What is the size of the smallest craater on the moon that you can see with a telescope with a resolution of 2 arc seconds at a distance of 384,400 km?away

1 answer

First, convert 2 arc seconds to radians.

2 arc sec*(1 degree/3600 arc sec)/57.3 degree/rad = 9.7*10^-6 rad

Finally, multiply that by the distance to the moon.

9.7*10^-6*384,400 = 3.7 km
is the smallest resolvable object size.

Two arc seconds is typical for a good earth-based telescope with about a 10 cm aperture under good seeing conditions.