Future settlers of the Moon observe the phenomenon of a meteor at the dark edge of the Earth’s disk, which is hardly

Future settlers of the Moon observe the phenomenon of a meteor at the dark edge of the Earth’s disk, which is hardly distinguishable visually through a telescope with a lens diameter of 30 cm. What brightness will this meteor have on Earth if it is observed at the zenith? What object in the sky is it comparable in brightness?

The human eye has a permeability of about 6m, but a short-lived and moving light source with such brilliance cannot be noticed. An experienced meteor observer with dark-adapted vision will notice these phenomena at magnitudes up to 5m. Using a telescope with a lens diameter D, it is possible to increase the permeability: m = 5 + 5 log D / d, where d is the diameter of the pupil of the eye (0.6 cm on average). For a 30-cm telescope, we get a penetration value when observing meteors: 13.5m. The meteor, which was hardly observed by astronauts, had about such a brilliance. The radius of the Moon’s orbit R is 384 thousand km. Since it is significantly larger than the radius of the Earth, it can be assumed that it was precisely this distance that separated the astronauts from the meteor. Observers on Earth are located much closer to it – if a meteor is visible at its zenith, the distance to it is equal to its height H. Typical meteor heights are about 100 km. From here we get the stellar magnitude of the meteor on Earth: m0 = m + 5 log H / R = 5 + 5 log (HD / Rd) ~ –4 m. It was a bright fireball comparable in brightness to Venus.