Newton's Law of Universal Gravitation - Vector Form

Vector Form

Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.


\mathbf{F}_{12} =
- G {m_1 m_2 \over {\vert \mathbf{r}_{12} \vert}^2}
\, \mathbf{\hat{r}}_{12}

where

F12 is the force applied on object 2 due to object 1,
G is the gravitational constant,
m1 and m2 are respectively the masses of objects 1 and 2,
|r12| = |r2r1| is the distance between objects 1 and 2, and
is the unit vector from object 1 to 2.

It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. Also, it can be seen that F12 = −F21.

Read more about this topic:  Newton's Law Of Universal Gravitation

Famous quotes containing the word form:

    Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them. This is the principle on which I bring up my own children, and this is the principle on which I bring up these children. Stick to Facts, sir!
    Charles Dickens (1812–1870)