“Our frustration has been that you keep dragging it in where it doesn’t belong.”
My apologies, I never intended to frustrate anyone. Bringing up the gradients in response to mwbrooks was intended to amusing. Your results may vary.
I apologize again for our loss of communication in our thought experiment. You are most likely intelligent and well educated and I don’t really believe that you think compasses and electric motors don’t work - which is what I was hearing from your answers to my questions (and you thought you were frustrated). In turn, I hope you don’t think that I’m hopelessly dense.
All I’m trying to do is find out if and where, exactly, my model of reality needs bodywork. If I keep swinging from pico-gravity to neutronium gravity examples it’s because if I can understand the behavior at each extreme I can have confidence in understanding it here where we live. Keeping in mind the difference between dominant forces, trivial forces, insignificant forces and non-existent forces, (don’t tell me it’s non-existent if it’s really insignificant – you’ll get me killed when I go play with a neutron star) lets see if we can agree on a few things:
- The original problem was “What if you fell into a tube through the Earth”.
- If we define ‘observation point’ as your center of mass, the pull of Earth’s gravity during falling (and subsequent oscillations about the Earth’s center) works like this: “The gravity at any point inside of the object is the same as a point-mass at the center with the mass of all the material at a depth greater than the observation point. The mass above the observation point has no effect.”
Now we add one further assumption, that you are not a geometric point, but are, in fact, a 6 foot tall human being. The second statement above directly states that, unlike the (non-existent) gravity inside a hollow sphere, your head and your feet at the center of the Earth will be compressed towards your navel with a force equivalent to a 6 foot diameter mass (insignificant force). Sorry I frustrated you asking about atom/pair stretching, gravitational gradients and such, but I was trying to find some mystery force opposing this gravity that makes the gravity truly 0 at the center like you said. I was also exploring these forces in trying to understand the difference between the hollow sphere and the Earth as described in the first statement.
We do not have a perfect hollow sphere to cancel gravity, even assuming the roundness and density to be perfect. While we never stated the size of the hole we cut through the Earth (it could be a little 3 footer that you bounce around in so much that nothing but hamburger and bone reaches the center or it could be a big 500 miler that we can go exploring in our flying suit) the physics of the missing pieces of sphere must hold true for a hole an angstrom wide (non-existent difference?) to one 7500 miles wide (which would leave only a ‘torus of mass’ with you in the center) whose effect would dominate the gravity analysis. How does the (previously) perfectly neutralized field behave now as you motor around in your jet pack? How does gravity change when your long axis is aimed at the equator within the imperfect hollow sphere compared to aligning it with, say 1000 miles of missing mass at the poles? If it is not a reduction in a positive stretching force does it manifest as a positive force at 90 degrees to your axis? If we start at 0g is it the Holy Grail of antigravity? This is what I’ve been trying to ask.