Q:

Newtons Cannon ball problem

Let's I have a Newton's Cannon ball of 15 kg and want to fire so it will round the earth and back to me. 

My query is which law can evaluate the speed that cannon ball will revolve round the sun ? 
  any hints  or answer will be appreciated.

A:

Newton's Law of Gravity + centripetal force:
$$F_g=\frac{GMm}{r^2}$$
$$F_c=m\frac{v^2}{r}$$
Combine them and solve for what you need (usually you're given $r$ and asked to solve for $v$). 
Those equations are for uniform circular motion (which is what you would encounter in an intro to physics course). More accurately, you would need the Lagrange function to derive the equation of motion for the cannon ball as a function of $\theta$, and in the process rediscover Kepler's laws of motion. It's a little lengthy, but you can find a derivation in Anderson's Intro to Flight, Chapter 8 (Astronautics). 

