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.)

Answer 1

g(n) = G*Mn/Rn^2 & g(e)= G*Me/Re^2

Mn=d*(4/3)*pi*Rn^3 (Mn->new planet's mass)
Me=d*(4/3)*pi*Re^3 (Me-> Earth's mass)
So, g(n)/g(e) = Rn/Re .....(1)

Now, Mn/Me = 2 (given)
So Rn^3/Re^3 = 2
or Rn/Re = 2^1/3 ......(2)
From (1) & (2)
g(n)/g(e)= Rn/Re = 2^1/3

So, if the mass of the object is m:
Wn/We = m*g(n)/(m*g(e))
= 2^1/3