How would one calculate where the earths gravity decreases?

I would assume objects below sea level experience a weaker g force than objects at sea level but I have only a rudimentary memory of calculus and can’t figure iut how to prove this or how much this decreases by.

I would assume cut the sphere into two pieces and act as though the entire mass is at the center point of each piece but I’m not positive on this. Can anyone verify or correct this?

I googled, “gravity at different altitudes” and got quite a few hits. I know you’re assumption is correct, but I don’t know remember the formulas.

I would assume objects below sea level experience a weaker g force than objects at sea level but I have only a rudimentary memory of calculus and can’t figure out how to prove this or how much this decreases by.
Wouldn't buoyant with depth overwhelm gravity's signals?

I’ll bet if you think out your question(s) carefully and send it to these folks, someone will get back to you.


Keep us informed.

There would be a couple of things at play here. First, altitude is affected only by the “inverse square law”. It’s the rate at which gravity drops off as you move away from a body.

Under the water would be a completely different thing. Gravity there would be affected by the inverse square law from all directions because there is matter dense enough to bother counting in all directions. So the deeper you go into the Earth, the less you would be affected by gravity. Technically, you would be affected by gravity the same, it would just be pulling from different directions, cancelling out. Theoretically at the center you would be weightless, though it wouldn’t be “actual” center any more than magnetic and true north are the same. This point of weightlessness would “float” around a bit, but would be near the actual center. NASA has observed that gravity on Earth is not constant because of the flow of material in the mantle. It’s not all evenly mixed down there, so the mass distribution changes.

Gravity is mass attracting mass.

If the mass of the small object is in a valley of the large object, then there is both less mass below the small one and some above, so there will be less gravity. It won’t be significant on earth, since no valleys are deep enough, but do a thought experiment where there’s a valley to the center of a planet and you’ll see that as you go lower you’ll feel less gravity pulling you towards the center of the planet.

At least that makes sense to me.

Yep, that’s pretty much right. Results in a “gravitational center” where there is zero gravity, though that’s unlikely to be in the exact center of a body because mass would have to be distributed perfectly evenly for the center of the body and the gravitational center to match exactly.

I suspect it would be something like a magnetic field where you can never reach equilibrium. For example, imagine a large body with a hollow center. You go to the center to hang out. Try as you might, you’ll never be able to just “float” in the gravitational center forever. There would always be tiny differences which would end up pulling you one way or another, though pretty slowly at first. It’s the same reason you can never balance one magnet on top of another to make it float there forever. It will pretty quickly fall off to one side or another, flip and be attracted to the other magnet.

Interesting that mass can cancel out gravity, if balanced properly.

If one is not near any object of mass, then one would be “weightless”.

But if one is at the center of an enormous spherical mass, then one is also “weightless”, but really, gravity is pulling him from all directions.

Hmm, I wonder if there are any other similarities between those two seemingly profoundly different contingencies for being weightless.


I don’t like the term “cancel out” because that’s not exactly what’s happening there. Not that there’s anything wrong with stating it that way. You’re just approaching it from a relativistic view, in which case that term is exactly right, relativistically speaking. It’s just not what is actually happening. Like any other relativistic view you cannot, from the position you described, measure anything but “zero” or nearly so. But unlike in much of relativity we have a point of reference in the bodies of mass on all sides. If you’re talking the effect you feel, which it is obvious you were, then yes, that’s right. But given that the mass on all sides is always quantifiable and we’re not just doing it for a purely mathematical purpose I don’t really like a relativistic approach to this.

Well, I bow to your thoughtful input on this.