Much more interesting, useful, and difficult than measuring angular separation between two objects on the celestial sphere is measuring actual distances to them. (The number of "degrees" between two stars by itself tells you nothing about the distance between).

Accurate distances to faraway galaxies (or equivalently, to objects within faraway galaxies), along with their redshift, are required to derive the value of Hubble's "Constant".

The main ways used for determining remote distances are parallax, standard bar, and standard candle.

  • Radar can be provide very accurate distances, but only to the near planets (~1 billion kilometers) because the signal fades quickly.
  • Parallax: Trigonometric parallax is the well-known effect of the Earth's rotation around the Sun giving rise to a change in the position of stars on the celestial sphere. For "very close" distances we can use trigonometric parallax, where "very close" means up to 1 kpc (kiloparsec: the diameter of the Milky Way is 50 kpc; our sun is 8 kpc from the center of the Milky Way). Secular parallax is similar, but uses the Sun's motion with respect to the local standard of rest (16.5 km/s around the galaxy).
  • A standard bar is an object whose actual size is known. Then the distance to it is easily determined using its angular size and trigonometry.
    • Ejecta from type II supernovae have predictable radii.
  • A standard candle is an object whose intrinsic brightness (absolute magnitude) is already known; thus using its flux (apparent magnitude: amount of light received at earth) we can figure out its distance.
    • Cepheids and other pulsating stars have luminosities predictable from their pulsation period. They are accurate up to 15 kpc.
    • Spectroscopic parallax (which is mis-named because it does not use the concept of parallax): some stars have specific features in their spectra that allow their type on the Hertzsprung-Russel diagram and thus their luminosity, to be determined. Accurate up to 7 Mpc (mega parsecs = million parsecs).
    • Tully-Fischer, Faber-Jackson: Spiral and elliptical galaxies, respectively, have luminosities related to their maximum rotation velocities and rotation dispersions. Reliable exceeding 100 Mpc.
    • Type Ia Supernovae all have the same maximum luminosities because they only occur when a White Dwarf in a semidetached binary system reaches an certain mass (1.4 solar masses). Reliable exceeding 1000 Mpc.

How do we know how bright or long something actually is? We use the concept called the extragalactic distance scale, or the cosmological distance ladder. For example, some Cepheids are close enough that we can use plain ol' parallax to find their distance. With their apparent magnitude and distance we determine their absolute magnitude, and thus the absolute magnitude of all Cepheids. By juggling the three variables of absolute magnitude, relative magnitude, and distance, we can climb the distance ladder and get the distances to objects literally billions of light years away.