redshift

Redshift is a lengthening of EMR wavelengths (e.g., seen in observed spectral lines), due to Doppler effects of radial motion of the EMR-source away from the observer (i.e., its recessional velocity). Given the expansion of the universe such that the more distant an object, the higher its recessional velocity, redshift is used as a measure of distance and lookback time, and a redshift due to this is called a cosmological redshift. Redshifts and blue shifts (the analogous shortening of the wavelength from sources moving toward the observer) are also measured to determine radial velocity of the source, such as in studies of peculiar velocity and of objects orbiting stars such as extra-solar planets and binary companions. Measurements of stars using high resolution spectrography (HRS) can determine 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, ignoring relativity (which is OK for low velocity) is z=v/c, where v is recessional velocity and c is the light speed. Incorporating special relativity using the Lorentz transformation (needed for relativistic speeds) is:

1 + z = γ ( 1 + v/c )

where γ is the Lorentz factor, (1-v²/c²)^-½. This is equivalent to:

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

Transverse motion has a small effect on redshift an z, as does gravity (gravitational redshift). Redshift determined through noting the different wavelength of absorption lines is termed absorption redshift (z_abs) and from emission lines is termed emission redshift (z_em).