The magnitude of the gravitational force between two objects having a
mass 
and 
and being at a distance r from each otheris
where 
.
Since the force exerted by the second mass on the first mass is
equal to the first mass times its acceleration, appears on
both sides of the equation and can be canceled. The acceleration
is thus independent of the mass. At the surface of the earth, the
acceleration communicated to any object is in good approximation
meter/second 
, where 
and 
are the mass and radius of the earth.
If an object of mass m is thrown vertically from the surface of the earth and is at a distance r from the center of the earth, its energy is
If E>0, the object has enough kinetic energy to escape from the earth attraction. If E<0, the object will reach a maximum value and fall back.
Before entering more complicated subjects, we learned about a tool commonly used by physicists when they do not want to solve complicated equations: dimensional analysis. This technique is presented in most introductory textbook, for instance Halliday, Resnick and Krane, Physics, Chapter 1 section 7.