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The average distance from Earth to Moon is 384,403 km (238,857 miles).
Before you put this answer into your homework you’ve got to understand that the Moon takes an elliptical path around the Earth. That number, 384,403 km is an average distance that astronomers call the semi-major axis. The Moon can get closer to the Earth and it can get further.
At its closest point, known as the perigee, the Moon is only 363,104 km (225,622 miles). And at its most distant point, called apogee, the Moon gets to a distance of 406,696 km (252,088 miles).
You can see that the distance from Earth to Moon can vary by 43,592 km. That’s a pretty big difference, and it can make the Moon appear dramatically different in size depending on where it is in its orbit. For example, take a look at this animation from the Goddard Space Flight Center Scientific Visualization Studio which shows the geocentric phase, libration, position angle of the axis, and apparent diameter of the Moon throughout the year (this was created for 2011), at hourly intervals.
It’s pretty amazing how well we know the distance between Earth and Moon so accurately. In fact, astronomers know this distance within a few centimeters. How do we know it so well? When the astronauts landed on the Moon during the Apollo program, they left smaller reflective mirrors on the surface of the Moon. Astronomers point lasers at the Moon, which travel all the way to the Moon and then bounce off and return back to Earth. By calculating the length of time light takes to make the return journey, and knowing the speed of light with incredible accuracy, they can calculate the Moon’s distance.
Here’s an article about how the ancient astronomer Aristarchus calculated the distance in 270 BC.
We have recorded a whole episode of Astronomy Cast focused just on the Moon. Give it a listen.