Any two point bodies with masses m1 and m2 will attract each other with a force directed along the line joining their centers of magnitude
F=Gm1m2
r2
where r is the distance between the centers. The quantity G is called the universal gravitational constant. Its value in SI units is G=6.67×10-11Nm2kg-2. This is a very small value so the gravitational force is normallu only important for very large masses.
Note: This is a force like any other so gravitational forces add as vectors.
When a force acts on an object and moves that object then we say the the force does Mechanical Work. The amount of the work is proportional to both the force and the distance moved in the direction of the force so
Work = |Force|×|displacement|×cos(angle between force and displacement)
In general if the motion is in the direction of the force then the work is positive, if the motion is in the opposite direction the work is negative, and if the force and motion are perpendicular then NO WORK is done.
NOTE that work is scalar quantity; it has no direction and is represented by a single signed number.
Mechanical energy is a measure of the ability of a body or system to perform mechanical work. In many systems work can be converted into energy and vice versa (we call such systems conservative). Like work energy is a scalar quantity.
The simplest form of mechanical energy is kinetic that a body has by virtue of its motion. In a frame in which a body of mass m has speed v we say that it has Kinetic Energy =½mv2.
In the presence of many forces we say that an object can have energy by virtue of its position. We call such energy Potential Energy and such a force Conservative.
One such force is near earth gravity. In this situation the force is constant, F=mg, independent of position. The gravitational potential is PE=mgh where h is the height of the object measured from some reference level. Just as the kinetic energy depends on the frame of reference so does the potential energy.
Another such force is the spring force, which obeys Hooke's Law, F=-k(L-L0), where L is the instantaneous length of the spring, L0 the unstretched length of the spring, and k a constant called the spring constant. For such a spring the elastic potential energy is given by PE = ½k(L-L0)2.
Non-conservative forces cannot be associated with an energy. They are forces like friction that convert mechanical energy into other non-mechanical forms. Such forces include sliding friction, air resistance, water viscosity, etc.
Experimentally it is found that work and energy can be interchanged following the rule
Work Done = Change in Energy = Final Energy - Initial Energy
In a system where all the forces are conservative (a system where there is no friction) we say that energy is Conserved. In such a case PEinitial+KEinitial=PEfinal+KEfinal.
Near to the Earth's surface the change in gravitational force with distance from the center of the earth is so slight that the gravitational attraction appears constant so we have
mg=GMm or g=GM.
r2 r2