intro
What the Copernican revolution hasn't done is move up to the fact that the falling of the planets towards the sun is not balanced in some way by a planet's 'inertial mass'. Courtesy of the motion of the sun's gravity field, the balance is a constantly changing direction of descent. Using numbers as the arbiter of right and wrong, the wash up is the same as the ascending Galilean 'inertial' direction on the school lesson diagram at the top of the page. In terms of physics, though, it is a vastly different circumstance.
In fact when the balance of the acceleration towards the sun is seen to be the advancement of the sun's gravity field around a galaxy, traditional views of the universe are out of their depth. The only way the constant falling of both the earth and moon towards the sun can fit together in a stable way is if they are held a part. Hence the push. The implication is gravity fields are extremely large moving particles filling up the universe and planets and stars are minute but more easily detectable particles in their centres.
So could mathematical geniuses be wasting away what the telescope is telling us about the solar system? In particular about the discovered motion of the sun and the rotation rates of the planets?
If you are a mathematical physicist of the Copernican revolution era, this is the simple point. Your craft is based on unproven presumptions. A mutual gravitation of the universe and motion having a reason that is intrinsic of matter. Each presumption is demonstrable as unfounded and relatively easily so.
Realistically physicists over the centuries could have and should have harboured suspicions about both those concepts. The absence of professional rat smelling can only really be attributed to Sir Isaac Newton having a hypnotic effect on future education systems with his dominance of the early Royal Society of England (link).
Sans hypnotism by now our knowledge base would easily contain the gravity field aspects of magnitude variations, motion and their rotations.
1/ Magnitude variations = tides
2/ Motion = orbits within
3/ Rotation in all probability = 'day' lengths
Twenty four hours in our day is almost certainly a factor of the twenty four hours in a Mars day.
The question looking for an answer is why would pairs of adjacent planets have rotation rates that are approximate of each other?
When the close synchronization of the three Venus days with every two earth years and the almost exact three Mercury days to every two Mercury years is added to the slower inner planet turn rates, observed rotation rates are pointing to the solar system being a gear box churning out numbers as it advances around the galaxy.
[(3 x 243.02 = 729.06) (2 x 365.26 = 730.52)]
[(58.65 x 3 = 175.95) (87.97 x 2 = 175.94)]
The Mercury day length - orbital period ratio of three to two would be an extremely unlikely coincidence. There are other near exact ratios between Mercury and Venus. Instead of black holes and big bangs, an updated Copernican revolution with the goal of understanding rotation rates set as a priority would be of tangible value to the way life on earth goes about itself.
One impeding problem is Sir Isaac Newton's law of gravity is more fib than truth. A smaller mass does not cause the acceleration of a larger mass towards itself. The other academic concern is failure to understand that a resistance to a change of motion is an acquired opposite force. Not a force mysteriously residing in the bowels of matter as Galileo's era began a belief thereof.
The world is unlikely to have a better or other way forward than beginning a respect of the telescopically discovered rotation rates of the planets. Just like Johannes Kepler's third law of planetary motion table, the rotation rate table is a riddle of knowledge about the solar system waiting to be solved.
If the sun was fixed in space, as per the diagram at the top of the page, this table would not be. The planets would simply fall into the sun. Without realizing it, though, space exploration has moved towards the right answer. All descents are relative motions is that correct answer. The principle of such is used to alter the speed of a spacecraft as it passes another planet.
Anything dropped falls around the universe. Not straight to a centre as Sir Isaac Newton stated once upon a time.