Gravitational Ramblings

I was never really interested in physics, preferring instead the more pure branches of mathematics. Given that, much of what I'll say in this little discussion is probably already out there or just total nonsense, still just in case it isn't, I figured I just write it down. You never know, it's a strange world.

I was watching a newly published lecture series with the eminent Richard Feynman. He said a couple of things that I had already learned about gravity, but I found fascinating anyways. The first was that Copernicus found that the planets traveled in a ellipse, with the sun being in the focal point. Quite well, known, but the relevance of the sun's position never really dawned on me before. Another thing he talked about was the measurements for a system far away, but the star's position wasn't at the focal point in the ellipse, he pointed out that this was because we were viewing the system from an angle. The final bit that I found interesting was that the earth and moon as a system pivot about a point slightly off center to the earth. The position is accounted for by the masses of both objects being proportionally closer to each other.

My understanding of gravity comes from the commercialization of Albert Einstein's theory of relativity. As scientists tried to explain it to the rest of us, they fell back on easily graspable perspectives. Watching enough of this stuff on TV, I tend to see gravity as being the displacement of space-time by a object of significant mass, much like a bowling ball would form an indentation in the sheets on a queen sized bed. The presence of the ball pushing into the mattress deforms the sheets. For space, if we could see our 3D world as a projection onto the sheet, much like a we can be cast as shadows on a wall, then mass tends toward bending that plane around it.

Somewhere else, I was told that objects in space keep moving in one direction forever. Once force has been applied, momentum cares the object along in a straight-line. Well, not really straight, in the 3D sense, but rather straight in the gravitational sense. In a simple system, with one large object in the center, and a smaller one caught in it's outskirts, the smaller object travels around and around the larger one at the same depth in the gravitation well. If it gets started circling the larger object at a specific gravitational force, the shortest and straightest path is to stay at that same level of force, and circle forever.

And so it was, that I could see in a simple system of two bodies, one body perpetually circling the other body at the same distance. Well, almost. Somewhere in the back of my head I did know that one small object doesn't not really "circle" the other one. That's what Feynman reminded me of, while watching the lecture.

Way back in school, we learned about conics. If you take a cone in 3D and slice through it at a 90 degree angle, the slice should be a perfect circle. If however you start tipping the slice, then it becomes an ellipse. If you tip it far enough, then it becomes a hyperbola. All three of these geometrical objects are related in that they can be generated by a plane intersecting a cone. It's kind of a neat result, in an odd way, and has always stuck with me because of that.

If we have a small object, called A, and a much larger one called B, then the AB system consist of the smaller object orbiting the larger one. In my little universe, this orbit is a perfect circle. If, in this universe, we add in another much much larger object called C, then gravity well caused by this new object should have some type of affect on the original AB system. If the AB system is trapped in the well of C, then it is rotating about C in a perfect circle. That sort of makes sense in this model. More interesting though, is what has happened to the AB system itself. It started as a perfect circle, with A orbiting B. Now however, this system itself sits at an inclined position in the well around C. It sits on a slope in space-time. If the effect of that slop is similar in nature to a plane intersecting with a cone, then the orbit of A around B will no longer be a perfect circle. It will be an ellipse, depending on the gradient of the slope from C. And if there is another even more massive object called D, then the effect of D on ABC will be to for the AB system to orbit C in an ellipse as well, and to change the specifics of the ellipse of A. In other words the effects are accumulative, and seen at every level in every system.

Gravity, like light, seems like it is inversely proportional. Some radicalizing increasing curve of some type. It doesn't really matter, other than it is not linear. From this, we can assume that there is some gravitational horizon in which the affects of an object in space-time exists, and beyond which they do not.

What I though interesting about this perspective is that the interaction between any two bodies is driven by their masses and the accumulative gravitational incline for any gravitation horizon that they sit in. The earlier point about the center of system of the earth and moon not actually belong the center of the earth was interesting. One would expect that two objects of the same size would form an interesting gravity well, much like a sombrero. The deepest regions of gravity would be on the lines of orbit from each other. The center of the system would have less of a gravitational effect.

We would expect, if any of the above were true, that in the many variations of the theme that exist in our universe, we'd see all sorts of different types of smaller solar systems, sitting at all sorts of different inclinations. We'd probably even see a few where the slope is so inclined that any other object is on a hyperbola, and kicked right out of the system.

As I was bouncing these ideas around, I also started thinking that one could view gravity in a number of different ways. One way was as a set of 4 parallel dimensions, the affect of which alters the movement through the other 4. After a bit, I though a nicer version would just be a straight-up 5D universe. Then all points would be (x,y,z,t,g), and we could refactor the laws of motion to always conserve momentum at the same depth of g. Thus (x1,y1,z1,t1,g1) -> (x2,y2,z2,t2,g2) requires no extra force, if g1 == g2. Although I'm not sure if that is equivalent to creating perpetual motion (would the other points on G bind in some ways to the other forces, like electromagnetic, or weak nuke?).

If we knew the slope at any point G, then we could calculate how that would affect a local system, also we could probably model the decomposition of G into various parameters caused by bodies such as the galaxy and the milky way. With each horizon having an affect, the local inclination is bound to change as the objects dance with each other.

Yes, I know, it's probably too simple of a model, but it just seems to tie together a bunch of loosely correlated bits. Worth writing about, even if it's totally wrong.