resolution

The resolution of a telescope, as we will learn, is the minimal angular size of features it can resolve. If we have a telescope with a resolution of 2'' (2 arc-seconds) what is the size, in kilometers (km), of the smallest crater we can make out on the moon, at a distance of 384,400 km? (The Moon's diameter is 3480 km, for comparison.) Round your answer to two significant figures.


ANS:

          a = 2"
     R = 384400km
   
     a/(360*3600)*(2pi*R)
     2/(360*3600)*(2pi*384400)    #I multiply 360 with 3600 for coversion to arcsec
     = 3.7272km

there is another way:

     (a/3600)*(pi/180)*R
     (2/3600)*(pi/180)*384400
     =3.7272km