Imagine viewing the Earth from some point in space over the North pole, and let's just assume Earth is at the perihelion of its orbit (for simplicity's sake, let's also ignore precession).
Take the plane $\pi$ which passes through the center of our planet, is orthogonal to the ecliptic and also containes the Earth's axis.
My question is: does this plane contain also the center of the Sun? It seems that this should be the case but it's not at all obvious to me.
As far as I can tell it's just a coincidence. Currently the solstice occurs on or around December 21, while the perihelion of Earth's orbit is on or around January 4. However, both the direction of the Earth's pole and the location of the perihelion precess with time; these are known as axial precession (aka precession of the equinoxes) and apsidal precession respectively. The periods of these precessions are not the same; Earth's axial precession has a period of about 26,000 years, while its apsidal precession has a period of about 112,000 years. Over time, then, the perihelion moves around Earth's orbit relative to the seasons:
(Image from Wikipedia)
This cycle is an important contributor to cyclical variations in the Earth's climate, known as Milankovitch cycles.
