Diameter of the Moon's Orbit
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Faugh, Jerry S. & Serway Raymond A. College Physics. Pacific Grove: CA: Thomson Brooks/Cole, 2003.  Average EarthMoon distance: 3.84 × 10^{8} m  768,000 km  
The World Book Encyclopedia. Chicago: World Book Inc., 2005: 783. 

768,934 km  
North, Gerald. Observing the Moon. United Kingdom: Cambridge University Press, 2005: 2.  "It orbits the Earth at a mean distance of 384,000 km"  768,000 km  
Sagan, Carl. Murmurs of Earth. New York: Random House, 1978: 226. 

768,800 km  
Jones, Brain. The Practical Astronomer. New York: Simon and Schuster Inc, 1990: 16.  "However, the distance between the Earth and Moon varies from 356,410 km (222,756 miles) at perigee, or closest approach to 406,697 km (254,186 miles) at aposee, its farthest point".  712,820 km to 813,394 km 
The moon is really just a large piece of rock, which was caught in the Earth's gravitational field. Because the moon has a smaller mass than the Earth, 7.35 × 10^{22} kg compared to 5.98 × 10^{24} kg, the moon orbits around the Earth, making the moon Earth's satellite. In fact, the moon is the Earth 's one and only natural satellite.
So how was the diameter of the moon's orbit determined? One possible way would be finding the EarthMoon distance. To find the EarthMoon distance, scientists could use a RADAR laser, in which they can fire electromagnetic waves or em waves at the moon and time how long it takes for the em waves to travel to the moon and back. Since em waves always travel at the speed of light (3 × 10^{8} m/s), and the time can be measured, one can use the equation v = s/t or s = vt, but don't forget to divide the measured time or the calculated distance by 2, as the em waves traveled twice the distance. The moon's distance from the Earth varies from 360,000 km to 406,000 km, making the mean distance from the Earth 384,000 km. Since its mean distance from the Earth is 384,000 km, the average length of the moon's orbit's diameter is 768,000 km.
Is the moon really moving farther away from the Earth? Yes, it is. The moon is moving about 3.8 cm farther away from the Earth every year. This occurs because of tidal interactions. The moon's gravitational force pulls on the Earth making it bulge ar the face of the Earth the moon is facing. These are called "tidal bulges". The tidal bulges would affect the force of gravity on the moon, as the bulge would have a greater gravitational pull on the moon than the center of the Earth. And since the Earth rotates faster than the moon orbits, the tidal bulges would move ahead of the moon and pull the moon towards the tidal bulge causing the moon to speed up and move ahead in its orbit. Note: The moon is only moved very little by this in a day, so don't get crazy.
Collin Tam  2005