Question

Ceres, the largest asteroid in the asteroid belt, has a mass of 9.23 x 1020 kilograms and a radius of 474 kilometers.What is the magnitude of the acceleration due to gravity on the surface of Ceres? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

Given,

The mass of Ceres, m=9.23×10²⁰ kg

The radius of Ceres, r=474 km=474×10³ m

From Newton's universal law of gravitation, the gravitational force between two objects is proportional to the product of the mass of the objects and inversely proportional to the square of the separation between the objects.

The acceleration due to gravity or the gravitational field strength is given by,

`g=(Gm)/(r^2)`

Where G is the gravitational constant.

On substituting the known values,

`\begin{gathered} g=(6.67*10^(-11)*9.23*10^(20))/((474*10^3)^2) \\ =0.274\text{ m/s}^2 \end{gathered}`

Therefore the magnitude of the acceleration due to gravity at the surface of Ceres is 0.274 m/s².