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*10^(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*10^3\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=(6.67*10^(-11)*9.23*10^(20)*64.5)/((474*10^3)^2) \\ F=(3970.9*10^9)/(224676*10^6) \\ F=0.0177*10^3\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.