Question

In The Expanse series of science fiction novels people live in tunnels in the dwarf planet Ceres. The planet has been given a spin, so that, according to the novels, it has a “gravity” of 0.3 g. Assume that this is the value in tunnels close to the surface at the equator.
i) what is the period of rotation?
ii) what is the value of the “gravity” in a tunnel that is near the surface but half way between the equator and one of the poles?

no ceres. is the name of the fictional planet. .

Answer 1

The problem involves using force equations :

1. Using universal law of gravitation, The gravitational force acts as an agent for centripetal force and one obtains an expression for velocity . Then one uses the expression for acc. due to gravity to find time period of planet in terms of time period of earth.

2. In next part one studies the variation of acc. due to gravity with a latitude angle phi. Using the fact that acc. is a vector quantity and a net force points towards center,during rotation , one obtains variation of acc. due to gravity with latitude angle.