If inverse square laws are larger particles comprised of infinitesimal particles, adjacent tidal axii subject to two relative speeds will or would most likely explain day lengths.
On these adjacent inner planet a quarter of an orbit advanced beyond a transit diagrams, planetary speed magnitudes come tidal axii speed magnitudes are relative to each other. With respect of the motion of the sun, the diagrams are all timeless and the push vectors instantaneous forces
You do sort of need a spatial picture of the structure of an inverse square law field in your head first for all this. If you live in lieu of one, next week Euclid or Sir Isaac may be able to help out in that department.
Apart from a transit being an alignment of two planets with the sun, the things to note from the rotation rate table are the inner two planets are like the moon. Have rotation periods of the order of their orbital periods. And outer adjacent planets are pairs with similar rotation periods. Thus the rotation aspect you can see on this table.
If you can note that and can consider the rotation aspect to be a possible/probable ingredient of our solar system, it's all pretty interesting. The same face of the moon always being towards the earth is a pretty good clue to the moon being turned by the tidal quadrant of its gravity field. The inexactness of the elements of the rotation aspect for the planets, well the rotations are going to be 'orbital' period conflict rotations of inverse square laws between planets. Not just a locked synchronisation with one other planet.
The facts we have are Venus turns backwards on its axis once whilst this fixed sun professor planet does 2/3's of its solar cycle. And, every 584 earth days, the same face of Venus is almost precisely towards the earth when Venus passes between the earth and the sun. There are a few other little rotational/cyclical near exact ratios between the inner three planets as well. For instance, a Venus sunrise occurs every 117. something earth days. Meaning there is almost precisely 5 Venus sunrises to each Venus transit of the earth. And Mercury rotates twice on its axis every 117.3 days.
The Venus - Mercury relationship is really a quite compelling suggestion of the idea of gravity field turn rates being the clue to planetary rotation rates. Hard to see why the Martians even doubt themselves on this. The Venus 'orbital' direction and the Venus rotation direction are opposite. As Venus advances around the sun, the face of Venus directed towards the sun changes. This face change is synchronised to the Mercury rotation period while the actually Venus rotation period is synchronised to the earth year.
That almost says it all. The lingering doubts of the Martians must be that it all means that the earth's lunar tides are really earth solar tides that are getting moved around the earth by the moon.
Anyway, if the tides of a planet get to be seen as factors of the equal and opposite quadrant nature of an inverse square law, in time we should see that, minus a moon or moons, the solar low tide axis of a planet becomes a circle around the motion of the sun at a planet's distance from the sun.
Then, if the earth - moon high tides run through the Venus inverse square law during a transit, the low tide axis of the earth - sun system gets marginally shifted out of this circle toward the 'orbits' of Venus and Mars as this earth planet moves forward.
At the same time the Venus inverse square law and the earth inverse square law are being turned backwards as Venus and the earth move forward.
If you get some spare time, you could do worse than having a go at it.
As mentioned, it appears that the earth's lunar tides are really solar tides but are getting moved around the earth by the moon.
To have some fun, the various ellipses could be whacked on. The interesting thing is the tangent from an inner planet is directed in the region of the next planet out a quarter cycle beyond the transit of the inner planet. As well the Venus - earth situation is very close to a right angle. And the Venus orbit of a fixed sun is very close to a perfect circle.
The way the planets are always tending towards a complete alignment suggests the inverse square laws of the planets are a tension within the motion of the sun's inverse square law.
On one hand the planets have the relative speed that the motion of the sun's inverse square law supplies at a planet's distance from the sun. (Kepler's third law)
On the other, adjacent planetary inverse square laws are tidally pushing on each other with their various relative speeds within the motion of the sun's inverse square law and inspiring mutual relative speeds for each other.
These mutual inspirations appear as the rotation rates of the planets and the ellipses (Kepler's second law). Maybe anyway. Future moving inverse square law professors will work it out. Pluto's inverse square law seems to be marginally outside the tension. Not sure. Not really the Bode perspective, but the distances of the planets from the sun looks like being to do with each other. Then there are the questions of what turns the sun's inverse square law? Is a planet's inverse square law its axis of rotation? Do the planetary cores turn with their inverse square law quadrants? Does the speed of the sun control day lengths. etc, etc.
If you are part of an up and coming generation of young people or whoever, have a think. After the journey to discern it, declaring that rotation rate table to be coincidence without certainty of such would be against your and your descendants best interests. In a hundred years time your descendants could be getting life on earth tuned in with the galactic journey they are on. Which should have more good than harm in it.
When personally bringing the table into focus, it is quickly realised finding a way of pointing the tidal flaw in mutual gravitation to fixed inverse square law ears is the more important chore at hand. But there is something going on between the rotations of the planets. Uranus seems to be tidally jammed between Neptune and Saturn. If it is on the right track, the 24 hours in our day would be a consequence of the uniqueness of the solar system. The more you involve your self with the table, the more magical our existence seems to be.
The way Kepler presented his great work is probably where the trouble is. Time squared in the third law means nothing. Likewise the fact that a planet sweeps out equal areas in equal times in his second law.
1/ The first law says the paths of the planets around the sun are elliptical when the sun is fixed and with the sun being at one foci of the ellipse.
2/ The second law says the speed of an individual planet relative to the sun varies with the inverse of its distance from the sun.
3/ The third law says the average speed of any planet relative to the sun varies with the inverse square of distance from the sun.
(link)Did Newton answer Halley's question.
The Galilean problem of the planets ascending and descending at the same time aside, the answer to Halley's question was a circle. Not an ellipse. Somehow Sir Isaac has attributed the equal areas in equal times to the inverse square law. All the equal areas in equal times means is as specified in 2/ above. Plus the striking conflict with the third law.