Question

Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice the radius of Earth). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth's?

Answer 1

Answer:

4 times the mass of Earth

Explanation:

$M_1$ = Mass of Earth

$M_2$ = Mass of the other planet

r = Radius of Earth

2r = Radius of the other planet

m = Mass of object

The force of gravity on an object on Earth is

$F=\frac{GM_1m}{r^2}$

The force of gravity on an object on the other planet is

$F=\frac{GM_2m}{(2r)^2}$

As the forces are equal

$\frac{GM_1m}{r^2}=\frac{GM_2m}{(2r)^2}\\\Rightarrow M_1=\frac{M_2}{4}\\\Rightarrow M_2=4M_1$

So, the other planet would have 4 times the mass of Earth