Last modified on 15 October 2011, at 20:29

Modern Physics/The Law of Gravitation

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

 F_g = G \frac{M_1 M_2}{r^2}

where G is the gravitational constant:

G \approx 6.67 \times 10^{-11} \frac{m^3}{kg \cdot s^2}

The force is always attractive, and acts along the line joining the centre of the two masses.

Vector NotationEdit

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:

|\vec{\mathbf{R}}| = r

We will also change our force into a force vector, acting in the direction of R:

\vec{F}_g = G \frac{M_1 M_2}{r^2} \cdot \frac{\vec{\mathbf{R}}}{r}

And this gives us our final vector equation:

\vec{F}_g = G \frac{M_1 M_2 \vec{\mathbf{R}}}{r^3}

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.