Today's sun points to Milky Way center.

[Anomalocaris]

The alignment would be transitory given that the Earth rotates around the Sun.

It happens once yearly, when the sun transits Sagittarius in late November and December.

However, in the long run, this is not a permanent state of affairs because as the sun revolves around the Milky Way, the ecliptic plane in which the planets orbit the sun does not pivot around in sync.   So the sun’s passage through the back ground sky over the course of a year will only appear to take it in front of the center of Milky Way for a period of a few million years every 120 million years.     During the rest of the time e the sun never comes anywhere close to passing in front of the center of the galaxy as seen from the earth. 

So the sun has been coming roughly between earth and center of the galaxy once each year since approximately when the first hominid walked the African savanna about 3 million years ago.    But before that the sun had not been comimg anywhere close to transiting in front of the center of the galaxy since the early Cretaceous period, and before that, just after than Permian Triassic extinction.

[Ranjr]

I expected more nugget.

[Jehanne]

The alignment would be transitory given that the Earth rotates around the Sun.

It happens once yearly, when the sun transits Sagittarius in late November and December.

However, in the long run, this is not a permanent state of affairs because as the sun revolves around the Milky Way, the ecliptic plane in which the planets orbit the sun does not pivot around in sync.   So the sun’s passage through the back ground sky over the course of a year will only appear to take it in front of the center of Milky Way for a period of a few million years every 120 million years.     During the rest of the time e the sun never comes anywhere close to passing in front of the center of the galaxy as seen from the earth. 

So the sun has been coming roughly between earth and center of the galaxy once each year since approximately when the first hominid walked the African savanna about 3 million years ago.    But before that the sun had not been comimg anywhere close to transiting in front of the center of the galaxy since the early Cretaceous period, and before that, just after than Permian Triassic extinction.

Interesting calculation. I wonder how the precession of the equinoxes and changing obliquity would factor into this?

[Anomalocaris]

Precession of equinox changed the orientation of the earth’s spin axis in space and by extension the obliquity between earth spin axis and the ecliptic plane.     But it does not change the orientation of the ecliptic plane in space.    It is the  orientation of the ecliptic plane in space that determines when, during the sun’s 240 million year orbit around the Milky Way, could the earth, sun and center of the galaxy come close to being arranged in a straight line during any part of earth’s orbit around the sun.    

Basically that happens twice during each of the sun’s 240 million orbit around the galaxy.    The closest angular approach the sun appears to make to the center of the galaxy during its annual passage around the ecliptic changes by about 1.5 degrees each million years.   So in about 120 million years,  it would move 180 degrees and the sun will transit the general region of sky that contain the center of galaxy in June.    Between roughly now and roughly 60 million years from now, the sun will move 1.5 degrees further from center of Milky Way during December each million years.   In the 60 million years after that, the sun will move closer to the center of Milky Way during June by 1.5 degrees each million years.