# Forum

Simon,

In ch. 7 you have diagrams showing when retrograde motion should start and stop with Venus and Mercury in the Copernican model. I do believe that your analysis is not correct. You show the start and stop points defined by the planet's velocity vector (at right angles to the radius from the sun) pointing at Earth. This is an incomplete analysis, not taking into account the relative velocity of Earth and Venus. A proper dynamic analysis would compare the velocity vector of both planets, both projected onto the line of sight connecting them to get the component in that direction. Retrograde would begin when the velocity component projected along this line is greater for Venus than for Earth, so that it would appear Venus is catching up. Using this analysis, you will get a shorter period for retrograde motion. How much shorter? That's a complex problem, to compute the exact angle when this happens. Should be simple vector math - mine is a bit rusty at the moment. Would you agree, though, that it should begin later and end sooner than you claim in Ch. 7?

OK, I did the math: retrograde begins when the angle between the two orbit vectors (sun to venus and sun to earth) is 31 degrees, continues through 0 degrees, and ends when it is once again 31 degrees, or 62 degrees of orbit total. How that translates into days is another problem - you can't just divide the "pie" of the orbit into approx. 6 slices and call it two months, because the angle is a relative angle of the two planets. It is going to be shorter, because Venus is catching up during that time. So 50 days of retrograde for Venus is entirely reasonable by my calculations.

Now, I'm not saying that this disproves your thesis, which is intriguing. I'm just saying that the retrograde argument does not work. I find it amazing that with both models, the retrograde math fits.

Dear Viking Lander,

I will concede that my argument about the observed durations of the Venus and Mercury retrogrades isn't among the strongest points in my book. However, I'm satisfied that the (variable) retrograde periods' durations - as shown in the Tychosium simulator - of ALL our solar system's planets are in full agreement with observations. And this, "in spite" of their orbital speeds remaining constant and their orbits being perfectly circular. In the TYCHOS, there simply is no need for Kepler's bizarre elliptical orbits and variable (accelerating / decelerating) orbital speeds.

I believe that it's a "golden rule"of science that the simpler a theory, the better.