A 1KW lamp was installed on the visible hemisphere of the moon. What will be its stellar magnitude when viewed from Earth?

A 1KW lamp was installed on the visible hemisphere of the moon. What will be its stellar magnitude when viewed from Earth? The luminosity of the Sun is 3.88 * 10 ^ 33 erg / s.

First, we will determine the stellar magnitude of the Sun if it were in the place of the Moon, that is, 389 times closer. She is equal
m1 = –26.8 – 5 lg 389 = –39.7.
In this case, the luminosity of the Sun is 3.88 • 10 ^ 26 W, that is, 3.88 • 10 ^ 23 times more than that of the lamp. Consequently, the stellar magnitude of the lamp on the moon will be
m2 = m1 + 2.5 lg (3.88 • 10 ^ 23) = 19.3.
Such a lamp could be seen in a large telescope if the light of the moon itself had not interfered.