Astronauts Did This To The Moon. Scientists Are Thankful For It.

Classical Mechanics Level 2

The Apollo 11 astronauts did not leave the moon unchanged. Besides some footprints and a flag, there was some equipment left on the moon, including a mirror pointed towards the earth. Earth-based scientists can measure the distance to the moon by firing a laser pulse at the mirror and measuring the time it takes for the laser pulse to return to earth.

How long does it take in seconds for a short laser pulse to bounce off the moon and come back?

Image credit: Neil Armstrong/NASA/Corbis

Details and assumptions

  • The moon is, on average, \(385,000~\mbox{km}\) away from the earth
  • The speed of light is approximately \(3 \times 10^8~\mbox{m/s}\),
  • Note: This experiment, the Lunar Laser Ranging Experiment, is one of the most accurate distance measurements ever made. For example, one can determine that the moon is moving away from the earth at a rate of 3.8 centimeters per year.
  • Note: Although the Ancient Greeks were able to rationally estimate the size of the earth using rudimentary mathematics, their calculations were hopelessly off for the size of the moon. Find out why.

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