Measuring Star Brightness

Measuring Large Distances

One of the ways to measure is parallax. It depends on the change of the observer's position. As seen in the illustration below, as the Earth orbits the sun, we move in respect to the star. After measuring the visual shift of the star in opposite ends of the orbit, the distance to the star can be calulated. For stars which are far away, the formula can be approximated to:

d = 1 p , where p is the parallax of the star in arcseconds (1 degree = 3600 arcsec), and d is the distance to the star in parsecs (1 parsec is approximately 3.26 light years).

The Magnitude Scale

An Ancient Greek astronomer, Hipparchus, developed a scale, where the stars in the sky were given one of six magnitudes. The brightest stars had a magnitude of 1, and the dimmest were marked with a magnitude of 6.

A similar system is still used by astronomers today. The scale is logarithmic due to human senses: the strength of the perception of a stimulus is proportional to the logarithm of the intensity of the stimulus.

The magnitude of a star can be calculated by this formula:

m = -2.5 log F + C, where m is the magnitude of the star in mag (magnitudes), C is a constant, and F is the flux in W⋅m^-2. From this formula, it can be found, that:

m₁ - m₂ = -2.5 log F₁ F₂

The brighter the star or other object, the smaller the magnitude. If one star is 100 times brighter than the other, it's magnitude will be smaller by 5. For more information about Flux and radiation, check the course 'How Stars Shine'.

Absolute Magnitude

Absolute magnitude is a measure that makes it possible to compare the brightness of stars regardless of how far they are from Earth. It is defined as the magnitude of the star when the observer is 10 parsecs away. It can be calculated by:

m - M = 5⋅log(d) - 5 , where d is the distance in parsecs, M is the absolute magnitude, and m is the apparent magnitude, both measured in mag.

Interactive Activity

Practice Question