A planet existed whose mass and radius were b | vedclass

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(B) We know that the acceleration due to gravity on Earth is given by $g_{e} = \frac{GM_{e}}{R_{e}^{2}}$.For the given planet,the mass $M_{p} = \frac{

Vedclass · Accepted Answer

$2g_{e}$

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(B) We know that the acceleration due to gravity on Earth is given by $g_{e} = \frac{GM_{e}}{R_{e}^{2}}$.For the given planet,the mass $M_{p} = \frac{M_{e}}{2}$ and the radius $R_{p} = \frac{R_{e}}{2}$.Substituting these values into the formula for the planet's gravity $g_{p} = \frac{GM_{p}}{R_{p}^{2}}$,we get:$g_{p} = \frac{G(M_{e}/2)}{(R_{e}/2)^{2}} = \frac{GM_{e}/2}{R_{e}^{2}/4} = \frac{GM_{e}}{2} 	imes \frac{4}{R_{e}^{2}} = 2 	imes \frac{GM_{e}}{R_{e}^{2}}$.Since $\frac{GM_{e}}{R_{e}^{2}} = g_{e}$,it follows that $g_{p} = 2g_{e}$.

$A$ planet existed whose mass and radius were both half of the Earth. What would be the acceleration due to gravity at the surface of the planet in terms of that on the surface of the Earth?

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