The average distance to the 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).
(Here’s a trick to remembering which is which – “apogee”, starts with “A”, just like going “away”).
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.
When it’s a Full Moon, and it’s a close Moon, that’s a Supermoon; also known as a perigee-syzygy.
The total illumination from the Moon can change more than thirty percent from Full Moon to Full Moon, depending on how far away the Moon is when things line up.
So, how do we know how far away the Moon is?
The light is moving at almost 300,000 kilometers per second, it takes a little more than a second to make the journey. And then it takes another second or so to return. Astronomers calculate the exact amount of time it takes for light to make the journey. They know exactly how far the Moon is at any time, down to millimeter accuracy.
As a result, Astronomers have discovered that the Moon is slowly drifting away from us, at a glacial 3.8 centimeters each year. Billions of years in the future, the Moon will appear smaller in the sky than it does today. Within a billion years or so, the Moon will be visually smaller than the Sun, and we won’t see total solar eclipses any more.
We have recorded a whole episode of Astronomy Cast focused just on the Moon. Give it a listen.