Imagine a planet having a mass twice that of the earth and a radius equal to 1.414 times that of the earth. Determine the acceleration due to gravity at its surface.


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Question Number 106928 by aurpeyz last updated on 07/Aug/20

$I m a g i n e a p l a n e t h a v i n g a m a s s t w i c e t h a t$ $o f t h e e a r t h a n d a r a d i u s e q u a l t o 1.414$ $t i m e s t h a t o f t h e e a r t h . D e t e r m i n e t h e$ $a c c e l e r a t i o n d u e t o g r a v i t y a t i t s s u r f a c e .$
	Answered by JDamian last updated on 07/Aug/20

	$g_{p l a n e t} = G \frac{M_{p l a n e t}}{R_{p l a n e t}^{2}} = G \frac{2 M_{E a r t h}}{{(\sqrt{2} \cdot R_{E a r t h})}^{2}} =$ $= G \frac{2 M_{E a r t h}}{2 R_{E a r t h}^{2}} = G \frac{M_{E a r t h}}{R_{E a r t h}^{2}} = g_{E a r t h}$
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