Hi i have a question: The radius of the Earth is approximately m and the acceleration due to gravity at the Earth’s surface is approximately 9.81 ms-2. If the acceleration due to gravity at the surface of the planet Mercury is approximately 3.59 ms-2 estimate the radius of Mercury. You may assume Newton’s Law of Gravitation but you do not require the value of the Gravitational constant in this law - list the other major assumptions that you make concerning the densities and shapes of the planets.

my attempt solution:

a = Gm/r²

for earth a = GM/R²

volume of sphere is ⁴/₃πr³

Assuming both have the same density

M = kR³

a = GM/R²

a = GkR³/R² = GkR

The ratio of the two values of a = 9.81/3.59 = 2.73

then the radius of mercury is 3.59=9.81*2.73R

gives R=0.13

is this incorrect? thx