The escape velocity from the earth is about 11. The escape velocity from a planet having twice the radius and the same mean density as the earth
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Escape Velocity ve=2GMeRe−−−−−√ve=2GMeRe
=2G(43πρR3ed)Re−−−−−−−−−−−⎷=2G(43πρRe3d)Re
=2G(43πρR2e)d−−−−−−−−−−−−√=2G(43πρRe2)d => veαRveαR
Since density is same.
When radius is doubled escape velocity gets doubled
2ve=2×11=22km/s
=2G(43πρR3ed)Re−−−−−−−−−−−⎷=2G(43πρRe3d)Re
=2G(43πρR2e)d−−−−−−−−−−−−√=2G(43πρRe2)d => veαRveαR
Since density is same.
When radius is doubled escape velocity gets doubled
2ve=2×11=22km/s
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