Standard Candles

Parallax only works for relatively nearby stars. For more distant objects astronomers use standard candles: astronomical objects whose luminosity is known.If L is known, measuring the intensity I received at Earth gives the distance by rearranging the inverse square law, I = L/4πd²:d = √(L ÷ 4πI)Two important standard candles are:• Cepheid variables: pulsating stars whose brightness rises and falls regularly, with periods of days to weeks. Their period is related to their luminosity (a longer period means a more luminous star), so measuring the period gives L. Cepheids are bright enough to be seen in nearby galaxies.• Type Ia supernovae: explosions of white dwarfs in binary systems. They all reach about the same peak luminosity, and are so bright that they can be seen in very distant galaxies.The luminosities of standard candles are calibrated using nearby examples whose distance is already known from parallax. Each method is used to check the next one out, building up a 'distance ladder'.Worked example: a Cepheid has L = 4.0 × 10³⁰ W and the intensity at Earth is 1.0 × 10⁻¹² W m⁻².d = √(4.0 × 10³⁰ ÷ (4π × 1.0 × 10⁻¹²)) = 5.6 × 10²⁰ mThat is about 18 000 pc, far beyond the range of parallax.