Question

In 1877 Giovanni Schiaparelli announced the discovery of “channels” on the surface of Mars; subsequent observers mapped what they interpreted as an extensive Martian canal system. If these astronomers were observing with a 30-inch telescope at a site that had 1.02" seeing, what physical width must the canals be in order to be resolved when Mars is at its shortest distance from Earth?

Answer 1

The shortest distance between Earth and Mars is, 54.6x10^6 km. The angular distance for proper resolution is given by,

d is the aperture diameter. The angular width is given as 1.02" =  1.02 arc seconds = 0.000283 degrees.

Let us say that the canal width is l, then we can relate this angular distance to the canal width by considering the distance between Earth and Mars, we can then write,

Substituting theta and values we can write,