E

Fig 22.11.

Librations, which allow us to see more than 50% of the Moon's surface. (a) The effect of the eccentricity of the Moon's orbit. The Moon rotates on its axis at a constant rate, but orbits the Earth at a variable rate, so at various times the rotation is ahead of or behind the orbital motion, allowing us to see an extra 6° around. Point P keeps track of the steady rotation of the Moon.We can see that the line from the Earth to the Moon passes through P at positions 1 and 3, but not at 2 and 4. (b) The effect of the inclination of the Moon's orbit, relative to the ecliptic, by 5°, allowing us to see over and under the poles. (c) The effect of the finite size of the Earth, allowing us to look from different directions, providing a 2° effect.

solution

The force on each body is proportional to its mass, and inversely proportional to its distance from the Moon. Therefore

GM0/rgM GMeAem a rEM y

V rSM J

This means that the Sun exerts twice as great a force on the Moon as the Earth does. It is therefore not really proper to talk about the Moon orbiting the Earth. The Moon actually orbits the Sun, with the Earth causing the curvature of the Moon's orbit to change. This is shown in Fig. 22.12. Notice that the Moon's path is always concave toward the Sun. This is because the net force on the Moon is always inward, even when it is between the Earth and the Sun.

When the Moon passes between the Earth and the Sun, it is possible for it to block some of the sunlight. This is called an eclipse of the Sun, or a solar eclipse. If the Moon completely blocks the Sun,

Moon's Path

Earth-Moon Center of Mass

Fig 22.12.

Earth-Moon Center of Mass

Orbit of the Moon, relative to the Sun. The Moon's orbit must always be concave toward the Sun.

of the surface of the Moon. Another contribution to the libration comes from the fact that the Moon is so close to the Earth that observers on opposite sides of the Earth see the Moon to be rotated through approximately 2°. These effects, as shown in Fig. 22.11, allow us to see 59% of the Moon's surface.

Example 22.1 Forces on the Moon

Calculate the relative strength of the forces exerted on the Moon by the Earth and by the Sun.

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