Let one consider the distribution of the planetary orbits
in the solar system.
The concepts outlined in the Mysterium Cosmographicum remained at the heart of Kepler's work: the rationality of the created universe, the mathematical relationships between planetary orbits
, the ratio between orbital period and distance from the sun, the force emanating from the sun.
Moreover, it is the theory of gravitational forces, and of their actions, which Newton required for the derivation of planetary orbits
using his dynamical geometry (in which figures move, shrink, approach limits, etc.) and the method of ultimate ratios which he employed throughout the Principia.
For nearly two thousand years, since Plato (see 387 B.C.), it had been taken for granted that planetary orbits
were circles, if only because the circle was the simplest curve and there fore the most elegant and esthetic.
His treatment of the Bohr atom, for instance, is pre-1925, he still believes in electronic planetary orbits
. But readers are bound to feel challenged and secretly complimented as the story marches through the intellectual centuries and they recognize so many old friends, if not many happy faces.
But most studies probe this early epoch using the laws of physics to simulate the evolution of planetary orbits
, given various starting conditions.
Wolszczan also pointed out that, as stars swell to the red-giant stage, planetary orbits
change and even intersect, and close-in planets and moons eventually get swallowed and sucked up by the dying star.
Four centuries ago Johannes Kepler was working on the then novel concept of elliptical planetary orbits
, using Tycho Brahe's legacy of positional observations of Mars.
For this simulation I assume that the planetary orbits
are circular and the Sun and Jupiter are the only objects affecting the spacecraft.
It's not so much the suspension of function as its absurd exaggeration that renders Slominski's run-of-the-mill items "aesthetic." Like those sublimely ludicrous watches that marshal the most extravagant human ingenuity, delivering up all manner of useless cosmic data (phases of the moon, planetary orbits
) only to remind us of the futility of our mortal labors, Slominski's baroque procedures have their own absurd beauty (and relentless truth).
If Kepler's elliptical planetary orbits
(see 1609) really presented an advance over the circular orbits of both Ptolemy and Copernicus, then using them ought to result in improved planetary tables.
That would cause the sun's gravitational pull to reduce enough for planetary orbits
in the solar system to increase by about half an inch (1.5 centimeters) every year, per AU (one astronomical unit is the distance between the sun and Earth, about 93 million miles or 150 million kilometers).
In the numerous multi-planetary systems around a single star for which we have checked the QCM angular momentum quantization restriction , not only do the planetary orbits
contribute much more angular momentum than the star rotation, but also each was determined to require additional angular momentum contributions from more planets and/or the equivalent of an Oort Cloud.
The planets suffer close encounters and "scatter" off one another, meaning that strong gravitational interactions can boost the eccentricity (elongation) of planetary orbits
. This picture is supported by the fact that Jupiter-mass behemoths in systems with no other detected planets generally have highly eccentric orbits.
According to the analysis, the planetary orbits
are very nearly coplanar and circular, reminiscent of the orderly arrangement of orbits in our solar system.