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Robert H. van Gent,
Thanks for the link. Then I guessed correctly that the main factor is the Moon (but the influence of Jupiter and Venus can also be significant).

Frank,
"some kind of parallax"
My starting point was that a satellite can be said to orbit the Earth because its mass is negligible compared to the Earth's. We can't say that about the Moon. Also, even if the mass of the Earth is negligible compared to the Sun, it is not the center of the Earth that orbits the Sun, but barycenter of the Earth-Moon system. If the center of the ecliptic coordinate system is the center of the Earth, then sometimes the Sun is seen from below, sometimes from above, relative to the ecliptic plane (also, the Sun-Earth distance matters). This was what I tried to draw in my first post.

Thanks for the JPL Horizons link, it's new to me.

"And I'm still interested in that funny wobble from the last graphic."
This is an interesting topic, I would be happy if I understood astronomy at that level.

Bela