Science Puzzle

Lunar Pendulum Clock

Space Science Charge ⚡⚡
Same pendulum clock. Different gravitational field. EARTH g = 9.8 m/s² MOON g = 1.6 m/s² (⅙ of Earth) The Moon clock runs slow. How much slower?
Fig. 1: The same pendulum swings more slowly on the Moon. The clock loses time.

You take a perfectly accurate grandfather clock to the Moon. The clock uses a pendulum to keep time. The Moon's gravitational field is about one sixth the strength of Earth's.

What happens to the clock on the Moon: does it run fast, slow, or keep perfect time?

The Answer

It runs slow. The period of a pendulum (the time for one complete swing) is proportional to the square root of the pendulum length divided by the local gravitational acceleration.

On the Moon, gravity is about one sixth as strong as on Earth. The square root of 1/6 is roughly 0.41. So the pendulum swings only 41% as fast as on Earth, and the clock runs at about 41% of its normal speed, losing roughly 35 seconds every minute.

To keep accurate time on the Moon, you would need to shorten the pendulum to about one sixth of its Earth length, or better yet, use a different timekeeping mechanism entirely such as a quartz oscillator, which does not depend on gravity.

The principle: Pendulum period. The time for one swing is proportional to the square root of length divided by gravitational acceleration. Weaker gravity means slower swings and a slower clock.