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# Distances within the Galaxy

The distance of the stars is so great that they appear to our eyes motionless on the sky. From ancient times to the beginning of modern astronomy, the stars were treated as fixed objects on a distant sphere. On this subject, Copernicus comments:

All these things [retrograde motion, planetary brightening at opposition, etc.] proceed from the same cause, which resides in the movement of the Earth. But that there are no such appearances among the fixed stars argues that they are at an immense height away, which makes the circle of annual movement or its image disappear from before our eyes since every visible thing has a certain distance beyond which it is no longer seen. (p. 27).1

The nearest stars do have observable motions that are a consequence of their motion through the galaxy and the motion of the Earth around the Sun; but these motions are observable only with fine instruments.

The star's motion that is associated with Earth's motion is called the parallax. By definition, the annual parallax is the apparent motion of a star when the Earth moves 1 AU perpendicular to the star, so a star moves by twice its annual parallax over the course of a year. The nearest stars have an annual parallax of less than 1 arc second. In contrast, the diameter of the Sun on the sky is 32 arc minutes, the diameter on the sky of Venus at inferior conjunction is 1 arc minute,2 the diameter on the sky of Jupiter at opposition is 47 arc seconds,3 and the diameter on the sky of Ganymede, Jupiter's largest moon, at opposition is 1.7 arc seconds. Proxima Centauri (V645 Cen), the closest star to the Sun, has a parallax of 0.77 arc seconds, so its motion is confined to a region of 1.5 arc seconds diameter, slightly smaller than Ganymede's diameter on the sky at opposition.

The distance of a star is derived from its annual parallax by dividing the parallax into the 1AU baseline. Out of convenience, astronomers use a unit of distance that is defined as the distance of an object with an annual parallax of 1 arc second. This distance is the parsec, abbreviated as pc; it is the natural scale of interstellar distances within our Galaxy. The parsec equals 206,264 AU, or about 31 trillion kilometers. Light travels 1 parsec in a little over 3 years. One of our spacecraft, moving at 10 AU per year, would achieve interstellar travel in several tens of thousands of years. From these numbers, you can understand why we astrophysicists are dismissive of claims that spacecraft from other star systems are casually visiting the Earth.

The natural scale of phenomena therefore takes a dramatic leap when we go from the Solar System to the Galaxy. Lets make ourselves feel small by comparing the size of the Galaxy to the size of the Solar System. Locally the distance between the stars is slightly more than 1 pc. Our Sun is in the disk of the Milky Way spiral galaxy. The local thickness of this disk is around 100 pc, our distance from the center of the Galaxy is about 7600 parsecs, or 7.6 kiloparsecs (kpc), and the radius of the galactic disk is about 15 kpc. Therefore, the Galaxy has a radius of 3 billion AU, and the scale of our Galaxy to Earth's orbit is about the same as the scale of a man to an atom. Feeling small yet? We have further to go.

1 Copernicus, Nicolaus. On the Revolution of Heavenly Spheres. Translated by Charles Glenn Wallis. Amherst, New York: Prometheus Books, 1995.

2 A planet is in inferior conjunction when it is between Earth and the Sun. This is an inner planet's point of closest approach to Earth.

3 A planet is in opposition when Earth is between it and the Sun. This is an outer planet's point of closest approach to Earth.