the Moon cycle daily, as different parts of the Earth-facing side of the Moon are illuminated by the Sun. Many people superstitiously believe that the Moon influences human behavior by some unknown force, causing people to act strangely during a full Moon. This is the origina of the word lunacy. However, this has never been convincingly proven. Occasionally, a study claims to find a correlation between Moon phase and murders or admissions to emergency rooms, but large scale statistical studies show the effect are not significant. (Though before articificial lights there was probably some tendency for more people to be out on full Moon nights, and hence for more interesting events to happen!)

As Newton discovered, Earth's gravity attracts the Moon toward the Earth, and keeps it in orbit around the Earth. But gravity is a mutually attractive force. So the Moon is attracting the Earth, too. Since the force of gravity depends on the inverse square of the distance, the side of the Earth facing the Moon has a stronger force pulling toward the Moon than the opposite side, because it is closer to the Moon. The two unequal forces cause a net stretching force along the Earth-Moon axis, called a tidal force. Tidal forces occur any time there is a difference between the gravity on the two sides of a celestial body caused by the attraction of another body. The actual effect is to stretch the whole planet into a slightly football-like shape. This elongation of the solid Earth is actually very subtle; it results in a difference in the radii at the poles and the equator of only about 20 centimeters!

The liquid ocean can move much more freely in response to tidal forces than the solid rocks inside the Earth. Water flows until it "piles up" in tidal bulges on each side of the Earth. You may wonder about the fact that tides occur on both sides of the Earth. Why doesn’t the attraction of gravity just cause the water to pile up on the side closest to the Earth? Just as the force of gravity is strongest on the side of the Earth facing the Moon, the force is weakest on the side away from the Moon. Less gravitational force on the far side means the water is not attracted as strongly, and it moves away from the center of gravity. Think of a spring as an analogy. When the spring is stretched, the distance between all parts of the spring increases. In the same way, the tidal stretching force applies to the oceans on both sides of the Earth. Since there are tides on opposite sides of the Earth, and the Earth rotates once per day, a given spot on the rotating Earth passes through two high-tide zones in one day.

If the tug of the Moon were the only thing causing tides, high tides would occur whenever the Moon is overhead, and then exactly 12 hours later. In fact, three effects complicate ocean tides. First, the Earth’s rotation drags the tidal bulges out of line with the direction to the Moon. Second, coastlines complicate the flow of water, so that actual high tides occur in a complex rhythmic pattern. Third, the Sun contributes its own tidal forces.

The Sun is much more massive than the Moon, but it’s also a lot farther away. When you calculate the resulting gravitational forces, the Sun’s gravitational force on the Earth is much stronger than the Moon’s gravitational force on the Earth. This is how the Sun keeps the Earth in orbit around it. However, because the Moon is so much closer, the differential force caused by the Moon is larger than the differential force caused by the Sun. So the Moon’s tidal force is larger. The Sun has some tidal force on the Earth, too, but solar tides are only about half as high as lunar ones. When the Sun and Moon line up (new Moon and full Moon), the tides on Earth are especially high (spring tides). When they are 90º in opposition, the tides partially cancel each other out, and the resulting lower tides are called neap tides.

The liquid oceans can move easily to respond to the Moon’s influence. But the rocky mass of the Earth feels the same tidal forces, and it can’t alleviate the stress by flowing freely. Land tides put extra stresses on the brittle rocks of the lithosphere. This can lead to earthquakes. Geologists have found that earthquakes do not occur randomly over time. There is a slightly higher chance of earthquakes near full Moon or new Moon, when the tidal forces are largest. 

You’ve probably noticed that the features of the Moon always appear the same. The Moon actually orbits the Earth in such a way that the same side always points towards the Earth. This is because the force of gravity is working both ways; the Moon is slightly elongated by its own tides, caused by the gravity of the Earth. Earth’s gravity has forced the long axis of the Moon to face the planet, so that the Moon is tidally locked in synchronous rotation.

Through a complex interplay of gravity, tidal forces are also slowing down the rotation of Earth. At the same time, the Moon is slowly spiraling further away from Earth. This is yet another example of the conservation of energy. As the Earth loses rotational kinetic energy by spinning more slowly, the gravitational potential energy increases as the Moon moves to a larger distance from the Earth. The total energy in the Earth-Moon system is conserved. If we follow these changes in reverse, backwards in time, we find that the Earth rotated faster. The Moon was closer to the Earth, so it orbited the Earth in fewer days.

What evidence do we have to support the theory that the spin of the Earth is slowing down? The Apollo astronauts placed laser reflectors on the Moon in order to measure lunar motions precisely. These measurements confirm that the Moon is moving very slowly away from the Earth, as predicted. The distance to the Moon is known with a precision of a few millimeters! The Moon is spiraling away from the Earth at a rate of 3.8 centimeters per years. In addition, paleontologists have studied the daily and monthly growth rings in fossilized coral and other organisms. The results show that one billion years ago, the Moon took only 23 days to go around the Earth, and the Earth rotated in only 18 hours! Somewhat controversial fossil data from 2.8 billion years ago suggest that the lunar month was as short as 17 days. The gradual spin down of the Earth means that our days are 23 milliseconds longer every year, giving us all more time to get things done.

 


The lunar phase depends on the Moon's position in orbit around the Earth and the Earth's position in orbit around the sun. This diagram (not to scale) looks down on Earth from north. Both Earth and the Moon's orbit are rotating counter-clockwise. Sunlight (yellow arrows) is coming in from the right. One can see, for example, that the full moon will always rise at sunset and that the waning crescent moon is high overhead around 9:00?am local time. Click here for original source URL.