Brightness and distance

Sirius looks brighter than Rigel, yet Rigel gives off thousands of times more light; it is about 100 times farther away.

Two kinds of brightness

A candle on the table can look brighter than a lighthouse on the horizon. Astronomers separate the two ideas. Apparent brightness is how bright a star looks from here. Luminosity is how much light the star actually gives off, measured in watts or in Suns. Sirius is the brightest star in the night sky because it is both fairly luminous, about 26 Suns by the formula from the last unit, and close, 8.6 light-years away. Rigel, about 860 light-years away, gives off about 120,000 Suns of light, yet looks fainter than Sirius.

The rule that links them is the inverse-square law. Light from a star spreads out over a sphere, and the area of a sphere grows with the square of its radius. Twice as far away, the same light covers four times the area, so each square metre gets a quarter as much. Ten times farther, one hundredth. Rigel is 860 ÷ 8.6 = 100 times farther than Sirius, which by itself makes it 10,000 times fainter. Its luminosity is only about 4,700 times Sirius A's, so it ends up looking dimmer.

Light-years and parsecs

Distances to stars are so large that kilometres stop being useful. A light-year is the distance light travels in one year, about 9.46 trillion km. It is a distance, not a time. NASA gives Proxima Centauri at 4.24 light-years, about 40 trillion km, and Alpha Centauri A and B at 4.37. Because light takes time, every star is seen as it was: NASA notes that when you look at Betelgeuse, about 700 light-years away by its estimate, you see light that left it about 700 years ago.

Professional astronomers more often use the parsec, which comes straight from how nearby distances are measured. As Earth goes round the Sun, a nearby star seems to shift a little against much more distant stars, the way your thumb jumps when you close one eye and then the other. Half of that yearly shift is the parallax angle. A star with a parallax of one arcsecond (1/3,600 of a degree) is one parsec away, about 3.26 light-years. Distance in parsecs = 1 ÷ parallax in arcseconds. Proxima's parallax is about 0.77 arcseconds, the largest of any star. ESA's Gaia mission measures parallaxes for well over a billion stars.

Magnitudes

The oldest brightness scale is usually credited to the Greek astronomer Hipparchus, who is said to have called the brightest stars first magnitude and the faintest he could see sixth. The modern version keeps the backwards direction, smaller numbers are brighter, and fixes the steps: 5 magnitudes is a factor of exactly 100, so 1 magnitude is a factor of about 2.512. The Sun's apparent magnitude is −26.74 and Sirius is about −1.46, so the Sun looks about 13 billion times brighter. Absolute magnitude is how bright a star would look from a standard 10 parsecs; for the Sun it is +4.83, a faint star you could barely see from a dark site.