Questions: Earth-Moon System Dynamics and Evolution

Question 1

The Moon is slowly receding from Earth. A student says: 'The Moon is gaining energy, so Earth must be losing energy, and total energy is conserved.' What is wrong with this claim?

• A. The Moon is actually approaching Earth, not receding
• B. It is angular momentum that is conserved, not total mechanical energy — tidal friction converts some mechanical energy to heat
• C. Earth is not losing any energy; the Moon gains energy from the Sun
• D. Both angular momentum and total energy are conserved, so the student is correct

Answer: (B)

Tidal friction dissipates mechanical energy as heat, so total mechanical energy is NOT conserved in the Earth-Moon system. Angular momentum IS conserved: Earth's rotational angular momentum decreases (its day lengthens) while the Moon's orbital angular momentum increases (it recedes). The student has the wrong conserved quantity.

Question 2

Why does the Moon always show the same face to Earth?

• A. The Moon does not rotate at all — it is held stationary by Earth's gravity
• B. The Moon's rotation period equals its orbital period, a state reached through tidal dissipation
• C. Earth's gravity physically prevents the Moon from rotating
• D. The Moon rotated freely long ago but stopped after a major impact

Answer: (B)

Tidal locking occurs when tidal friction slows a body's rotation until its spin period matches its orbital period. The Moon is NOT non-rotating — it completes exactly one rotation per orbit. This is tidal locking, the natural end state of tidal dissipation for the smaller body in a gravitationally coupled pair. Option A is a very common misconception.

Question 3

Earth's rotation is gradually slowing because the Moon's gravity acts as a brake on Earth's rotation.

• T. True
• F. False

Answer: True

True. Earth rotates faster than the Moon orbits, so Earth's tidal bulges are carried slightly ahead of the Earth-Moon line by rotational drag. The Moon's gravity pulls back on this offset bulge, slowing Earth's rotation. This effect is measurable: Earth's day lengthens by about 2.3 milliseconds per century, confirmed by historical eclipse records and atomic clocks.

Question 4

The Moon stabilizes Earth's axial tilt by actively correcting any wobble in Earth's rotation through tidal forces.

• T. True
• F. False

Answer: False

False. The Moon stabilizes Earth's obliquity not by actively correcting wobbles but by gravitational torque that suppresses resonant oscillations of the axial tilt. Without the Moon, Earth's axial tilt would vary chaotically over millions of years — as Mars's does — potentially causing extreme seasonal swings. The mechanism is a gravitational anchor effect, not a real-time wobble correction.

Question 5

Explain why the Moon is spiraling outward from Earth rather than inward, and what principle governs this evolution.

Model answer: Earth's tidal bulges are carried slightly ahead of the Earth-Moon line by Earth's faster rotation. The bulge's gravity pulls the Moon forward in its orbit, adding energy and angular momentum to the Moon's orbit. In gravitational mechanics, more energy means a higher orbit, so the Moon recedes. Angular momentum is conserved: Earth loses rotational angular momentum (its day lengthens by ~2.3 ms/century) and the Moon gains orbital angular momentum (its orbit widens by ~3.8 cm/year).

The key insight is angular momentum conservation coupled with the geometry of the offset tidal bulge. Energy is not conserved (some is dissipated as heat in tidal friction), but angular momentum is. The offset bulge transfers angular momentum from Earth's spin to the Moon's orbit — slowing Earth while pushing the Moon outward. This same mechanism, applied to the Moon long ago, eventually tidally locked it.