Respuesta :
Given data:
* The mass of the Ceres is,
[tex]M=9.23\times10^{20}\text{ kg}[/tex]* The mass of the astronaut is,
[tex]m=64.5\text{ kg}[/tex]* The radius of the Ceres is,
[tex]\begin{gathered} R=474\text{ km} \\ R=474\times10^3\text{ m} \end{gathered}[/tex]Solution:
The gravitational force acting on the astronaut due to the Ceres is,
[tex]F=\frac{\text{GMm}}{R^2}[/tex]where G is the gravitational force constant,
Substituting the known values,
[tex]\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}[/tex]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.
