Digital Computers can only draw a straight line. To draw a circle, a digital computer draws a lot of very short straight lines and forms them into a circle. The circle has bumps, lots of bumps.

If you use a digital computer to position a gun the gun jumps because of the bumps in the circle or arc the digital computer makes.

If you are trying to photograph stars the photographic plate must be exposed for hours and the telescope must smoothly follow the star or the image will be blurred on the photographic plate. 

Analog computer outputs are smooth and have no bumps or jerks, which is why the telescopes of the world are positioned by analog computers.

For details of the fire control problem, how the US Navy used analog computers from 1910 to the 1950's and how analogs were used for bomb sights, please see the following:

The Mechanical Analog Computers of Hannibal Ford and William Newell  (700 kb PDF file)

by A.Ben Clymer, IEEE Annals of the History of Computing, Vol 15, No. 2, 1993

Related Pages

Fire Control Analog Computer 1953 Two Videos