Question

State the vector form of Newton's law of gravitation.

Answer 1

Newton's law of gravitation : when two bodies of mass $m_1$ and $m_2$ are separated r distance then, experienced gravitational force is given by $F=\frac{Gm_1m_2}{r^2}$
where G is gravitational constant.

now in vector form,
Let $r_1$ is the position vector of $m_1$
$r_2$ is the position vector of $m_2$
then, $\vec{r_{12}}=\vec{r_1}-\vec{r_2}$ is the point from $m_2$ to $m_1$ and $\vec{r_{21}}=\vec{r_2}-\vec{r_1}$ is the point from $m_1$ to $m_2$

now, $\hat{F}=\hat{r}$

or, $\frac{\vec{F}}{|F|}=\frac{r}{|r|}$

or, $\vec{F}=F\frac{\vec{r}}{|r|}$

now, $\vec{F_{12}}=-\frac{Gm_1m_2}{|r_1-r_1|^3}\vec{r_{12}}$

and $\vec{F_{21}}=-\frac{Gm_1m_2}{|r_2-r_1|^3}\vec{r_{21}}$

Answer 2

Hii dear,

◆ Newton's law of gravitation in vector form-
Gravitational force of attraction between two bodies is given by Newton's law as-
F = Gm1m2r̂ / r^2

Where
G = universal gravitational constant
m1 = mass of first body
m2 = mass of second body
r = distance of separation
r̂ = unit vector along radius vector

Hope this is useful...