Chapter 13, Problem 35A

The moon 'falls' 1.4 mm each second. Does this mean that it gets 1.4 mm closer to Earth each second? Would it get closer if its tangential velocity were reduced? Explain.

To determine

To identify: Whether the moon is coming closer to Earth each second for the given specification. Also, will the moon come closer to Earth if its tangential velocity is reduced.

Answer to Problem 35A

The moon does not gets $1.4\text{ mm}$ closer to Earth each second.

The moon gets closer to Earth if its tangential velocity is reduced.

Explanation of Solution

Introduction:

The Moon’s tangential velocity is the parallel to the Earth’s surface and perpendicular to of the Earth’s gravitational pull.

The gravitational pull of Earth provides centripetal force which is required for the revolution of moon around the Earth.

The Moon always moves in a fixed orbit around the surface of the Earth, under the influence of the Earth’s gravitational pull.The “Moon falls $1.4\text{mm}$ each second” means it falls $1.4\text{mm}$ per second below the straight line and follows its orbit around the Earth.The distance between the surface of the Earth and the Moon’s orbit is constant.Hence, the moon does not gets $1.4\text{ mm}$ closer to Earth each second.

The Moon’s tangential velocity is sufficient enough to maintain the Moon in the fixed orbit.When the Moon’s tangential velocity is reduced, the Moon will leave the orbit and falls towards the Earth as the balance between its centripetal force and the Earth’s gravitational pull is disturbed.Hence, the Moon comes closer to the Earth if its tangential velocity is reduced.

Conclusion:

Thus, the moon does not gets $1.4\text{ mm}$ closer to Earth each second.

Also, the moon gets closer to Earth if its tangential velocity is reduced.