The Moon is being pulled into the Earth. Both are being pulled into the Sun.
But don’t duck and cover. That’s what orbits are all about. I find a common misconception among students about why astronauts float around the Space Station. They sometimes think that this is because the astronauts are out the reach of Earth’s gravity. That, or because they drink Tang.
Neither is true. Orbiting astronauts, Space Stations and satellites are being pulled by gravity toward the center of the Earth just as we are. At the Space Station’s altitude, about 185 miles above the Earth’s surface, the astronauts experience a pull of gravity that is still about 90% as strong as down here. The astronauts you see floating still have nearly their entire weight.
The astronauts are falling, but so is the floor of the station. Just like when you go on the free fall ride at an amusement park you experience weightlessness, not because you have no weight, but because the floor falls away from you at the same rate you are falling. You weigh the same. On Earth, the ride can can last only a couple of seconds. The astronauts and the Space Station fall for years and years. The astronauts still have 90% of their weight, but you just can’t tell by putting a bathroom scale on the floor, since the floor is falling away. The astronauts don’t drink Tang any more either.
The reason the astronauts don’t hit the ground is that they are moving fast, over 17,000 miles per hour, at a right angle to the downward direction. In the absence of any other force, they would move in a straight line forever, disappearing from our solar system. The pull of the Earth changes their direction, not enough to pull them to the ground, but to keep the astronauts and the station in a circular orbit that takes them around the earth every hour and a half. (Physicist nitpickers would probably want to comment that the orbit is not perfectly circular, so in the spirit of full disclosure: the orbits can be ellipses rather than circles.) It is just as if you were to swing a cat over your head by its tail. You pull inward but the body of the cat stays at the same distance from you, moving perpendicularly to the direction you are pulling. When the speed and distance are just right, the astronauts and station stay forever at the same altitude above the Earth.
The same thing happens for the Earth orbiting the Sun. It is why we haven’t yet fallen into the Sun even though the Earth feels a large gravitational force towards it. The Moon orbits the Sun too. If it didn’t we’d have lost it by now.
So the Earth and Moon are falling into the Sun. Like Galileo dropping one-pound and ten-pound objects from the Tower of Pisa we can ask, “Do they fall at the same rate?” This is where a “lunar ranging” experiment such as performed by the boys comes into play. They can bounce a laser off of mirrors left by the Apollo astronauts on the Moon. The mirrors are the corner of a cube and any light ray that hits them bounces of all three mirrors at just the right angles so that it returns from the direction it came.
It takes about 2.5 seconds for the light to travel to the Moon and back. By measuring the exact timing to better than a hundred billionth of a second, these laser lunar ranging experiments have measured the distance to the Moon to better than a millimeter. Now astrophysicists can check that the Moon is behaving exactly as it should.
The central principle of Einstein’s theory of general relativity is the “equivalence principle”, that objects should fall at the same rate regardless of their mass or chemical composition. This gives a testable prediction. The Moon are Earth are significantly different materials and size. Yet the lunar ranging experiments show the Moon and the Earth fall together towards the Sun. Actually this is only just the “weak” version of the equivalence principle. There is more to mass than just the composition of the objects. Since the energy of assembling the Earth and Moon is so much different, according to Einstein’s famous m = E/c2 , they have a different amount of this source of mass as well. Yet still, lunar rangers measure that we and the Moon fall at the same rate. The best test of this “strong equivalence principle” comes from this lunar ranging.
The lunar ranging experiments are the best tests of many other aspects of Einstein’s theory of relativity. In addition their close monitoring of the Moon have told us that it actually has a liquid core. The lunar ranging experiment is one of the longest running experiments in physics. In its 35 year history it has marked that not only is the Moon not in danger of actually hitting the Earth, but it is moving away from us at about 1.5 inches per year, due to energy lost as it creates high and low tides for surfers. In about five hundred million years the Moon will be so far away, there will never again be a total eclipse of the Sun. So go out and enjoy one while you still can.
Last (and certainly least), as Leonard explained to Zack, the presence of reflections from the retro-reflectors often are used to rebut claims that humans did not really go to the Moon. Actually Leonard’s argument is specious. After all, unmanned missions could have left the reflectors, just as the Russians did. I’m still waiting for the producers to invite me to see NASA’s soundstage on the backlot.
While preparing the set, a few BBT crew members asked a question I never thought of. Two and a half seconds later, the apartment, and detecting apparatus has moved since the Earth is rotating. So why doesn’t the laser spot miss their detector? The experiment still works because the laser’s spot spreads out as it travels. The spot size when it returns to Earth is over 10km, much bigger than a laser pointer, and smaller than the distance Pasadena moves in 2.5 seconds due to the Earth’s rotation.
Tonight was the season three finale. Thanks to those who followed this blog after each show this year. Tune in next season, when ***SPOILER ALERT*** the Moon will be about an inch farther away.