How Do You Measure the Distance to the Moon, Planets, Stars and Beyond?

Credit: B. Viana/NIST

 From ancient Greek mathematicians to modern-day astrophysicists, the quest to measure the distances to the Sun, Moon, planets, stars and galaxies has fueled the advancement of science and is expanding our understanding of the universe.

These measurements range from simple observational techniques to sophisticated methods that probe the farthest reaches of space.

Parallax Method

One of the earliest methods used to measure distances to celestial bodies is parallax, which involves observing the apparent shift in the position of a distant object against a background of more distant stars as the observer's viewpoint changes. This method can be easily demonstrated by holding out your thumb and looking at it with one eye closed, then switching eyes. The apparent shift in your thumb's position is parallax in action.

The Earth is on opposite sides of the Sun every six months. From these different vantage points, a celestial object will appear to be in different parts of the sky. Scientists can calculate the distance to a heavenly object by measuring the angle between those two positions. The greater the shift in the position, the closer the object is to Earth. The smaller the shift, the farther away it is. This method, formally described by the Greek mathematician Hipparchus in the second century B.C.E., laid the groundwork for future advances.

Significant progress came in the late 17th century when Giovanni Domenico Cassini used parallax to measure the distance to Mars. Later, during the 18th century, astronomers calculated the Earth-to-Sun distance more accurately by using Venus transits — the shift in Venus’ position as it moves across the Sun.

The first accurate measurements of the average distance between the Sun and Earth, which came to be known as the astronomical unit, were made during the transits of Venus in 1761 and 1769 by an international group of astronomers positioned at different places around the world.

Measuring Great Distances

While parallax is helpful for measuring the distance to objects that are relatively close to us, it becomes increasingly difficult to measure the distance to objects that are farther away. The angle between the object and the background becomes extremely small, making it difficult to measure accurately.

In 1908, astronomer Henrietta Swan Leavitt developed the concept of stars as “standard candles” while studying Cepheid variable stars, which pulse in brightness predictably over time. The amount of time it takes for a Cepheid to go through a complete pulsation cycle — known as the period — is related to its intrinsic brightness, or how bright it would appear at zero distance from the star. If astronomers observe two Cepheid stars with the same period, but different brightness, they know the dimmer one is farther away. This allows astronomers to calculate their distances based on how dim they appear from Earth.

Since then, other types of standard candles, such as exploding stars, or supernovae, have been discovered, enabling measurements of even greater cosmic distances.

Around the same time Leavitt discovered standard candles, American astronomer Vesto Slipher observed a phenomenon known as redshift, another crucial technique for measuring distances to galaxies. When an object moves away from us, its light stretches to longer wavelengths, appearing redder. More distant stars move away from us faster than closer stars. The redder a star appears, the farther away it is.

Redshift is a kind of “Doppler effect,” which we experience in everyday life. When an ambulance moves away from you, you hear its siren become lower-pitched — that’s because as the vehicle recedes in the distance, the sound waves spread apart as they reach your ear, resulting in a longer-wavelength, lower-frequency sound. The faster it moves away, the lower-pitched it sounds, just as the faster a star is moving away, the more its light shifts to a redder, longer-wavelength color.  

Redshift is crucial for understanding the expansion of the universe. By measuring the redshift of distant galaxies, astronomers can determine not only their distance but also their velocity relative to Earth. This has led to the discovery that the universe is expanding, with more distant galaxies moving away from us faster than closer ones.

In 1964, American radio astronomers discovered the cosmic microwave background (CMB), the faint glow of microwave radiation that fills the universe, left over from the Big Bang. By analyzing how the temperature and intensity of the CMB varies across the sky, astronomers can obtain accurate values of the Hubble constant, which currently describes the rate at which the universe is expanding. With that information, we can more accurately calculate the distance to far-off galaxies based on their redshift. This method provides a cosmic scale that helps us understand the structure and evolution of the universe.

Modern Measurements for Our Solar System and Beyond

Exploring distance in deep space is all well and good, but to measure nearby objects within our own solar system, modern-day scientists employ highly precise laser and radar techniques.

For instance, a technique known as lunar laser ranging uses powerful lasers to measure the Earth-Moon distance with millimeter-level accuracy. Because we know the speed at which light travels, scientists can calculate the distance to an object by sending a pulse of radio or light waves toward it and measuring the time it takes for the waves to bounce back.

To measure the distance between Earth and the Moon, scientists time how long it takes for laser pulses to bounce back from retroreflectors that were placed on the Moon’s surface by Apollo astronauts.

The National Institute of Standards and Technology (NIST) plays a vital role in these measurements by providing ultraprecise time and frequency standards. NIST’s atomic clocks are essential for many astronomical measurements.

NIST’s work on frequency combs and ultrastable lasers has enhanced the precision of distance measurements within our solar system and gravitational wave detection, which relies on measuring extremely small changes in distance caused by ripples in space-time.

The calibration standards and measurement techniques defined by NIST are crucial for missions like NASA’s James Webb Space Telescope, which aims to observe some of the most distant objects in the universe.

The measurement of celestial distances has come a long way since the early days of parallax observations. As our technology and understanding advance, we can explore even deeper into the cosmos. These measurements not only satisfy our natural curiosity about the scale of space but also provide crucial data for understanding our universe and our place within it.

The work at NIST was funded in part by the National Aeronautics and Space Administration.