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How Far Is It, and How Do We Know?

by Katie Whitman

Astronomers often quote distances to the Sun, the planets, and other objects in the solar system, such as "the Sun is 93 million miles away" or  "Jupiter orbits an average of 483 million miles from the Sun." These distances are so vast compared to those we experience in our everyday lives that you might begin to wonder, "How do we really know?"

The story of humanity's attempts to understand the size of the solar system begins with the Greek mathematician Eratosthenes (276-192 BCE), who set out to measure Earth's circumference. By comparing the angle of the Sun's rays in the cities of Seyne  (now Aswan) and Alexandria, Egypt, on the summer solstice, he was able to calculate the circumference of the Earth to approximately the correct size. Eratosthenes used a unit called a stadium, whose exact length is not known, since it varied with time and place. Depending on which value he used, the circumference may have been somewhere between 16 percent too large and 1 percent too small.

Sun's rays parallel

The assumption that the Sun's rays are parallel to each other when they arrive at Earth is a good one because the Sun is so far away. Eratosthenes used this assumption to determine the circumference of Earth. Art by Katie Whitman.

In the 17th century, the French mathematician Jean Picard (1620-1682) used triangulation to measure large distances over Earth's surface, resulting in an even more accurate value for Earth's circumference. In the 20th century, satellites provided the key to measuring highly accurate distances on Earth. Now, because of information collected from satellite laser ranging and a specialized network of Global Positioning System (GPS) satellites, we know Earth's equatorial and polar circumferences to within a tenth of a millimeter.

The first to tackle the distance to the Moon was a Greek astronomer, Aristarchus of Samos (310-230 BCE). By carefully observing solar and lunar eclipses, he was able to use geometry to determine the approximate distance to the Moon in terms of Earth's diameter. Today, we know the precise distance to the Moon, thanks to reflector arrays left on the surface of the Moon by the Apollo astronauts. By bouncing laser pulses off of these arrays and measuring the round-trip travel time, scientists are able to measure the distance with submillimeter accuracy.

The struggle to find the distances to the planets and the Sun was a much more difficult one. Using geometry to make these measurements was hampered by the extremely small angles that had to be measured to get meaningful answers. Additionally, until the time of Polish astronomer Nicolaus Copernicus (1473-1543), most people believed that Earth was the center of the solar system, making it difficult to match observations to models of the solar system. In the 1600s, the German mathematician and astronomer Johannes Kepler (1571-1630) made great strides in understanding the solar system by analyzing the extremely accurate and meticulous positions of the planets recorded by Danish astronomer Tycho Brahe (1546-1601). Kepler adopted a Sun-centered solar system and discovered that the planets followed elliptical orbits instead of circular ones, as previously believed. He also found a relationship between a planet's distance from the Sun and the time it takes it to complete an orbit. With Kepler's findings, it was possible to calculate the distances to the planets simply by measuring their orbital periods. The only problem was that these distances were in terms of Earth's orbit. To determine the absolute distances, the distance from Earth to the Sun or another planet was required.

In 1673, the Italian-French astronomer Giovanni Domenico Cassini (1625-1712) was the first to calculate such a distance. He sent his assistant to French Guiana while he remained in Paris. The two observed the parallax of Mars using Earth's diameter as a baseline. They were able to get a distance to Mars that was in error by only 7 percent. Throughout the 18th and 19th centuries, astronomers attempted to measure the distance to the Sun by observing Venus from different locations on Earth as it transited across the Sun's disk. Captain Cook took part in one such transit observation in 1769 from Tahiti. These measurements were fraught with problems and inaccuracies, though the later measurements did differ by only about 3 percent. In 1961, the distance to Venus was measured directly by bouncing a radar signal off of its surface. This enabled us to finally know the scale of the solar system with an uncertainty of only a few thousandths of a percent.

The ability to calculate distances to the heavenly bodies in our solar system is one that was thousands of years in the making. Despite the ingenious efforts made throughout the centuries, it was the technological advances of the 20th century that led to a complete understanding of the vast size of our solar system.

Katie Whitman is a science writer and public outreach specialist for the Center for Computational Heliophysics in Hawaii at the IfA.