> The fact that the axial precession's period is much longer than a year means that the angle of the axis can be considered approximately constant during a year. Why would that mean there is no systemic difference between the northern and southern hemispheres?

Well, you're citing the conclusion of point B and then responding to the conclusion of point A. (Yes, they have identical premises, but B is more technically accurate.)

If the obliquity[1] of the earth is constant during a year (which it effectively is), then there is no difference in the obliquity of the earth between summer of year X and winter of year X, and therefore the obliquity of the earth cannot be responsible for any difference between the northern hemisphere and the southern hemisphere. This should be painfully obvious.

Back on point A, in order for there to be a systematic difference between the seasons in the northern and southern hemispheres, precession would need to have a period that was a multiple of the solar year. This would keep the difference in place over time. Without meeting that requirement, the hypothetical precession-based phenomenon would wander through the calendar year, which would prevent it from systematically having different effects in different hemispheres.

Being a multiple of the solar year is not ruled out by the fact that the precessional period is on the order of tens of thousands years, but it becomes vanishingly unlikely.

> Did you just wrote "much" with capitals and reworded that there is no effect?

No.

> What is the difference between your point a and b?

They are addressing different points.

One is talking about year-to-year differences; if summer in December 2437 is hotter than summer in June 2437, does it follow that summer in December 12437 will be hotter than summer in June 12437? (No, because the precessional period is not related to the orbital period.)

The other is talking about within-year differences. If summer in June 2437 is whatever temperature it is, does it follow that summer in December 2437 will be hotter than that? (No, because the precessional period is much longer than the orbital period.)

> Axial precession makes seasonal contrasts more extreme in one hemisphere and less extreme in the other. Currently perihelion occurs during winter in the Northern Hemisphere and in summer in the Southern Hemisphere. This makes Southern Hemisphere summers hotter and moderates Northern Hemisphere seasonal variations.

This is logically incoherent. There are two problems:

1. Axial precession isn't doing any work here. The difference, as described, comes from an interaction between the earth's orientation and the eccentricity of its orbit. Axial precession has no role to play in the phenomenon; the conclusion ("southern summers are hotter and southern summers are colder") would be equally true if there was no precession. (In fact, more true, since in that case it would remain true into the future.) The effect of precession is described in the following sentence:

> But in about 13,000 years, axial precession will cause these conditions to flip, with the Northern Hemisphere seeing more extremes in solar radiation and the Southern Hemisphere experiencing more moderate seasonal variations.

2. Perihelion is not a concept related to the obliquity of the earth or the axial precession. As such, once you've invoked perihelion, you can't attribute responsibility to obliquity or precession. Going by the description here, there is a period (perihelion) which causes the seasons in one part of the earth to be more extreme, and axial precession is the phenomenon that causes which part of the earth experiences that greater extremity of climate to shift over time. How do you get from "axial precession distributes the effect of perihelion evenly over the earth" to "axial precession is why the seasons are more extreme in the southern hemisphere"?

So, going back to the original claim:

>> but the fact we tilt slightly closer to the sun in summer than the northern hemisphere makes 6-7% difference

This is not a fact. It's false. There is no significant difference in tilt. The difference is in physical distance to the sun, not angular distance to the sun.

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[1] You're making a mistake here; the angle of the earth to the orbital plane ("which latitude points directly at the sun?") is not affected by axial precession ("where in the sky is the north pole?"). I was making the same mistake.