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. All answers must be in 3 significant digits.

Answer 1

a)

The formula for calculating the magnitude of the acceleration due to gravity on the surface of Ceres is expressed as

g = GM/R^2

where

g is the magnitude of the acceleration due to gravity

M is the mass of Ceres

R is the radius of Ceres

G is the gravitational constant whose value is 6.67408 x 10^-11 Nm^2/kg^2

From the information given,

M = 9.23 x 10^20

R = 474 km

We would convert 474km to meters. Recall,

1 km = 1000m

474km = 474 x 1000 = 474000m

By substituting these values into the formula,

g = (6.67408 x 10^-11 x 9.23 x 10^20)/474000^2

g = 0.274 m/s^2

b) The formula for calculating weight is expressed as

W = mg

where

m = mass of object

g = acceleration due to gravity

From the information given,

m = 64.5 kg

g = 0.274 m/s^2

By substituting these values into the formula,

W = 64.5 x 0.274

W = 17.673 N

The weight of the astronaut is 17.673 N