Question

Ceres, the largest asteroid in the asteroid belt, has a mass of 9.23 x 10^20 kilograms and a radius of 474 kilometers. a. What is the magnitude of the acceleration due to gravity on the surface of Ceres? Include units in your answer.b. How much would an astronaut of mass 64.5 kilograms weigh on Ceres? Include units in your answer.

Answer 1

M=mass=9.23 x 10^20 kg

R=radius= 474 Km=474000m

a) we will use the next formula

`F=G\text{ }(Mm)/(R^2)`

F is the force of attraction

G is the universal gravitational constant

M is the mass of the larger object and

m is the mass of the smaller object

R is the distance

Using the formula of Newtons second law

`F=ma`

we have

`ma=G(Mm)/(R^2)`

we simplify

`a=(GM)/(R^2)`

we can change a by g

`g=(GM)/(R^2)`

We substitute the data

`g=6.67408*10^(-11)\cdot(9.23*10^(20))/(474000^2)=0.274\text{ m/s}^2`

b.

m=64.5 kg

In order to calculate the weight, we will use the next formula

`W=mg`

we substitute the values

`W=64.5(0.274)=17.7\text{ N}`

ANSWER

a. g=0.274 m/s^2

b. 17.7N