in agreement with a value of g . m s - and the value of a m from Eq. ( . ).
These observations led Newton to propose the following Universal Law of Gravitation : Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The quotation is essentially from Newton’s famous treatise called ‘Mathematical Principles of Natural Philosophy’ (Principia for short). Stated Mathematically, Newton’s gravitation law reads : The force F on a point mass m due to another point mass m has the magnitude | | ( . ) Equation ( .
) can be expressed in vector form as where G is the universal gravitational constant, ɵ r is the unit vector from m to m and r = r – r as shown in Fig. . . The gravitational force is attractive, i.e., the force F is along – r .
The force on point mass m due to m is of course – F by Newton’s third law. Thus, the gravitational force F on the body due to and F on the body due to are related as F = – F . Before we can apply Eq. ( .
) to objects under consideration, we have to be careful since the law refers to point masses whereas we deal with extended objects which have finite size. If we have a collection of point masses, the force on any one of them is the vector sum of the gravitational forces exerted by the other point masses as shown in Fig . . Fig.
. Gravitational force on point mass m is the vector sum of the gravitational forces exerted by m , m and m . The total force on m is Gm m Gm m Gm m Example . Three equal masses of m kg each are fixed at the vertices of an equilateral