Law of GravitationEdit
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.