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No. 2195:
How Far the Moon?

Today, we keep track of the moon. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

The Moon rides an average distance of thirty Earth diameters away from us. It has a quarter of our diameter, a 50th of our volume, and only an 80th of our mass. Earth, with its iron core, is denser than the Moon; but it also reflects more light. 

relative sizes and spacing of Earth and Moon

Yet the moon still exerts its influence upon us in many ways. While it's a universal metaphor for peace and tranquility, it also churns our oceans -- pulling two high tides and two low tides in just a bit more than one day. With each tidal change, a tiny bit of Earth's rotational energy is chewed up and dissipated; and we slow down. Each day is now a twelfth of a second longer than it was when the Egyptians built the Pyramids. 

Earth's tidal influence on the Moon was once much greater than hers on us. Our influence on anything movable on the Moon's surface slowed her rotation down to the point at which she can no longer rotate relative to us. That's why we only see one side of her.

But the rotational inertia that we share with the Moon has to stay the same even though Earth spins more slowly. So we remember the ice skater stretching her arms outward or pulling them in. To have the same inertia when she spins slowly, her arms have to be further outstretched. Likewise, as we slow, the Moon (our outstretched arm) moves away; and our combined rotational inertia stays unchanged. 

And we can now measure the movement: When astronauts walked on the moon in 1969, they did a small but important thing -- largely forgotten today. They installed a special 18-inch reflector. Now we now bounce laser beams from Earth off it. Since we know almost exactly how fast light travels, we can measure the distance to the moon within an inch. We now know that the Moon drifts away from us at the rate of an inch and a half per year. 

None of this will mean much in our lifetimes, of course. But in the larger scheme of things it's important. Long ago, a day lasted only twelve hours with the moon only half as far away. And the speed of rotation has influenced Earth's shape: 

Earth's equatorial diameter is about 26 miles greater than her polar diameter. She's just a bit squat in shape -- not a perfect sphere. That's because the force of gravity can't quite overcome centrifugal forces. Still gravity does keep us from spreading out like a big spinning pizza. Long ago, when Earth spun more rapidly, it was even less spherical than it is today. 

So our celestial companion, the Moon, moves through the night sky, haunting our dreams. She influences us constantly and methodically. Far into the future, after our species is gone, Earth and Moon will continue their stately spin across the dance floor of the Heavens -- an old couple, their seasons altered, their pace slowed -- but linked by the same silken threads of gravity and inertia that've bound them for the last four billion years.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

A great deal of relevant material is on the web. See for example:

The reflector that the astronauts left on the moon is much more than a simple mirror. For details, see:

Earth and Moon

Earth and Moon in their approximate relative size and brightness 

(all images above adapted from government photos)