How does gravity change between points within a spinning sphere? [duplicate]

In a world where life exists within a spinning sphere (so you are standing with your head toward the center), how would gravity change as you traveled? Would the rate of reduction be the same as you move toward the poles, or would the change be slight at the beginning, and grow larger as you move, or visa versa?

• This reads like a physics problem. Apr 29, 2020 at 21:39
• Does that mean I should bring the question elsewhere? Apr 29, 2020 at 21:39
• I think this question is technically on topic but in general the clearer you make it that you're asking a question related to building a fictional world, the better the question will be received. Apr 29, 2020 at 21:43
• I will see if I can change it to seem better. Apr 29, 2020 at 21:43
• The gravitational force exerted on a body inside a shell of uniform density is exactly zero. While counter intuitive, the math is fairly simple. Thus, the only way this scenario would work is for there to be high density areas within the spherical shell which would result in non-zero gravitational forces at those locations. Apr 29, 2020 at 22:04

It will change little near the equator and much more rapidly decrease as you near the poles.

At a set rate of rotation centripetal force is linearly related to distance from the axis of rotation. You can visualize this by thinking of the slope of the Earth as the rate of change in centripetal force at that location.

Cosine

Start at the equator (0 degrees from the equator) and walk towards the north pole (90 degrees from the equator). As you walk the gravity changes according to the cosine of the angle you are from the equator.

As you see the change is small near the equator and almost a straight line when you're near the poles.

Of course you can never actually walk to the poles because -- even though you would like the gravity to look like this

-- the centrifugal force will make it look like this:

So you cannot actually walk to the poles.

• But you could mountain climb to the poles, and once there jump along the axis of the world for the longest skydive ever. I think that’s a plot point in one of the Rama books, actually... Apr 30, 2020 at 8:15
• @JoeBloggs: Mountain climbing is an option. But it will be a VERY long skydive since there is no gravity at the poles and you'll just float there without falling. Apr 30, 2020 at 12:18
• That was kinda my point... You could reasonably be expect to be buffeted out of the centre eventually by the atmosphere, but it would take a long time. Apr 30, 2020 at 12:51