## The Distance To The Moon

Above is a picture of the earth-moon system, roughly to scale. When I was a child, I memorized that the average (mean) distance to the moon was 238,857 mi. Now it's 238,856 which is probably more accurate. The moon's orbit is elliptical, and the distance varies quite a bit (it varies from 225,745 mi. to 251,967 mi.).

Now they actually know the distance to the moon to within a few inches. Apollo 11 astronauts left an array of corner mirrors on the moon. A corner mirror is three mirrors arranged like a corner of a box, all at right angles to each other. Such a mirror reflects light directly back toward the source of the light. Scientists shine a laser at the moon, and measure the time it takes to reflect back. They can measure this time to within a tiny fraction of a second. So they deduce the distance to the moon (at any given time) to within a few inches.

The speed of light in a vacuum is a constant. But it is not known very accurately, not anywhere as accurately as the distance to the moon is known. What this means is:

1. They have a very accurate "yardstick" (based on the speed of light).
2. They know the distance to the moon very accurately (based on the yardstick).
3. They don't know the length of the yardstick very accurately, in any normal units (feet, meters, whatever).

So essentially, they measure the distance to the moon in fractions of a light-second, not in inches or meters.

These scientists really measure the distance from their telescope to the Sea of Tranquility. And, if they want to know the distance between the earth and the moon, they have to adjust for the distances which these places are from the centers of the earth and the moon. And these are not known with tremendous accuracy, either.

All the great accuracy of their measurements is not lost, however. Mainly, these scientists are studying the way in which the distance changes over time. This helps them predict the orbit of the moon with great accuracy.

Addendum: The moon is slowly getting farther from the earth. This is a result of the earth losing energy because of the tides. The moon gains energy. And the earth-moon system does not gain or lose any energy. I have recently found out that the orbit of the moon probably oscillates from near to far and back to near, over and over.