# Newtons Cannon ball problem [closed]

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.

## closed as too localized by Brandon Enright, Emilio Pisanty, David Z♦Jun 4 '13 at 18:04

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• Most people would use all three of Newton's laws plus Newton's law of gravity, as well as some kinematical facts about circular motion. However, because this is at the earth's surface it's possible to do it using a much more minimal approach. Basically, find the horizontal velocity such that the rate at which the ground curves out from under the cannonball matches the acceleration of the cannonball. – Ben Crowell Jun 4 '13 at 4:46

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).
• @Physics_guy, $r$ is equal to the distance of the cannon ball to the center of mass of the earth (probably slightly higher then the radius of the earth). And when calculating the velocity $v$, also keep in mind the rotational speed of the earth (initial velocity). – fibonatic Jun 4 '13 at 15:19