@metal-brain said
Yes, but is there a calculus prediction that appears to confirm an orbital change every 100,000 years? Then it must change back for the warming part of the cycle. How the heck does that happen?
Do you have any information explaining that?
The Earth's orbit has a set of parameters that specify the ellipse that it follows. In the idealized two body problem the ellipse's parameters are all constants. In the perturbed case the parameters can change. Because the Sun is an oblate spheroid there is a correction term. So instead of:
V(r) = -GMm/r
We have
V(r) = - GMm(1/r + α( θ )/r^3 + ...)
where α( θ ) is a parameter that depends on the angle of the orbit relative to the line between the Sun's poles.
So the direction of the major axis is an angle we'll call φ = A, where A is constant. This then becomes φ = A + Bt, where B is calculated using perturbation theory. Because φ = φ + 2π, we have the major axis eventually returning to it's original direction.
The relevant orbital quantity for the 110 kyr cycle is the argument of periapsis ω (I suggest looking at the diagram on the eponymous Wikipedia page). This is the angle between the ascending node (when it crosses the Sun's equatorial plane) and perihelion (point of closest approach to the sun).
Perturbations are due to the Sun being an oblate spheroid, the other planets, and a tiny correction from General Relativity. The Earth's orbit has been calculated for the next billion years or so and they can measure the change in the argument of periapsis (or perihelion since it's an orbit about the Sun) and compare the results.