I am pretty new to astronomy and the project I am currently working on requires some knowledge of equatorial coordinate system. As long as I have been researching this question, I understood that vernal equinox is the origin of this system. At this moment I am stuck with task of finding distance on celestial sphere between west(on horizon) and vernal equinox. So, how do you count this distance?
The right ascension of the point on the horizon and due west is LST - 6 hours, where LST is the Local Sidereal Time. The LST can be calculated from knowing the date, time, and longitude. The declination of the west point is 0 degrees. So the angle between that right ascension and 0 hours right ascension (the vernal equinox) is just the difference between the two.
Unless you want to develop the answer from first principles, then I suggest you use formulas already published. One source is "Astronomical Algorithms", by Jean Meeus. http://www.willbell.com/math/mc1.htm
I don't have a copy of this boo, so I can't guarantee that it contains what you want.
I have no connection with the author or the publisher.