Question

Ceres, the largest asteroid in the asteroid belt, has a mass of 9.23 x 1020 kilograms and a radius of 474 kilometers. How much would an astronaut of mass 64.5 kilograms weigh on Ceres? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

Given data:

* The mass of the Ceres is,

$M=9.23\times10^{20}\text{ kg}$

* The mass of the astronaut is,

$m=64.5\text{ kg}$

* The radius of the Ceres is,

$\begin{gathered} R=474\text{ km} \\ R=474\times10^3\text{ m} \end{gathered}$

Solution:

The gravitational force acting on the astronaut due to the Ceres is,

$F=\frac{\text{GMm}}{R^2}$

where G is the gravitational force constant,

Substituting the known values,

$\begin{gathered} F=\frac{6.67\times10^{-11}\times9.23\times10^{20}\times64.5}{(474\times10^3)^2} \\ F=\frac{3970.9\times10^9}{224676\times10^6} \\ F=0.0177\times10^3\text{ N} \\ F=17.7\text{ N} \end{gathered}$

The weight of the astronaut on the Ceres is equal to the gravitational force acting on the astronaut.

Thus, the weight of the astronaut on the Ceres is 17.7 N.