Show me the sky!

The brightness of celestial objects in the sky is a key characteristic that astronomers observe. This brightness can either be emitted directly by the object, such as in the case of stars, or reflected from a star, like planets.

Objects vary in their brightness, with some being brighter than others. For instance, the Sun is brighter than the Full Moon, which in turn is brighter than Venus, and so on.

To quantify the brightness of objects, astronomers use a scale known as apparent magnitude (m), which is closely related to the object's brightness (E). The formula used is:

$$ m = {-2.5 * log(E) + C}$$

In this equation, C represents a constant. According to the apparent magnitude scale, a one-magnitude difference corresponds to a 2.5-fold variation in brightness.

It's important to note that the lower the magnitude, the brighter the object. For example, an object with an apparent magnitude of -26.8 (the Sun) is much brighter than an object with an apparent magnitude of -12.6 (the Full Moon). The brightness ratio between these two objects can be calculated using the formula:

$$ ratio = {10^{(-12.6 - (-26.8)) \over 2.5}=10^{5.88} = 758,578}$$

Hence, the Sun appears approximately 758,578 times brighter than the full Moon to us.

Absolute magnitude

Another magnitude scale is the absolute magnitude (M), which takes into account the object's distance from Earth. The formula for absolute magnitude is:

$$ M = m - 5*{log(d) -1} $$

In this equation, d represents the distance in parsecs (1 parsec = 3.26 light years) between the object and Earth.

Below, you can compare the apparent and absolute magnitudes of a few stars.

Object	apparente magnitude	absolute magnitude
Sun	-26.8	4.83
Alpha Centauri	-0.3	4.1
Rigel	0.14	-7.1