From Mechanics
Consider a particle on the surface of the planet.
F=d2Gm1m2
where
F
is the gravitational force on a particle on the surface of the planet, in other words, its weight.
m1
is the mass of the planet,
m2
is the mass of the particle and
d
is the radius of the planet.
As
F=m2a
where
a
is the acceleration of the particle very close to the surface of the planet,
a=d2Gm1
Thus
d2=aGm1
As
G=6.67
10−11 kg-1m3s-2
we get
d2=3.2
6.6710−11
51020=3.233.35109=10.4109=1.041010d=
1.04105=1.02105 m=102 km
