Question

Planet Z is 8000 km in diameter. The free-fall acceleration on Planet Z is 9.00 m/s2 .

a) What is the mass of Planet Z?

b) What is the free-fall acceleration 1.00×104 km above Planet Z's north pole?

Answer 1

Diameter of Planet Z is $D=8000\,km$

Radius of Planet Z is $R=4000\,km=4*10^6\,m$

Free fall acceleration on Planet Z is $g=9.00\,m/s^2$

a) On the surface of Planet Z , $g=\frac{GM}{R^2}$

Mass of Planet Z is $M=\frac{gR^2}{G}=\frac{9.0*(4*10^6)^2}{6.67*10^{-11}}=2.159*10^{24}\,kg$

b) At a height h from the surface of Planet Z ,   $g'=\frac{GM}{(R+h)^2}$

Given that $h=1.00*10^4\,km=1.00*10^7\,m$

$g'=\frac{GM}{(R+h)^2}=\frac{6.67*10^{-11}*2.159*10^{24}}{(4*10^6+1*10^7)^2}=0.735\,m/s^2$

Free fall acceleration at height h is $0.735\,m/s^2$