Modern Physics/The Law of Gravitation

From Wikibooks, the open-content textbooks collection

Jump to: navigation, search
Modern Physics : Gravity


Stub

This page or section of the Modern Physics book is a stub. You can help Wikibooks by expanding it.


[edit] 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

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

where G is the gravitational constant:

G = 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.

[edit] Vector Notation

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.

Retrieved from "http://en.wikibooks.org/wiki/Modern_Physics/The_Law_of_Gravitation"