Is the force of gravity stronger or weaker in valleys compared to mountains?

[LoveandHate]

The force of gravity on Earth attracts things to the centre of the Earth, no? I understand why the gravitational force is less on mountains, as one is farther away from the centre of the Earth, so when using F_g=GMm/d², then distance is larger, therefore the squared number would be larger than at standard level, and you'd be dividing by a larger number. But why is it that in a valley the gravitational force Earth has on you is still less.. would it not be greater? The distance is smaller, so you'd be dividing by a smaller number when using the formula and F_g will consequently be greater. Am I missing something here or am I totally off track?

 

[D H]

Gravitational acceleration varies not only with altitude, but also with latitude and with the density of the surrounding material.

 

[LoveandHate]

So, because of the shape of the Earth, the gravitational force is stronger at the poles than at the equator.
And can you explain the part about density? How does this effect the formula?

 

[TurtleMeister]

Once you go below the Earths surface (a valley could be considered below the surface) the pull towards the center decreases because the Earth above you is pulling in the opposite direction. I don't think Newton's formula was meant to be used below the surface. The force of gravity is less at the poles because of the Earths rotation. Centrifugal force causes the pull to be less at the equator and gradually increases as you move toward the poles. Another interesting effect is that the direction of pull changes slightly also. This is because while gravity is mostly radial, the centrifugal force is parallel to the equatorial plane. So a plum-bob at the equator or at the poles will point towards the center of the Earth, but in between it will shift slightly in the direction of the equator.

 

[aaryan0077]

The Earth's pull with this formula is valid, but under the surface things are different. As you keep going under and under, you'll reach a point (the core), where if you figure out according to formula, d = 0, so gravity must be infinite, but its not, infact it is 0.
The formula is based on distance of object from Earth's surface and not center.

 

[LoveandHate]

I understand all of this, but why was I told to use Earth's radius as distance?

 

[D H]

LoveandHate, could you supply some context? We are flailing a bit in answering your question because you have not said what the question is. What problem are you working on, and what are the relevant equations?

 

[LoveandHate]

LoveandHate, could you supply some context? We are flailing a bit in answering your question because you have not said what the question is. What problem are you working on, and what are the relevant equations?

I know, and I'm sorry I'm being confusing. I'm just confused with the whole concept, but I think I may understand, if not fully, than a lot better than before.

 

[A.T.]

The formula is based on distance of object from Earth's surface and not center.

No, you have to put the distance to the center into the formula. Put it is only valid outside of a perfectly spherical mass with a perfectly symmetrical mass distribution. If you want to consider stuff like mountains, you cannot expect such a simple formula to work. The answer to the OPs question really depends on how the valley is formed.

 

[aaryan0077]

No, you have to put the distance to the center into the formula. Put it is only valid outside of a perfectly spherical mass with a perfectly symmetrical mass distribution. If you want to consider stuff like mountains, you cannot expect such a simple formula to work. The answer to the OPs question really depends on how the valley is formed.

I know that it is valid for perfectly spherical mass with a perfectly symmetrical mass distribution, but for the question LoveandHate asked we need to have the physical details of the valley, and not only for this, but for the other stuff you said, like as mountains and all.
But I think we should be provided with the more details.

 

[D H]

The Earth's pull with this formula is valid, but under the surface things are different. As you keep going under and under, you'll reach a point (the core), where if you figure out according to formula, d = 0, so gravity must be infinite, but its not, infact it is 0.
The formula is based on distance of object from Earth's surface and not center.

No, it isn't. The formula is based on the distance of an object from the center of the Earth but is only valid for objects above the surface of the Earth. Inside the Earth one has to discount the material whose distance from the center of Earth is greater than that of the point in question. I suggest we forego the discussion of what happens inside the Earth because LoveandHate is having problems understanding what is happening on the surface of the Earth.

The equation a=GM/r² is only approximately correct because it ignores the non-spherical nature of the Earth. This equation also ignores the distinction between "gravitation" and "gravity". Physical geologists distinguish between the gravitational force (Newton's law of gravitation) and gravity in that gravity is the apparent force on an object as assess by an observer fixed to the surface of the Earth. Gravity is less than the gravitational force due to the centrifugal force resulting from Earth's rotation.LoveandHate, you still have not supplied enough information. It would help a lot if you were a bit more specific in your questions.

 

[Cantab Morgan]

The Earth's pull with this formula is valid, but under the surface things are different. As you keep going under and under, you'll reach a point (the core), where if you figure out according to formula, d = 0, so gravity must be infinite, but its not, infact it is 0.
The formula is based on distance of object from Earth's surface and not center.

Sorry, I have to disagree. If the $$d$$ in the formula represented the distance from the Earth's surface, then gravity would be infinite at the surface, because you'd be dividing by zero. That's not the case.

However, as you drill into the Earth, $$M$$ decreases, because there is less of the Earth's mass below you to exert a pull. As you go towards the center of the Earth, $$M$$ gets smaller, and it gets smaller faster than $$d^2$$. So by the time you get to the Earth's center, the force on you vanishes.

 

[aaryan0077]

Okay, I just got that.
I checked out on Wikipedia, and guess what?
I found that I am wrong, and I am really sorry for this, but thanks to all (AT, DH, and Cantab Morgan) for correcting me. I'll look forward for more support.
Thanks.
For LoveandHate : I thing you can be more precise for your question.