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Explain briefly about Newton's law of gravitation

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Newton's law of Gravitation-

According to Newton's law of gravitation, the gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Due to gravitational force, Each particle in this universe attracts every other particle.

The direction of this force is along the line joining the particles.

Let two particles of masses $m_1$ and $m_2$ separated by a distance r exert a Force F on each other

And Magnitude of F is given as

$F\; \alpha\; \frac{m_{1}m_{2}}{r^{2}}$

Or, $F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}$

Where

$F\rightarrow$ Force

$G\rightarrow$ Gravitational constant

$m_1,m_2\rightarrow$ Masses

$r\rightarrow$ Distance between masses

The vector form of formula

According to Newton's law of gravitation

$\vec{F}_{12}=\frac{-Gm_1m_2}{r^{2}}(\hat{r}_{21})$

Or $\vec{F}_{12}=\frac{-Gm_1m_2}{r^{3}}(\vec{r}_{21})$

Where $\hat{r}_{21}\rightarrow$ Position vector

Here negative sign indicates that the direction of $\vec{F}_{12}$ is opposite to that of $\vec{r}_{21}$

And $\hat{r}_{12}=-\hat{r}_{21}$

So, $\vec{F}_{12}=-\vec{F}_{21}$

Means Gravitational force between two bodies form an action and reaction pair.

i.e. the forces are equal in magnitude but opposite in direction.

This is in accordance with Newton's third law of motion

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avinash.dongre

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