Brightness & Apparent Magnitude

The Hipparcos scale

• The Hipparcos scaleThe original brightness classification system devised by the ancient Greek astronomer Hipparchus, ranking stars from 1 (brightest) to 6 (faintest visible to the naked eye). classified visible stars on a scale from 1.0 (brightest) to 6.0 (faintest visible to the naked eye).
• As astronomy progressed, this was refined into a precise logarithmic scale, such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star.
• This means that each step of 1 in magnitude corresponds to a brightness change by a factor of $100^{1/5} \approx 2.51$.

Comparing brightness using apparent magnitude

• The key part is that the scale runs backwards: the more negative the apparent magnitude, the brighter the object. For example, the Sun has $m = -26$ while Pluto has $m = +15$.
• To compare the brightness of two objects A and B, use the intensity ratio:

• Where $I_A$ and $I_B$ are the intensities (W m$^{-2}$) and $m_A$, $m_B$ are the apparent magnitudes of objects A and B respectively.
• The naked eye can detect objects as faint as magnitude $+6$. The Hubble Space Telescope can detect objects as faint as magnitude $+31$, which is $2.51^{(31-6)} \approx 10^{10}$ times dimmer than the faintest naked-eye object.