The escape speed from Planet X is 20000 m/s . Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?
Escape speed
V₀ = √(2GM/r)
where M is mass of the central body and r is radius of the central
body.
First we have to convert "twice as dense" to mass.
Call planet X mass m.
planet Y mass m₂ = density x volume. since radius is the same,
volume is the same. So if the density is twice, than the mass is
twice.
back to V₀ = √(2GM/r)
If you double the mass, keeping everything else constant, then V₀
goes up by √2 = 1.414
20000 m/s x √2 = 28284.27 m/s
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