Question
On what factor does the escape speed from a surface depend?
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Answer
Value of escape speed at the surface of a planet is given by the relation,
$\text{v}_\text{es}=\sqrt{\frac{2\text{GM}}{\text{R}}}=\sqrt{2\text{gR}}$
Thus, the value of escape speed from the surface of a planet depends upon (i) value of acceleration due to gravity gat the surface and (ii) the size (i.e. radius) R of the planet only. It is independent of all other factors. e.g. The mass and size of the body to be projected, angle of projection, etc.
$\text{v}_\text{es}=\sqrt{\frac{2\text{GM}}{\text{R}}}=\sqrt{2\text{gR}}$
Thus, the value of escape speed from the surface of a planet depends upon (i) value of acceleration due to gravity gat the surface and (ii) the size (i.e. radius) R of the planet only. It is independent of all other factors. e.g. The mass and size of the body to be projected, angle of projection, etc.
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