Question

12. An astronaut experiences a force of gravity on Earth of 800 N. Neptune has 17 times the mass and 3.9 times the radius of Earth. What would the astronaut weigh, in newtons, on Neptune?

Answer 1

Given:

$F_E=800\:\rm N$

$M_N=17M_E$

$R_N=3.9R_E$

The force of gravity on an astronaut with mass $m$ at the surface of planet with mass $M$ and radius $R$ is given by

$$F=G\frac{Mm}{R^2}$$

Hence

$$\frac{F_N}{F_E}=\frac{M_N}{M_E}*\frac{R_E^2}{R_N^2}$$

$$\frac{F_N}{F_E}=17*1/3.9^2=1.1$$

Finally

$$F_N=F_E*1.1=800*1.1=880\:\rm N$$