Astronomical Distances

The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. Credit: SciTech Daily
The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. Credit: SciTech Daily

The Cosmic Distance Ladder

The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are close enough (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances with methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.

The ladder analogy arises because no one technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.

The Astronomical Unit (AU)

An astronomical unit (abbreviated as au) is a unit of length now defined as exactly 149,597,870,700m (92,955,807.3 mi), or roughly the average Earth–Sun distance. Historically, observations of transits of Venus were crucial in determining the AU; in the first half of the 20th Century, observations of asteroids were also important. Presently the AU is determined with high precision using radar measurements of Venus and other nearby planets and asteroids, and by tracking interplanetary spacecraft in their orbits around the Sun through the Solar System. Kepler’s Laws provide precise ratios of the sizes of the orbits of objects revolving around the Sun, but not a real measure of the orbits themselves. Radar provides a value in kilometers for the difference in two orbits’ sizes, and from that and the ratio of the two orbit sizes, the size of Earth’s orbit comes directly.

Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties and the rarity of observations. Source: NASA
Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties and the rarity of observations. Source: NASA

Parallax

The most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits around the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in a right triangle, with 2 AU making the short leg of the triangle and the distance to the star being the long leg. The amount of shift is quite small, measuring 1 arcsecond for an object at a distance of 1 parsec (3.26 light-years), thereafter decreasing in angular amount as the reciprocal of the distance. Astronomers usually express distances in units of parsecs; light-years are used in popular media, but almost invariably values in light-years have been converted from numbers tabulated in parsecs in the original source.

Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars whose parallax is larger than the precision of the measurement. Parallax measurements typically have an accuracy measured in milliarcseconds. In the 1990s, for example, the Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond, providing useful distances for stars out to a few hundred parsecs.

Using Parallax  to measure a star as seen from earth 6 months aparts. Credit: ESA Science & Technology:
Using Parallax to measure a star as seen from earth 6 months aparts. Credit: ESA Science & Technology:

Standard Candle

A standard candle is an astronomical object that has a known absolute magnitude. They are extremely important to astronomers since by measuring the apparent magnitude of the object we can determine its distance using the formula:

m-M = 5 log d – 5

where m is the apparent magnitude of the object, M is the absolute magnitude of the object, and d is the distance to the object in parsecs.

The most commonly used standard candles in astronomy are Cepheid Variable stars and RR Lyrae stars. In both cases, the absolute magnitude of the star can be determined from its variability period.

The Standard Candle approach to measuring distance. Credit: Univ. of California
The Standard Candle approach to measuring distance. Credit: Univ. of California

A Complete Chart of Measuring Objects in the Universe

A Complete Chart of Measuring Objects in the Universe
A Complete Chart of Measuring Objects in the Universe. Credit: Univ. of California