The acceleration due to gravity is approximately the product of the universal gravitational constant G and the mass of the Earth M, divided by the radius of the Earth, r, squared.
Finally, Newton reasoned that if the cannon projected the cannon ball with exactly the right velocity, the projectile would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the projectile falls.
As a first example, consider the following problem. He then surmised that if gravity can act at the top of the tree, it can also act at even larger distances. The Law applies to all objects with masses, big or small.
Imagine launching a satellite eastward above the Earth's equator in geosynchronous orbit: then the satellite will stay over the same spot on the Earth at all times in its orbit. Bruce Brackenridge, although much has been made of the change in language and difference of point of view, as between centrifugal or centripetal forces, the actual computations and proofs remained the same either way.
When the launch point is on the Earth's surface, then R would be the radius of the Earth. Note that the formula does not depend on the mass of the smaller object.
Newton's second law of motion states that force equals mass times acceleration.
Thinking Proportionally About Newton's Equation The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration.
But once it is at that speed, it will stay in orbit without subsequent rocket propulsion. In the same year  I began to think of gravity extending to the orb of the moon, and having found out how to estimate the force with which a globe revolving within a sphere presses the surface of the sphere, from Kepler's rule of the periodical times of the planets being in a sesquilaterate proportion of their distances from the centres of their orbs I deduced that the forces which keep the Planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve: and thereby compared the force requisite to keep the moon in her orb with the force of gravity at the surface of the Earth, and found them to answer pretty nearly.
Since the circular velocity varies inversely with the square root of R, an object in a smaller orbit has faster speed because the gravity is stronger. That is, if a rocket is shot from the Earth and consumes all of its fuel to accelerate to this velocity, then even after the rocket is no longer burning fuel, it will coast to infinity and the Earth's gravity cannot pull the rocket back to Earth.