# How Far Away is the Moon? And How Do We Measure Distance?

Last Updated June 6, 2023 by Tim Trott. First Published in 2008.

Hipparchus first calculated how far away is the Moon in 190BC using a simple method involving trigonometry and was accurate to 1,000km!

The moon has fascinated humans for centuries, but have you ever wondered how far away it really is? Scientists have developed several methods to measure the distance between Earth and the moon, including using lasers and radar. In this article, we'll explore these methods and learn more about the moon's distance from our planet.

## Hipparchus Was the First to Answer the Question How Far Away is the Moon?

In 190 BC, Hipparchus calculated the distance to the moon as 397,000km using simple trigonometry. Modern laser-guided measurements have shown that the average distance to the Moon is 382,000km. So how did Hipparchus achieve this remarkably accurate measurement over 2,000 years ago?

Hipparchus wasn't the first to try and calculate this distance. Both Eratosthenes and Aristarchus tried, but it was Hipparchus who was able to satisfy all his peers that his assumptions and hypothesis were accurate.

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 the same time.

The distance between the two observers can be used to calculate the angle, theta θ, and using some basic trigonometry we can solve for *d*.

Equation 4 - Moon distance calculation

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.

Equation 5 - Tan theta solved for d

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.

## How Far Away is the Moon Using Modern Equipment and Techniques?

Radar ranging is a method which involves bouncing a radar signal off the surface of the moon and measuring the time it takes for the signal to return to Earth. By knowing the speed of the radar signal and the time it takes to travel to the moon and back, scientists can calculate the distance to the moon. This method was first used in the 1960s during the Apollo missions and has since been used to refine our understanding of the moon's distance and orbit.

Laser ranging is another method used to calculate the distance to the moon. This method involves firing a laser beam at a reflector placed on the surface of the moon by the Apollo missions and measuring the time it takes for the beam to return to Earth. By knowing the speed of light and the time it takes for the beam to travel to the moon and back, scientists can calculate the distance to the moon with incredible accuracy. Laser ranging has been used since the 1960s and continues to be a valuable tool for studying the moon's distance and orbit.

## The Importance of Accurate Distance Measurements

Accurate distance measurements to the moon are crucial for a variety of scientific endeavours, including space exploration, astronomy, and geology. Knowing the exact distance to the moon allows scientists to calculate its orbit, study its surface features, and plan missions to explore it. In addition, precise measurements of the moon's distance can help us better understand the dynamics of the Earth-moon system and the effects of gravitational forces on our planet.

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