The effect is small as already stated by SoD. Whether is small enough to be ignored is another matter.

]]>The sun crosses the equator twice a year = seasons.

The variation of obliquity on much longer time scales is something that affects the strength of seasons.

]]>tanks.

I would use as an approximation for the cross section

A = (pi/2) R_e ((R_e + R_p) – (R_e – R_p) cos(2 phi))

where phi is the angle between sun and equator plane, R_e und R_p are the equatorial and polar radius.

Have you already took into account that the sun position crosses the equator two times the year? So phi goes from -ε to +ε and back? ]]>

Interesting point.

“*The angle between Earth’s rotational axis and the normal to the plane of its orbit (obliquity) oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. It is currently 23.44 degrees and decreasing.*”

Taking your two radii, which match those in Wikipedia, and assuming a linear change with angle between these two extremes (because the exact spherical geometry seems like a lot of work)..

So we get 0.0037% change per degree of obliquity, or 0.009% for the obliquity change experienced by the earth.

This is over a 41,000 year cycle, so min-max in half the cycle equates to 0.009% over 20,000 years..

.. or 0.2 mW/m^{2} per century.

Compare with the calculation in Part Four of 0.8 mW/m^{2} per century due to eccentricity.

The rate of change of insolation received due to the changing “blocking” radius of the earth due to obliquity changes is about 1/4 of the rate of change of the insolation received due to the negligible eccentricity effect.

]]>I think not only the eccentricity, also the change of obliquity should change the total amount of solar insolation received at top of atmosphere. This is due the flattening of the earth which changes the cross section. The equatorial radius is 6378137 m but the polar radius is only 6356752 m. Neglecting the atmosphere the ellipse that block the sunlight is 6378 x 6357 km if the sun is above the equator but 6378 x 6378 km in the (hypothetical) case if the sun is above the pole. The difference between these extrem cases is 0.34%.

Maybe you can quantify also these (small) effects of the obliquity change on total solar radiation at TOA? (And compare them to the from eccentricity change?) ]]>

Here are the two figures from *In defense of Milankovitch*, Roe, GRL (2006):

And yes, I expect to discuss this paper, it is one of the ones in my list to cover.

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