Precession of the Equinox I just learned about precession of the equinox, i.e. the Earth's axis tilts one degree every 72 years. 

And it takes 72 years/degree x 360 degrees =  25,920 (years in one cycle)

There are many theories to this, i.e.


Sun's gravity is affecting the tilt of Earth's axis
Sun itself is revolving around another star, and it takes 25,920 years, hence the slow tilt of Earth's axis


I googled whether the Sun revolves around something else, and according to NASA.gov, Sun revolves around center of Milky Way it it takes 230 million years.

Now, I am confused between precession of the equinox and Sun revolving around another star.

Does precession of the equinox have anything to do with the Sun revolving around another star? Or is it simply the Sun's gravity acting on the Earth?

What is the explanation according to modern science? I understand there were astronomers in the past who deduced that the Sun revolved around another star and it took 25,920 years.
The sun does not orbit another star. A star, even a very small brown dwarf, would have been seen, if not in visible light then in the infra-red by the WISE survey.

However there is no mystery about precession. The Earth is non-spherical, it is wider around the equator, and because the Earth is tilted with respect to the ecliptic, there is an asymmetry in the force of the sun, and the moon, on the Earth. This force pulls the axis of the Earth's rotation in a circle. The basic maths of this is not so hard, and is in the Wikipedia page on Axial precession. This explanation of axial precession was known to Newton. There is nothing controversial about it. 

The sun does orbit the galaxy it takes about 230000 years to complete one orbit. This has nothing to do with axial precession.

The page you link to is worthless. It offers an "alternate explanation" of a phenomenon that is very well understood, and pretends that there is some mystery, where there is none. It the uses this to justify a lot of astrological nonsense. 

To repeat. 


There are not "many theories" explaining Axial precession. 
Axial precession is a well understood phenomenon, due to the Earth not being a sphere and the axis of the Earth not being perpendicular to its orbit 
The sun does not orbit another star. We know this because we could have seen it.
No astrology based on the presence of another star is valid.