Stellar Distances

The universe is so vast and the distances that separate one object from another so immense that if we were to use the same units of measure we use on earth to measure the distance between one object to another, it would require too many zeros in the measured quantity. To measure distances in the solar system, astronomers use the astronomical unit (AU) which is the distance that separates the earth from the Sun (150 million km or 93 million miles).

Mercury is 57.9 million km (36 million miles); Venus 108.2 million km (67 million miles); Mars 227.9 million km (141 million miles); Jupiter 778 million km (482 million miles); Saturn 1427 million km (885 million miles); Uranus 2871 million km (1780 million miles); Neptune 4498 million km (2789 million miles). The Kuiper belt, extending beyond the orbit of Neptune and which is home to the short-period comets, the dwarf planets Pluto, Haumea, Makemake, and an infinite number of icy bodies, is 50 AU from the Sun.

The Oort cloud, which is the source of all long-period comets lies at approximately 50,000 AU from the Sun. the distance from the Sun to Proxima Centauri, the nearest star, is 278,457 AU. The AU can be used to make precise direct measurements within the solar system; however, for greater measurements, astronomers had to come up with other methods of measurement.

One of the most useful resources of distance measurement is obtained from the method of trigonometric parallax. This method uses the fact that a small triangle can be related to a big triangle. Thus, using this method, the parallax angle of a star can be measured when one star is observed against the background of one star on January the 8th, and the same star is observed six months later on July the 8th against the background of another star.

The apparent position of the star in the sky will have shifted a little, forming an angle (parallax angle). Taking the distance that earth traveled on its orbit around the Sun from January the 8th to July the 8th in AU will give you the base of the triangle. Two lines that connect the parallax angle to the base will form a big triangle. Now the rules of trigonometry can be applied and the parallax angle in arc seconds can be obtained.

The parsec is a unit of distance derived from trigonometric parallax. One parsec equals 1/parallax in arc seconds. One arc second is equal to 1/60th of a minute which in turn is equal to 1/60th of one degree. When the parallax shift of a star is one arc second, then the distance in parsecs to that star is one parsec. One parsec is equal to 206,265 AU. The nearest star is at a distance of 0.742 arc seconds, or 1.35 parsecs, or 278,457 AU.

One light year is the distance that light travels in one year. The speed at which light travels is 300,000 km/sec. One light year is equal to 0.31 parsecs or 63,270 AU. If a beam of light were to travel to the nearest star, it would take four hours to cross the orbit of Neptune and 4.4 years to reach Proxima centauri. To get the distance of a star in light years, turn the parallax into parsecs and multiply it by 3.26.