Sunspots influence climate

Think about the phase space - how much of the enery is kinetic and how much is gravitional potential (from being farther out). Put those on x and y axes (that is what phase space is, just you can have more than two when there are other components of energy).

In the near circular orbit, you've got nearly a line in phase space (portions in each near constant, therefore velocity and distance both near constant). In the eccentric one, you've got a wavy thing, like a sine, around where that line would be.

That is for energy. Then notice that angular momentum (also conserved) is in units of mass times length squared divided by time, so the same units as energy times time. If the kinetic energy were constant, then conservation of angular momentum would be trivial. But when it changes, the change in the kinetic portion implies something else with angular momentum must change.

The earth doesn't have anything to "push against", so it can't change its angular momentum in the plane of the orbit by spinning slower or faster overall. It can however change the vector projection of its angular momentum onto the plane of the orbit, by changing the angle between its spin and the orbital motion.

As the angle between the plane of its axial spin and the plane of its orbit precesses, net angular momentum moves into or out of the orbital component of the motion. (Akin to the movement of energy into and out of gravitational potential or kinetic, over on the conserved energy side).

Naturally, these are small effects, because the axis of spin precesses very slowly. It takes tens of thousands of revolutions for them to add up to anything. But the ice age variation time scale is 10,000 to 100,000 years, so small effects (in one orbit) have plenty of opportunity to add up.

I hope that helps.

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