|MadSci Network: Astronomy|
Hi Jeremy, The Moon is indeed moving farther away from the Earth at a rate of about 3.8 cm per year. At the same time, the Earth's rotation is being slowed by 1.5 milliseconds per century. This is due to the tidal interaction between the two bodies. Tides are due to the difference in force between the side of Earth facing the Moon and the side facing away. The force due to gravity between 2 bodies is F = GMm/R^2 where G is the gravitational constant, M and m are the masses of the 2 bodies involved (Earth and the Moon in this case), and R is the distance between the two bodies. The difference in force from the side of Earth facing the Moon and the side of Earth facing away from the Moon (called the differential tidal force) is proportional to 1/R^3. This means that as objects get closer together, the gravitational force between them increases as 1/R^2 and the differential tidal force increases as 1/R^3. As an example, if the Moon were half as far from Earth as it is now, the gravitational force would be 4 times stronger and the differential tidal forces would be 8 times stronger. Here's a diagram to help visualize this concept. The arrows represent the strength of the force due to gravity from the Moon on Earth (note, the sizes aren't exact, they are just meant to illustrate the concept) The + represents the Moon. The side of Earth closest to the Moon experiences the greatest force. --> ---> ----> + From the point of view of the center of Earth, these forces look like <- . -> + which shows that the Earth gets "stretched" by the Moon. Now, let's see the same diagram if the Moon is half as far away. --------> ------------> ----------------> + so from the center of Earth, we see <-------- . --------> + The Moon's gravity pulls a tidal bulge on Earth. Earth is rotating faster than the moon is revolving around Earth, so the bulge gets a little ahead of the Moon. The Moon's gravity pulls back on this bulge creating a torque on Earth. (The Earth also creates a bulge on the Moon, but since the Moon orbits Earth in the same amount of time it takes to rotate on its axis, the bulge is always facing Earth directly and this torque action does not occur.) Likewise, the gravitational attraction due to Earth's bulge accelerates the Moon slightly, causing it to move away from the Earth. In the distant past, the Moon was closer to Earth than it is now. That means the gravitational force and the differential tidal forces would have been greater. The tides would have been much higher than they are now. Models of the formation of the Moon estimate that it formed at a distance of about 12,500 to 20,000 miles from Earth. The Moon is currently about 240,000 miles from Earth. That means Early in the Moon's history, it was about 12-20 times closer to Earth than it is now. The tidal forces would therefore have been more than a thousand times greater--resulting in tides of about a mile high or so. Early in Earth's history, most of the surface would have been covered by water every high tide. By the time land animals evolved, however, the Moon had moved far enough away that the tides were much lower. Eventually, far in the future, the Earth's rotation will be slowed until a day is 47 days long. At this time, a month will also be 47 days long. Earth will always have the same side facing the Moon and the Earth and Moon will no longer move apart. For general information about the Moon, visit http://seds.lpl.arizona.edu/nineplanets/nineplanets/luna.html and the links therein. Erika
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