redshift

Redshift is a lengthening of wavelengths, e.g., of spectral lines, due to Doppler effects of radial motion of the radiation source away from the observer (i.e., its recessional velocity). Given the expansion of the universe, redshift is used as a measure of distance and time, and a redshift due to this is called a cosmological redshift.

Smaller redshifts and blue shifts (for the analogous shortening of the wavelength from sources moving toward the observer) are also measured to determine radial velocity in studies of peculiar velocity and of objects orbiting stars such as extra-solar planets and binary star companions. Measurements using specially developed spectrographs can determine radial velocities and radial velocity differences as small as 1 meter per second.

The redshift parameter (often just called redshift) z is:

     observed wavelength - rest wavelength
z =  —————————————————————————————————————
              rest wavelength

The relationship between z and the recessional velocity is:

              1 + v/c
1 + z = sqrt( ——————— )
              1 - v/c

Transverse motion and gravity also produce/affect redshift.

Redshift derived from absorption lines is termed absorption redshift (z_abs) and from emission lines is termed emission redshift (z_em). A difference between the two implies distance and/or velocity differences between the emitting and absorbing material, and can motivate some analysis to determine the "true" cosmological redshift.

When a body's redshift is determined, assuming the redshift is cosmological allows a distance estimate to be calculated using the redshift and the Hubble constant (70 km/s/Mpc). Below are some calculated values. "Linear" was calculated using a simple linear approximation (workable for z less than 0.1) and "Relativistic" takes special relativity into account (the above formula) and is suitable for all redshifts. "GYears" (for gigayears) is how far in the past we're viewing the body and is also its distance in billions of light-years.