How far away is the Moon? Hipparchus first calculated the distance in 190BC using a simple method using trigonometry and was accurate to 1,000km!
In order to calculate the distance to the Moon, we must first consider two observers on the surface of Earth.
The first observer, A, can see the Moon on the horizon, while the second observer, B, sees the Moon directly overhead at exactly the same time.
The distance between the two observers can be used to calculate the angle, theta Θ, and using trigonometry we can solve for d.
Where a is the angular distance between the two observers and r is the radius of the Earth. The radius of the Earth had already been calculated nearly one hundred years earlier by Eratosthenes so we just need to measure the distance between the two observers to find the angle tan Θ. We can then calculate d using the formula below.
Using this exact method, Hipparchus was able to calculate the distance as 59 Earth radii, or 397,000km. This is very close to the modern measured figure of 382,000km.
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