# Gravity varies at different point

1. Feb 23, 2009

### TofuManiac

1. The problem statement, all variables and given/known data
Question : All things being equal, the acceleration due to gravity is less at the equator than at the poles. Explain why. (from (NZ) NCEA Physic Scholarship (lv4) practice paper.)

The confusing part about this question is that it states "all things being equal". What things does the question means here? =/

2. Relevant equations
No equation required for this question, but we can still use F = (GMm)/r^2 , then F = ma
so derive formula, ma = (GMm)/r^2 , therefore a = (GM)/r^2 to view the question.

3. The attempt at a solution
This is what i wrote:
The Earth is not a perfect sphere, but rather an oval. Thus, the gravitational field on the surface varies at different places. Since the surface of the equator is closer to the core of the planet (i.e. radius is smaller), the gravitational field is larger than the gravitational field at the poles.. Therefore, the acceleration due to gravity is less at the equator than at the poles.

Second kind of solution : Putting this in "Using a=(GM)/r^2, derived from F = (GMm)/r^2 and F = ma, therefore the shorter than radius, the larger the acceleration."

Which one is suitable to answer the question?

2. Feb 23, 2009

### Phrak

Forget about the oval. That comes under the rather ridiculous statement "all things being equal." Pretend the Earth is round.

The radius of the Earth is about 4000 miles? What's the angular acceleration?

To be fair, the Earth is tends to be an oblate spheroid (oval) for the very same reason that it rotatates, and the gravitational force is less, but it's a much smaller effect on par with the distoration in the shape of the Earth due to the distribution of the continents.

A really good answer would compare the magnitude of the two effects.

Last edited: Feb 23, 2009