Recent content by Dirkg

Thank everyone. I am realizing that if I want to understand this better I need to brush up on the calculus that I forgot 30 years ago. Nobody else has bothered to investigate this situation close enough to show me a nice diagram that clears it all up; probably because it is such a special case...

Yes, and in #15, I realized that is a reasonable explanation. It also seems like a paradox though, just because I try to visualize gravity with an equation in the form of GMm/r^2 and the only way for the magnitude of the force from a hemisphere to be more than half is if r gets shorter. That is...

Actually, that makes sense to me, and I can now visualize how it works for a sphere because of this thread. Maybe I should start a new thread to bring up the paradox I think I see with respect to a hemisphere. Namely, that the force of gravity from a hemisphere must be more than half the force...

Yes, That is what I said. My point is that the magnitude of the force from a hemisphere (by itself) must be more than half of the magnitude of the force of gravity from the whole sphere. It seems counter-intuitive, but the vector addition is pretty straight forward. That was the whole point of...

No, Standing at the north pole and slice the Earth along a meridian. Since the pull from the two halves together equals the pull from the whole sphere, The pull from each hemisphere must be larger than half, because the direction of the pull from a hemisphere is at angle. The vertical component...

Actually I can visualize the sphere as a point. My sticking point is more with the gravitational pull from a hemisphere being more than half the pull of the sphere.

Oh, right. So maybe it does make sense that the hemisphere pulls with more than half the force of the sphere, given the asymmetry of the hemisphere.

That doesn't really help in understanding my conundrum. If that were the case, the mass of a sphere and a point mass would not have the came gravity. The point mass is perfectly aligned.

Well it is nice to know I'm in good company. It led to me thinking about hypothetical non-spherical planets (i.e. hemisphere) and started to make my brain hurt. I naturally assumed someone had already worked out all the math and I just couldn't find it on the internet. Turns out that it isn't...

YES! thank you, that is what is bothering me. It is not intuitive that the hemisphere would cause a force greater than 1/2 the force from the sphere. But it would have to if two hemispheres added together are going to add up to F=mg

That was the part that was bothering me. Starting from a more basic case, if you start with a hemisphere with a person at the rim. The mass is half of the sphere and r is greater than it was for the sphere. Therefore GMM/r^2 is less than it would be for half of the sphere. Also the force is...

Thanks, although my calculus is (very) rusty, I understand the concepts well enough to grasp what is happening. It still seems odd to me that it should work out, but numbers don't lie. I will work on understanding the math better. It is intuitive to me that from inside a shell, all the forces...

I am having a problem with visualizing why Newton's Law of Universal Gravitation (NUGR) holds true when objects get close together. F=Gmm/r^2 makes sense for planets that are far away because each object can be treated as a point with gravity acting at the center of each object. For a person...

Hello .