Modern Physics/The Law of Gravitation
Law of Gravitation
Of Newton's accomplishments, the discovery of the universal law of gravitation ranks as one of his greatest. Imagine two masses, M1 and M2, separated by a distance r. The gravitational force has the magnitude
where G is the gravitational constant:
The force is always attractive, and acts along the line joining the centre of the two masses.
Let's say that we have two masses, M and m, separated by a distance r, and a distance vector R. The relationship between R and r is given by:
We will also change our force into a force vector, acting in the direction of R:
And this gives us our final vector equation:
Notice that since the ratio between R and r is normalized, the addition of these terms does not alter the equation, only the direction in which the force is acting.