## Q&A: How We Measure the Distance to the Moon

5 May 2014, 07:01 UTCQuestion: I know we’ve been to the Moon, but how do we know exactly how far away it is? I mean, it’s not like you can use a standard odometer in space. Or is it done with GPS or radar or what? — JV, Nantes, France

Answer: An excellent question. The methods for measuring that distance have greatly improved since the first estimates were made. The first attempt was by Hipparchus, around 200 BCE, using the geometric method of parallax. He calculated a distance within 6.8% of the correct value: 384,400 km (238,855 miles).

When Sir Isaac Newton developed his theory of gravity back in the late 17th century, it became possible to calculate the distance to the Moon based on the mass of the Earth and the Moon’s orbital period. That formula is:

R = [(GmT2)/(4π2)]1/3

R = distance to the Moon

G = universal gravitational constant

m = mass of the Earth

T = Moon’s orbital period

The mass of the Earth could be calculated using that same theory (but a different equation), and the Moon’s orbital period was known from direct observation. The universal gravitational constant, however, was not accurately measured until 1798, nearly 71 years ...