Parallax

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Parallax

Parallex, in astronomy, is the apparent shift (that is, change of angular position) of two stationary objects relative to each other as perceived by an observer whose position is changing (as in an astronomer on a moving Earth). Astronomers must use very indirect methods to measure the distances to stars and other astronomical objects. Measuring a star’s parallax is a way to find its distance. This method takes advantage of the apparent shift in position of a nearby star as it is observed from different positions as the Earth orbits the sun. Because the parallax effect depends upon the Earth’s motion about the sun, it is often referred to as the heliocentric parallax.

How parallax works

To understand how parallax works, hold one’s thumb in front of the face. Alternately open and close each eye and notice how the thumb appears to move back and forth with respect to the background wall. Now move the thumb closer to the face and notice how this effect increases as the distance between the eyes and thumb decreases. This apparent motion (its only apparent because the thumb did not really move) is called the parallax. The brain subconsciously uses information from both eyes to estimate distances. Because the distance estimates require observation from two points, people who have lost an eye will lack this depth perception. Thus, a parallax is any apparent shift in the position of an object caused by a change in the observation position.

As Earth orbits the sun, astronomers can observe a nearby star at six-month intervals with Earth on opposite sides of the sun. The nearby star appears to move with respect to the more distant background stars. Note that the star (like the thumb) is not really moving. The parallax effect is an apparent motion caused by the motion of the observation point (either to the other eye or to the opposite side of the sun). The closer the star, the larger will be its apparent motion. This parallax, when combined with the principles of geometry and trigonometry, can be used to find the distance to stars that are relatively close. Closer stars will have a larger parallax.

Astronomers measure the parallax in the form of an angle. For even nearby stars these angles are quite small. The closest star to the sun, Proxima Centauri, has a parallax angle of less than 1 second of arc. A second of arc is 1/3600th of a degree (1°= 60 minutes of arc= 3,600 seconds of arc, 1 minute of arc= 60 seconds of arc). At a distance of 3 mi (5 km), a quarter will have an angular diameter of roughly 1 second of arc. Measuring such small angles is obviously difficult, but astronomers have managed to overcome the difficulties, detecting parallax for the first time in 1838.

The parallax angle is defined as one half of the apparent angular motion of the star as Earth orbits from one side of the sun to the opposite side. This definition is the same as the apparent motion that would be observed if the two observation points were the sun and Earth. Once this angle is measured, the distance between the sun and the star is the Earth-sun distance divided by the tangent of the parallax angle.

To simplify this calculation astronomers use a distance unit called a parsec (short for parallax-second). A parsec is the distance to a star that has a parallax angle of exactly one second of arc. One parsec is 206,265 times the distance between Earth and the Sun, 3.086 × 10¹³ kilometers, or 3.26 light-years (where one light-year is the distance that light travels in vacuum in one year). The distance to a star in parsecs is then simply 1 divided by the parallax angle measured in seconds of arc.

Parallax measurements

In the sixteenth century, Polish astronomer Nicolaus Copernicus (1473–1543) proposed that Earth and planets orbited the sun. At the time, one of the arguments proposed against the Copernican view was that there should be a heliocentric parallax if the sun was indeed the center of the solar system. However, no such parallaxes had been observed. Copernicus countered rather simply by stating that the stars were much farther away than anyone had ever imagined, so the parallax was too small to observe. When astronomers finally managed to measure a parallax, it turned out that Copernicus was right.

Astronomers did not succeed in measuring a parallax angle until 1838, when three astronomers working independently measured the parallaxes of three different stars. German mathematician and astronomer Friedrich Wilhelm Bessel (1784–1846) in Germany, Scottish-South African astronomer Thomas James Henderson (1798–1844) in South Africa, and Baltic-German astronomer Friedrich Georg Wilhelm von Struve (1793–1864) in Russia measured the parallaxes of the stars 61 Cygni, Alpha Centauri, and Vega, respectively.

From the ground, astronomers are now able to measure accurately parallaxes for only about 1,000 stars that are within 20 parsecs of the sun. This

KEY TERMS

Heliocentric parallax —The parallax caused by the Earth orbiting the Sun.

Light-year —The distance light travels in one year, roughly 9.5 trillion kilometers or 6 trillion miles.

Parallax —An apparent change in position of an object caused by a change the observation position.

Parsec —The distance at which a star will have a parallax angle of one second of arc, 3.26 light years.

Second of arc —An angular measurement, 1/3600th of a degree.

ground-based limit requires measuring parallax angles that are as small as 1/20th of a second of arc. The quarter mentioned above is now 62 mi (100 km) away. For greater distances, astronomers must use even more indirect methods, which build on the distances found by parallax measurements. Improving the accuracy of parallax measurements will also improve the accuracy of the indirect methods that depend on parallaxes.

Earth’s atmosphere limits the accuracy of parallax measurements from the ground, by limiting the resolution (sharpness) of a stellar image. Sharper images, and therefore more accurate parallax measurements, require getting above Earth’s atmosphere. In 1989, the European Space Agency launched the Hipparcos (High Precision Parallax Collecting Satellite), with the mission of measuring the parallaxes of roughly 120,000 stars. It accomplished its goal, and was shutdown in August 1993. NASA’s Hubble Space Telescope is also capable of measuring parallaxes far more accurately than they can be measured from the ground. These accurate parallax measurements from these space missions enable accurate distance measurements to a large sample of stars. Accurate distances will both help scientists attain more accurate measurements of the fundamental properties of stars, therefore increasing scientific understanding of stellar structure, and improve the accuracy of the cosmic distance scales.