Suppose a new extrasolar planet is discovered. Its mass is double the mass of th

Question

Suppose a new extrasolar planet is discovered. Its mass is double the mass of the Earth, but it has the same density and spherical shape as the Earth. How would the weight of an object at the new planet's surface differ from its weight on Earth? (Let Wnew be the weight of the object at the new planet's surface and WE be the weight of the object at the surface of the Earth. Use any variable or symbol stated above as necessary.)

My thought process is that doubling the mass for the same density means doubling the volume. Doubling the volume doubles r^2 so r increase by a factor of sqrt 2

some answers I've come up with are 2We, sqrt2We, We, (2We)/sqrt2

Explanation / Answer

m = 2Me

volume of new planet = m/density = 2Me/(Me/Ve) = 2Ve

Volume is twice that of earth.

Radius of new planet = cube root (2Re^3) = Re*cube root 2, r = Re*2^1/3

value of g on that planet = (Gm/r^2) = [(2MeG/((Re^2)*2^(2/3))] = g*2^(1/6)

Therefore weight on earth is We then weight on that planet = We*2^(1/6)

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