Cosmic Distances

The Universe is huge. Astronomers think the visible part is some 92 billion light years across – and it may stretch out well beyond that. It is so vast that measuring distances in feet, miles, and kilometers just doesn’t work.

Planets in our Solar System are millions or billions of miles away, but it is more convenient to use something called an Astronomical Unit (au). This is the average distance of the Earth to the Sun, which is just under 93 million miles. As an example, Mars is on the average 141.6 million miles from the Sun (around 1.5 au). Neptune, the farthest official planet from the Sun, is around 2.8 billion miles out in the Solar System, which is 30 au. As an aside, the IAU says that the appropriate abbreviation for astronomical unit is au, not AU or A.U.

As we move out to stellar distances, a light year is a more useful unit. A light year is the distance light travels in a year (5.88 trillion miles). This is based on the speed of light in a vacuum, which is 300,000 km/sec or 186,000 miles/sec. Proxima Centauri, the closest star to the Sun, is 4.25 light years away. The Andromeda galaxy is around 2 ½ million light years. Just to make sure, a light year is a DISTANCE measurement and NOT a time measurement.

Parallax

Astronomers use parallax to find the distance to nearby stars. As the Earth moves from one side of the Sun to the other, nearby stars appear to shift their position in a way your finger will appear to move when you hold it at arm’s length and alternate opening and closing one eye.

We can use parallax to find the distance to a star (D) using the distance from the Earth to the Sun (d), and the angle (2a) with which the star appears to shift over a six-month period. From the diagram below, tangent (a) = d/D, therefore the distance to a star is, D = d / tangent (a). If the angle, a, is small, then tangent (a) = a when measured in radians. Therefore, D = d / a_radians.

A parsec (PARalax SECond) is the distance at which a star’s parallax, using the Earth-Sun distance (1 au) as a base, is 1 arcsecond. In other words, the star’s apparent position will shift by 2 arcseconds over a six-month period. A parsec turns out to be 3.262 light years. A Megaparsec (Mpc) is one million parsecs or 3.262 x 10⁶ light years.

This page is taken from a previous FAS Astronomers Blog, Cosmic Distances, Stellar Brightness, and the Hubble Constant.