prove Fg=G((m_1 m


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Question Number 98270 by M±th+et+s last updated on 12/Jun/20

$p r o v e$ $F g = G \frac{m_{1} m_{2}}{r^{2}}$
	Answered by Rio Michael last updated on 12/Jun/20

	$Newton : s law of universal gravitation states that :^{″} the force$ $between two point mass m_{1} and m_{2} seperated by a distance r$ $is directly proportional to the product of thier masses and inversly$ $proportional to the square of the distance seperating {them}^{″}$ $thus F \propto m_{1} m_{2} . . . . . (i)$ $F \propto \frac{1}{r^{2}} . . . . . . (i i)$ $\Rightarrow F \propto \frac{m_{1} m_{2}}{r^{2}} \Rightarrow F = k \frac{m_{1} m_{2}}{r^{2}}$ $\Rightarrow k = \frac{{F r}^{2}}{m_{1} m_{2}} according to the cavendish experiment,$ $this ratio = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}$ $in physics this constant = G$ $\Rightarrow k = G$ $thus F = G \frac{m_{1} m_{2}}{r^{2}}$
	Commented by M±th+et+s last updated on 12/Jun/20

	$t h a n k y o u s i r$
	Answered by smridha last updated on 13/Jun/20

	$t h i s i s v e r y s i l l y q u e s t i o n!! {d o n}^{'} t$ $m i n d . . b u t i t i s . w e d e r i v e d$ $t h i s f o r m u l a f r o m N e w {t o n}^{'} s$ $g r a v i t a t i o n a l l a w . . . w h i c h i s a$ $s t a t e m e n t w h o e s m a t h e m a t i c a l$ $e x p r e s s i o n i s t h a t . . . y o u c a n n o t$ $p r o v e a n y p o s t u l a t e!!$ $b u t {i t}^{'} s t r u e t h a t i t c a n b e s h o w n$ $f r o m E i n s t e i n G e n e r a l r e l a t i v i t y$ $w i t h m u c h m o r e a p p r o x i m a t i o n .$ $A n d o n c e m o r e f a c t I w a n t t o$ $s h a r e t h a t d o n t c a l l {N e w t o n}^{'} s$ $g r a v i t a t i o n a l L a w i s u n i v e r s a l$ $l a w . . . b e c a u s e i t d o e s n o t v a l l i d$ $f o r s t r o n g g r a v i t a t i o n a l f i e l d,$ $b u t E i n {s t e i n}^{'} G T R c a n e x p l a i n$ $h o w g r a v i t y w o r k s . . . t h i s t h e$ $r e g o r u s d e s c r i p t i o n a b o u t$ $g r a v i t y . . . . .$ $G_{μ ν} = R_{μ ν} - \frac{1}{2} {R g}_{μ ν} = \frac{8 π G}{c^{4}} T$ $t h i s i s c a l l e d t h e {E i n s t e i n}^{'} s$ $t e n s o r {e q}^{n} . t h i s i s t h e e x p l a n a t i o n$ $o f h o w g r a v i t y w o r k s . . . w h a t i s$ $g r a v i t y ? ? ?$
	Commented by M±th+et+s last updated on 13/Jun/20

	$n i c e e x p l a i n i n g s i r$
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