Apparent magnitude

Apparent magnitude, $$m$$, describes how bright a star appears when observed from Earth. Brightness is a subjective visual perception; the received light intensity is a physical quantity that can be measured. Apparent magnitude uses received intensity to express apparent brightness numerically.

The scale runs in the opposite direction to intensity: a star with a lower apparent magnitude has a greater received light intensity and appears brighter.

Origin of the magnitude scale

The scale originated with Hipparchus’s classification of visible stars. He assigned smaller magnitudes to brighter stars and magnitude $$6$$ to the dimmest visible stars. Under good observing conditions, magnitude $$6$$ is approximately the limit for seeing stars with the naked eye.

Comparing apparent magnitudes

A difference of one magnitude corresponds to an intensity ratio of approximately $$2.51$$. For example, a magnitude $$2$$ star has approximately $$2.51$$ times the received intensity of a magnitude $$3$$ star.

For two stars with apparent magnitudes $$m_1$$ and $$m_2$$ and received intensities $$I_1$$ and $$I_2$$, respectively:

The order in the exponent preserves the reversed scale. If star 1 has the lower magnitude, $$m_2-m_1$$ is positive, so $$I_1/I_2$$ is greater than $$1$$. For example, a star of magnitude $$1$$ has approximately $$2.51^2 \approx 6.3$$ times the received intensity of a star of magnitude $$3$$.