On 10/24/2010 06:28 PM, OrionWorks - Steven Vincent Johnson wrote: > >From Mauro: > > ... > > >> It is interesting to continue reading the explanation, >> for the force exerted on points inside the sphere. >> > Indeed, I bet it does get interesting! In my own computer simulations, this > is where I've had to play god, so-to-speak, and change the algorithm used > when the orbiting body presumably passes underneath the "planetary" surface > of the main attractor body. At that point one has to jigger a different set > of rules since, technically speaking, a point source no longer exists. It's > like diving into a swimming pool. The water (the source of gravity) is all > around you. > > I would also imagine the point source formula works best for perfect > spherical bodies, and also where the volume of "mass" is assumed to be made > of the same material and evenly distributed throughout. Obviously, in nature > such uniformity never happens. Take the Earth for example. We have a > nickel-iron core. The aggregate "mass" of the core of our planet is > decidedly heaver than the collection of elements that make up the > surrounding crust. This would imply that if one had a magic elevator shaft > that could take a collection of geologists safely all the way to the center > of the earth in order to measure one's weight what would systematically be > recorded would not necessarily change in ways one might initially predict. > For one thing I suspect one's weight would NOT necessarily become gradually > less as one travelled through the Earth's crust. It is even conceivable to > me that the geologist's weight might even increase slightly as they > approached the boundary "surface" of where Earth's nickel-iron core begins. > A significant portion of the planet's aggregate planetary mass is located > there. Therefore, as the geologist approached this surface boundary the > inverse square of the distance (1/R^2) formula might still, more or less, be > in effect. I suspect only after our magic elevator has penetrated the > surface of the nickel-iron core will our geologists begin to notice that > their weight begins to gradually approach zero. Only when the elevator > reaches the center of the planet will they feel weightless due to the fact > that the collective "mass" of the entire planet is evenly distributed all > around them. >
And all this is highly speculative, of course. I must have said before: "It is interesting to continue reading the explanation, for the *supposed* force exerted on points inside the sphere." We'll probably never know for sure what forces are really exerted inside a solid mass, due to the simple fact that bodies don't move inside solids. Measurements of acceleration and velocity in the gaseous giants, or in Venus's atmosphere, can be very interesting to analyze. The problem would be drag, of course. Even if the density gradients can be adequately modeled, I assume drag would be very difficult to model. Besides, the force exerted inside a hole in a solid body does not necessarily need to be the same force that is exerted inside the solid body itself. There are reported anomalies for the behavior of gravity inside bore holes. See this paper by Reginald Cahill, by example: http://arxiv.org/abs/physics/0512109 If gravity is not caused by mass, but by an in-flow of space, as Cahill suggests, the anomalies can be the result of channeling or tunneling of the flow inside or outside of the bore hole, by example. Gravity is such a curious mistress. A very curious mistress indeed, which is everywhere but is nevertheless extremely discreet and secretive.
