Wednesday, June 22, 2022

'Neath Tarhuna's baleful gaze

Before opining further on HIP 29724 I should pause to consider the forces involved upon the Kirkwood Gaps. Prompted by news like this.

Say you are sailing a Solar orbit this side of Jupiter. Let's use Jovian units for mass; the Earth "AU" semimajor for distance. As Lagrange intuited, Jupiter's strength is most salient when you are between the Sun and this planet... and then, when you are ON THE OTHER SIDE of the Sun. Vector calculus, baybee!

1047/r2 Jovian units of Pull go to the Sun. When between the Sun and ol' Jove, that's against 1/(Rj-r)2; Rj here being 5.2038 AU.

The Hungaria between 4:1 and 5:1 has proven not great for worldbuilding. Mars exists beneath that, so let's r = 1.524 AU. 450.7926 Junits pull to the sun. On the other side 0.07276 Junits pull to Jupiter. Now: compare the other side. 1/(Rj+r)2 = 0.0221 units toward Jupiter ADDED to the Sun's pull. So for the delta, per half-revolution of 343.49 Earth days is about 0.09485 Junits, all pulling you toward Storm God Baal. I'm sure someone could come up with some better equations, involving radians and Newtonian Integration; but this is just a blog, I'm thumbing it.

I admit: against Solar 450.7926 Junits, 0.095 is negligible year by year - yes, we work by full sidereal revolutions here. As to that, Mars has had 1/1.88 the number of years as we've had on Earth. But it's still - what - 2439 million revolutions, which do add up. Hence why Mars has eccentricity, which I am sure would be a lot worse if Earth/Venus weren't here to force some mild synodality upon it.

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