We know that the major axis of the ellipse is the longest diameter of the ellipse and passes through both foci. The sum of the distances from any point on the ellipse to the two foci is constant and equal to the length of the major axis.
Let's call the distance from the center of the ellipse to one focus "c." We can find "c" using the equation:
c^2 = a^2 - b^2
where "a" is half the length of the major axis and "b" is half the length of the minor axis.
a = 474000/2 = 237000
b = 473000/2 = 236500
c^2 = 237000^2 - 236500^2
c^2 = 11225000000
c = 105889.77 miles (approximately)
So one focus of the ellipse is about 105,889.77 miles from the center of the ellipse. The distance from the earth to the center of the ellipse is equal to "a," or 237,000 miles.
Therefore, the greatest and least distances from the earth to the moon are:
- Greatest distance: 237,000 + 105,889.77 = 342,889.77 miles
- Least distance: 237,000 - 105,889.77 = 131,110.23 miles
So the moon's distance from the earth varies by about 211,779.54 miles over the course of its orbit.