X 0 1 2 3 4 5 6 7 8
Section Three
F and G Forces
11. Relativity vs CM
X 0 1 2 3 4 5 6 7 8 |
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Section Three |
| F and G Forces |
| ___ |
| 11. Relativity vs CM |
| 12. Kepler's 2nd |
| 13. Complex Plane |
| 14. Szebehely Eqn. |
| 15. Transitioning |
| 16. Shock Wave |
| 17. Quaternions |
| 18. Envelope Curve |
( ONE )SECTION THREE
A THEORY OF F AND G FORCESABSTRACTThe overall objective of this project has been to find a faster, safer, cheaper mission to Mars. The computer simulation of the Earth to Mars trajectory found a flight path that is so much better than expected it was necessary to develop a formal theoretical basis for the trajectory, to justify the existence of the superlative results. In all things orbital, the must fundamental theory is the Three Body Problem (3BP) of Celestial Mechanics, and so that famous mathematical anomaly was investigated, leading to a possible explanation to the fast Mars trajectory. This explanation was not all together convincing, especially to experts in orbital mechanics. So this section takes a different approach, building a whole new theory which, not unexpectedly, leads right back to the 3BP.
Reconsider the solar system cosmology in light of the new developments in trajectory optimization. The planets were formed because of not just local dynamical influences, but also because of a "system wave" that differentiated the invariant (angular momentum) plane and the original symmetric plane, the latter being still active and is presumably some kind of galactic norm.
In the same way, large and small forces were put to good use in seeking a minimum energy trajectory from Earth to Mars. The key turned out to be a very subtle phenomena of the sun-Mars system (e.g. existing in any such two body system) called a "free return" trajectory. This phenomena is what links two separate fractal regions - the solar system as a whole and Mars the planet's realm of local influence.
Fractal theory investigates a well known phenomena observed in so many different natural systems as to be assumed ubiquitous. Fractal theory is the idea that patterns repeat at subsequent levels of all natural systems. For example, the sun-Jupiter system is a Three Body Problem (3BP) and behaves just like the Earth-moon system, absent external influences. There is also a 3BP of quantum physics, on the subatomic level because the prevalent forces for gravity and electrostatics are both inverse distance squared forces. In theory, an atomic bond is analogous to the sun-Mars free return trajectory, like comets link our solar system to other solar systems in the neighborhood (or, at least, to a common center of mass).
Be that as it may, the question is how to quantify these phenomena. Fractal realms are individually well known, but next to nothing is known about the laws governing activity between the domains.
( 32 ) Discussion so far suggests that 3BP Theory is what links these realms, the free return trajectory being actually the plot of the lines of zero velocity or constant energy in the circular restricted 3BP.Presumably a similar scheme governs the alleged transition between fractal domains formed by the invariant and symmetric planes. This is itself a very subtle thing - despite the scale of the solar system, and our intricate knowledge of it - so the analogous mechanism on the scale of a small satellite orbiting Earth would be much more subtle, if discernable at all.
A first guess might be Relativity, but that has been explained away in the first section,
( 5 ) and will be further undermined by the first paper in this section. The answer seems to lie in the realm of Celestial Mechanics, but the answer is far from obvious. This section is devoted to a tentative avenue of investigation.