# How many moons could fit in the Earth?

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Earth has a radius of 6,371 km giving it a volume of 1.083 * 10^{12} km^{3} while Moon has a radius of 1,737 km and a volume of 2.195 * 10^{10} km^{3}. With a simple division we can conclude that the volume of Earth is 49.3 times that of Moon.

If you actually wanted to place spherical.......... moons in a similar space as occupied by Earth and do that without breaking apart the moons then the actual number would be somewhat less than 49. This is because there would be unused space between the spheres where you couldn't fit a whole another moon.

The exact number isn't exactly trivial to calculate. The problem of filling some space with spheres is known as sphere packing. It has been proven that the best possible packing method uses 74% of the space. However this assumes infinite space to be filled with spheres. We can use this to get upper bound for the number by dividing volume of Earth times 0.74 with volume of Moon. This gives us 36. The actual number would still be slightly lower than this.