Kepler’s ‘MARS discrepancy obsession’ explained


Dear all,

Today I made the most unexpected – yet quite marvelous – realization with regards to Kepler’s notorious “War on Mars”, as he liked to call it. The readers of my TYCHOS book will recall that Kepler struggled for many years trying to make sense of the motions of Mars, using the observational data provided by his master Tycho Brahe. What few will know however, is that Kepler - famed for having ‘invented’ the purportedly elliptical orbits of our planets - was initially convinced that all orbits had to be uniformly circular (which in fact is the correct assumption, as thoroughly demonstrated in the TYCHOS model).

Now, as widely reported in astronomy literature, Kepler’s “problem” (which he obsessed about for years) was that of a recurring discrepancy of Mars’s predicted circular motions amounting to about 8’(eight minutes of arc). I was of course aware of this 8-minute discrepancy which caused Kepler so much distress but, for some reason, I had never made much of it – nor put it to the test in the context of the TYCHOS model. That is, until today.

Today I stumbled upon this extremely brief blogpost by Mr John D. Cook, dated October 2022:

“CIRCULAR” – by John D. Cook (October 2022) Planetary orbits are very nearly circular

Please spend a minute reading Mr.Cook’s brief blogpost before continuing. Thank you.

As you can see, Mr. Cook basically states (and rightly so) that:

  • The orbits of our planets are virtually circular; their purported “ellipticities” (as of the heliocentric theory) are ridiculously small, yet most people are unaware of this fact.
  • Kepler obsessed about an 8-minute-of-arc discrepancy that plagued his calculations for Mars’s observed celestial positions – and this was the reason why Kepler eventually concluded that the orbit of Mars - and all the other planets - must be (very slightly) elliptical.
  • 8 minutes of arc represent 0.037% of a perfect circle.

QUOTE: “It was only by obsessing over a discrepancy of 0.037% of a circle that Kepler was able to discover that Mars has an elliptical orbit.”

Alright. So let me now remind you of the last section of Chapter 13 of my TYCHOS book where I show that our Moon’s apogee and perigee oscillate by 42108km – i.e. by 3 times the amount of Earth’s annual motion around its PVP orbit (14036km).

This is when we need to consider, conceptualize and envision that the PVP orbit represents the “nucleus” around which our entire Solar System revolves. In other words, any observed oscillations of our surrounding moons and planets due to the Earth’s annual 14036-km translational motion should, in all logic, affect them equally (i.e. by the same percentage rate).

Now, the “nucleus” of the TYCHOS model (which I have called the PVP orbit) has a diameter of 113 230 656 km. As we just saw, our Moon oscillates around Earth by a total amount of 42108 km (something that would be interpreted as “a discrepancy” by anyone unaware of the PVP orbit’s existence).

Well, Kepler interpreted the “discrepancy” of Mars’s motions as amounting to about 0.037% of a perfect circle, didn’t he?

And it “just so happens” that 42108km (our Moon’s observed oscillation) amounts to just about 0.037% of the PVP orbit’s diameter!

I will thus rest my case: ALL the orbits of our planets, moons, comets and asteroids are perfectly and uniformly circular (albeit, of course, trochoidal - since they all revolve around the revolving Sun). The only reason why Kepler (et al) have decided that they are (very slightly) elliptical is due to their ignorance of the Earth’s motion along its PVP orbit.