Explain briefly about Newton's law of gravitation

Answers (1)

 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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