Earth-Moon System Scale Model

It turns out that the balls in two popular sports, basketball and tennis, are almost exactly the right size for an Earth-Moon system scale model. This is a practical follow-up to my article Earth-Moon System to Scale.

Take a standard NBA basketball, which has a circumference of 29.5 in (74.9 cm). The diameter of the basketball is then 9.39 in (23.85 cm). If we let this ball represent the Earth, then it turns out that a standard tennis ball, with a diameter of 6.7 cm (2.64 in), is almost exactly the right size to represent the Moon. The appropriate size to represent the Moon is 23.85 ÷ 12742 x 3475 = 6.5 cm, where 12742 km is the diameter of the Earth and 3475 km is the diameter of the Moon. So, the tennis ball is a mere 2 mm too large.

Again taking the basketball for the Earth, the distance between both should be 0.2385 ÷ 12742 x 384400 = 7.20 m, where 384400 km is the distance between the Earth and the Moon. To be precise, 7.20 m is the distance between the middle of the balls. To get the distance between the outside of the balls, we need to subtract half the diameter of each, which results in 7.20 - (0.2385 + 0.067) ÷ 2 = 7.04 m.

Earth-Moon system scale modelEarth-Moon system scale model

So, if you put a basketball and a tennis ball 7.04 m (7.70 yards) apart, you have an almost perfect scale model of the Earth-Moon system.

As an additional demonstration, you can also show the difference between the shortest and the longest distance in this way. The average distance between the Earth and the Moon is 384400 km, but, since the orbit is not a circle, this distance varies between 363104 km and 405696 km. This takes the distance between the balls from 6.64 m (7.26 yards) to 7.44 m (8.14 yards), a difference of 80 cm (31 in).

If you try any of this and send me a photo, I might add it to this page…

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Submitted by Tom Roelandts on 20 April 2013

Comments

Your picture does not look right but reading everything makes a lot of sense. I think if you have a photo that shows exactly what you did it would look alot better

I agree that the picture doesn't look right, but that's because it's not a real photo. I've just put a basketball and a tennis ball on top of a photo of grass... I count on you to do this in practice and send me the photo! :-)

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