9.2.1 Brightness & Apparent Magnitude

• Apparent magnitude m is defined as

The perceived brightness of a star as seen from Earth

• The value of m is a number with no unit
• The Hipparcos scale of apparent magnitude initially classified brightness by assigning values from 1.0 to 6.0, where
  • Magnitude 1.0 represented the brightest stars that could be seen with the naked eye
  • Magnitude 6.0 represented dimmer stars that were only just visible to the naked eye

• As astronomy progressed, the Hipparcos scale was able to be defined more precisely as a logarithmic scale
• This allows stars to be compared meaningfully in terms of their brightness, or intensity, such that:

A magnitude 1 star is 100 times brighter than a magnitude 6 star

• This means that a change of 5 orders of magnitude corresponds to:
  • m = 6 → m = 1:  an increase in brightness by a factor of
  • m = 1 → m = 6:  a decrease in brightness by a factor of

• Therefore, for a change of 1 order of magnitude:
  • Magnitude decreases by 1 (e.g. m = 6 → m = 5):  brightness increases by a factor of
  • Magnitude increases by 1 (e.g. m = 1 → m = 2):  brightness decreases by a factor of

• To compare the brightness of two objects, A and B, we can write an expression in terms of the ratio of their intensities:

• Where:
  • = intensity of object A (W m⁻²)
  • = intensity of object B (W m⁻²)
  • = apparent magnitude of object A
  • = apparent magnitude of object B

The Relationship between Apparent Magnitude & Brightness

Each order of magnitude on the apparent brightness scale represents an increase or decrease in brightness by a factor of 2.51

• Since the invention of the telescope, the scale has been expanded, so that
  • The more negative the apparent magnitude, the brighter an object appears e.g. the Sun has an apparent magnitude of −26
  • The more positive the apparent magnitude, the fainter an object appears e.g. Pluto has an apparent magnitude of 15

Apparent Magnitudes of Common Astronomical Objects

This scale shows that the most visible object in the sky is (unsurprisingly) the Sun and that objects such as Venus and the star Polaris are easy to spot with the naked eye, whereas Pluto is not

• The full apparent magnitude scale is a powerful tool for comparing and quantifying differences in brightness
  • For example, the naked eye can detect objects as faint as magnitude +6
  • The Hubble Space Telescope (HST) can detect objects as faint as magnitude +31

• This means that the faintest object that can be detected by the HST is 10¹⁰ times dimmer than the faintest object that can be detected by the naked eye!