- #1
jackiefrost
- 140
- 1
Hi all - I broke my foot and had surgury so I'm bored (for a couple more weeks) which explains my recent posts.
[This isn't "Homework" like some class assignment - it's just something I've been playing with since reading some thought experiments that John Wheeler expressed - and some Feynman stuff on the E field inside a charged sphere]
I'm kind of interested in the nature of fields inside of variously shaped "sources" and would be interested to here any comments about how to best think about any of the following problems so they can be simply expressed mathematically. I could just go look up the appropriate equations but what fun is that?
1. If the Earth (mass M) were a perfect sphere with a perfectly homogenous rigid mass distribution, what would be the vector field equation for the Earth's gravitational field at any location on the inside region of the sphere? Disregard all external forces and interactions. Any coordinate system is OK but let the origin be at the center of the sphere.
2. Assume a test mass m is suspended in a cylindrical tube of negligible total volume, bored perfectly along a diameter, from one side of the planet to the other through its center. The tube contains a perfect vacuum except for the presence of the test mass, and its walls exert no influence on the test mass. The test mass is initially suspended at the surface level of the Earth and is motionless relative to it. What would be the vector equation of motion for the body after it's released to free fall?
3. Disregarding any relativistic effects, would the Earth's rotation matter at all to any of the above?
4. Would the equations remain unchanged for any diameterical path we could choose for the tube; e.g. pole to pole vs two diametrical points on the equator.
5. What happens to G (the gravitational constant) inside the sphere?Any little feedback would be welcome - except maybe "hey jackiemoron - go kill yourself... slowly!" or "get well VERY, VERY, VERY, soon, we're all beggin' ya..." or something in that vain
jf
[This isn't "Homework" like some class assignment - it's just something I've been playing with since reading some thought experiments that John Wheeler expressed - and some Feynman stuff on the E field inside a charged sphere]
I'm kind of interested in the nature of fields inside of variously shaped "sources" and would be interested to here any comments about how to best think about any of the following problems so they can be simply expressed mathematically. I could just go look up the appropriate equations but what fun is that?
1. If the Earth (mass M) were a perfect sphere with a perfectly homogenous rigid mass distribution, what would be the vector field equation for the Earth's gravitational field at any location on the inside region of the sphere? Disregard all external forces and interactions. Any coordinate system is OK but let the origin be at the center of the sphere.
2. Assume a test mass m is suspended in a cylindrical tube of negligible total volume, bored perfectly along a diameter, from one side of the planet to the other through its center. The tube contains a perfect vacuum except for the presence of the test mass, and its walls exert no influence on the test mass. The test mass is initially suspended at the surface level of the Earth and is motionless relative to it. What would be the vector equation of motion for the body after it's released to free fall?
3. Disregarding any relativistic effects, would the Earth's rotation matter at all to any of the above?
4. Would the equations remain unchanged for any diameterical path we could choose for the tube; e.g. pole to pole vs two diametrical points on the equator.
5. What happens to G (the gravitational constant) inside the sphere?Any little feedback would be welcome - except maybe "hey jackiemoron - go kill yourself... slowly!" or "get well VERY, VERY, VERY, soon, we're all beggin' ya..." or something in that vain
jf
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