Let them alone: they be blind leaders of the blind. And if the blind lead the blind, both shall fall into the ditch.
(Matthew 15:14) KJV
Why are planetary orbits elliptical? Supposedly Sir Isaac Newton solved this problem mathematically in his Principia Mathematica (1687).
As the planet is differently situated in these conjunctions, its eccentricity is sometimes augmented, sometimes diminished; its aphelion is sometimes carried forward, sometimes backward, and its mean motion is by turns accelerated and retarded; yet the whole error in its motion about the sun, though arising from so great a force, may be almost avoided (except in the mean motion) by placing the lower focus of its orbit in the common centre of gravity of Jupiter and the sun (according to Prop. LXVII, Book I), and therefore that error, when it is greatest, scarcely exceeds two minutes; and the greatest error in the mean motion scarcely exceeds two minutes yearly.
Sir Isaac Newton, Principia Mathematica PROPOSITION XIII. THEOREM XIII
Quoted in Newton & Kepler: Effect & Cause
We all have the same evidence. Our choice of paradigm determines what we think it’s evidence of.
– Matty’s Razor
Newton’s describing the apparent error in the orbit of Jupiter, an effect. By “error” he means that Jupiter’s orbit of the sun isn’t circular, as one would expect in a heliocentric system, but it has varying degrees of eccentricity which makes it elliptical. The tacit assumption is that the sun is the most massive body in the solar system, although there’s no statement or mathematical proof provided which substantiates this. Newton’s rationalizing the orbit of Jupiter to get it to fit the the premise of heliocentricity. It’s how he’s chosen to imagine the relative motion. Here’s the problem: it’s an effect, not a cause. He’s using math to explain an effect but the cause of the effect is a premise, not an observation. This is known as inductive reasoning.
Inductive reasoning (as opposed to deductive reasoning or abductive reasoning) is reasoning in which the premises are viewed as supplying strong evidence for the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.
– Inductive Reasoning, definition (Wikipedia)
Fortunately for us Newton’s making his case based on the fact that an ellipse has two foci.
By saying that the lower focus (f2) is the common center of gravity between the Sun and a planet (the barycenter) Newton is acknowledging the fact that an ellipse has two foci.
By a totally staggering coincidence, the solar system on which his observations are based just happens to be orbiting the Earth every day. Every. Single. Day. The observations and measurements we make of the cosmos are possible because we’re standing on one foci of the ellipse. He ignored the most profound of all observations: he’s observing the relative motion of the planets and stars from a stationary Earth, and imputing an imaginary frame of reference as the cause of the observation. It’s scientific sleight-of-hand, it looks like Newton pulled a switcheroo on cause and effect.
Matty's Paradigm 
The other day I asked, @asknasa, why Europa’s orbit is eliptical. Their answer to me was that Io and Ganymead influence gravitational pull over Europa causing the eclipse. I can’t argue from an educated position and I’m not trying to challenge you, just discuss.
I understand your point about the absence of another focus causing eliptical orbits. But as I study your moving diagrams the concentric one illustrates pathways that offer proximity and planetary alignment such as what we experience with our moon causing ocean tide changes and earthquakes. The focus of attention is the natural cause of eliptical orbits but moreover, the conspicuous mostly circular orbit of Earth which begs the question of why, since life is fragile.
The cardioid track is most strange. When Mars orbit decays and is headed for Earth the Sun is aligned behind the Earth pulling Mars even more. But as your Sun moves to 6:00 o’clock then Mars is pulled into a U-turn and runs away from the pull.
The argument has to be that when the Sun is South it pulls Mars down and in its turn is slung away. If so that timing would need to be close and science would note a conspicuous anomaly. In addition in my layman’s opinion your cardioid pattern, there would be predictable violent tides and quakes every two years.
Again, I’m only trading ideas, not trying to stir up an argument. I appreciate that you question because it makes me think about it. It seems to me that if the rocket scientists are wrong about gravity and solar system mechanics that it would be impossible to track and predict positions of the planets and their moons.
LikeLike
Thanks for your comments, I appreciate the thought you have put into it.
The important thing to realize about the Earth and sun is that they are a constant distance apart. It is not an elliptical orbit. The Earth and sun are F1 and F2 in the elliptical orbits of the other planets.
Rocket scientists have an accurate model for predicting the relative position of the planets which is why their missions are successful. The difference between heliocentric and geocentric models is relative motion, so it is possible for them to be right and wrong at the same time.
I also suggest that you take a look at my post Matty’s Constant for the Calculation of Planetary Mass if you have the time.
mattysparadigm.org/?p=1400
Thanks!
LikeLike