« What Is Parallax? »

" Astronomers use a technique called parallax to precisely measure to distance to stars in the sky. Using the technique, which requires observing targets from opposite sides of Earth's orbit around the sun, astronomers have pinpointed the distance to the famed "Seven Sisters" star cluster, the Pleiades. Astronomers estimate the distance of nearby objects in space by using a method called stellar parallax, or trigonometric parallax. Simply put, they measure a star's apparent movement against the background of more distant stars as Earth revolves around the sun.Parallax is “the best way to get distance in astronomy,” said Mark Reid, an astronomer at the Harvard Smithsonian Center for Astrophysics. He described parallax as the “gold standard” for measuring stellar distances because it does not involve physics; rather, it relies solely on geometry. The method is based on measuring two angles and the included side of a triangle formed by the star, Earth on one side of its orbit and Earth six months later on the other side of its orbit, according to Edward L. Wright, a professor at UCLA.If we do not know the distance to an object, it is not possible to measure an apparent sideways change in its position against the background in length units. However, we can measure it in angular units, i.e., the portion of a complete circle the object appears to move against the background.Once we have determined the apparent angular displacement of the object caused by viewing it from a different angle, or its parallax, we need to measure the distance between the observation points, or the baseline. We then take the baseline measurement and divide that by the tangent of the parallax angle to obtain the distance to the object.To measure the distance of a star, astronomers use a baseline of 1 astronomical unit (AU), which is the average distance between Earth and the sun, about 93 million miles (150 million kilometers). They also measure small angles in arcseconds. One arcsecond is a tiny angle. It is equivalent to a lateral shift in position of 0.017 inches seen from 100 yards (0.48 millimeters at 100 meters).If we divide the baseline of one AU by the tangent of one arcsecond, it comes out to about 19.2 trillion miles (30.9 trillion kilometers), or about 3.26 light years. This unit of distance is called a parallax second, or parsec (pc). There is a reciprocal relationship between distance and parallax. For example, a star with a parallax of half an arcsecond would have a distance of 2 pc, and a star with a parallax of one-tenth of an arcsecond would have a distance of 10 pc.However, since no stars are close enough to have a parallax of 1 arcsecond, measurements have to be even more precise than that. This made measurement of parallax quite difficult for early astronomers.The first known astronomical measurement using parallax is thought to have occurred in 189 B.C., when a Greek astronomer, Hipparchus, used observations of a solar eclipse from two different locations to measure the distance to the moon, Reid said.Hipparchus noted that on March 14 of that year there was a total solar eclipse in Hellespont, Turkey, while at the same time farther south in Alexandria, Egypt, the moon covered only four-fifths of the sun. Knowing the baseline distance between Hellespont and Alexandria — 9 degrees of latitude or about 600 miles (965 km), along with the angular displacement of the edge of the moon against the sun (about one-tenth of a degree), he calculated the distance to the moon to be about 350,000 miles (563,300 km), which was nearly 50 percent too far. His mistake was in assuming that the moon was directly overhead, thus miscalculating the angle difference between Hellespont and Alexandria.In 1672, Italian astronomer Giovanni Cassini and a colleague, Jean Richer, made simultaneous observations of Mars, with Cassini in Paris and Richer in French Guiana. Cassini computed the parallax, determined Mars' distance from Earth. This allowed for the first estimation of the dimensions of the solar system.The first person to succeed at measuring the distance to a star using parallax was F.W. Bessel, who in 1838 measured the parallax angle of 61 Cygni as 0.28 arcseconds, which gives a distance of 3.57 pc. The nearest star, Proxima Centauri, has a parallax of 0.77 arcseconds, giving a distance of 1.30 pc.Parallax is an important rung in the cosmic distance ladder. By measuring the distances to a number of nearby stars, astronomers have been able to establish relationships between a star’s color and its intrinsic brightness, i.e., the brightness it would appear to be if viewed from a standard distance. These stars then become “standard candles.”Then if a star is too far away to measure its parallax, astronomers can match its color and spectrum to one of the standard candles and determine its intrinsic brightness, Reid said. Comparing this to its apparent brightness, we can get a good measure of its distance by applying the 1/r2 rule."