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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-




Question Number 106928 by aurpeyz last updated on 07/Aug/20
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.
$${Imagine}\:{a}\:{planet}\:{having}\:{a}\:{mass}\:{twice}\:{that} \\ $$$${of}\:{the}\:{earth}\:{and}\:{a}\:{radius}\:{equal}\:{to}\:\mathrm{1}.\mathrm{414} \\ $$$${times}\:{that}\:{of}\:{the}\:{earth}.\:{Determine}\:{the} \\ $$$${acceleration}\:{due}\:{to}\:{gravity}\:{at}\:{its}\:{surface}. \\ $$
Answered by JDamian last updated on 07/Aug/20
g_(planet)  = G (M_(planet) /R_(planet) ^2 ) = G((2M_(Earth) )/(((√2) ∙R_(Earth) )^2 )) =  = G ((2M_(Earth) )/(2R_(Earth) ^2 )) = G (M_(Earth) /R_(Earth) ^2 ) = g_(Earth)
$${g}_{{planet}} \:=\:{G}\:\frac{{M}_{{planet}} }{{R}_{{planet}} ^{\mathrm{2}} }\:=\:{G}\frac{\mathrm{2}{M}_{{Earth}} }{\left(\sqrt{\mathrm{2}}\:\centerdot{R}_{{Earth}} \right)^{\mathrm{2}} }\:= \\ $$$$=\:{G}\:\frac{\mathrm{2}{M}_{{Earth}} }{\mathrm{2}{R}_{{Earth}} ^{\mathrm{2}} }\:=\:{G}\:\frac{{M}_{{Earth}} }{{R}_{{Earth}} ^{\mathrm{2}} }\:=\:{g}_{{Earth}} \\ $$$$ \\ $$

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