Calculating the time a star is at my local meridian based on its right ascension I've been watching an astronomy course on YouTube and I'm struggling to calculate stars' positions based on their right ascension.
What I'm trying to achieve: Calculate when a star (Sirius in this example) will be exactly on my local meridian.
What I know: The star's right ascension and the &quot;noon&quot; time (=when the sun will be exactly on my local meridian).
Let's assume we are on March 21st: According to https://stellarium-web.org/ The sun will be on my meridian at 12:10. Sirius's right ascension is 6h46m, which means Sirius should be at the meridian 6h46m later which is 18:56. According to Stellarium Sirius will indeed be at the meridian at 18:52 (I suppose that 4 minute difference is because the sun is already 4 minute behind due to Earth rotation).
But when I try to do the same calculation for today (Feb 10th) I get a 20 minute error.
The &quot;noon&quot; on Feb 10th where I live is at 12:18. We add Sirius' right ascension to get 19:04. But this time we also have to take into account the fact that we are 41 days away from March 21st. Each day the sun falls behind by ~4 minutes, so that's 2h44m. If we add that to 19:04 we get 21:48. So that's the time Sirius should be at my local meridian on this particular day. But Stellarium shows that Sirius will actually be at the meridian at 21:26. So there's 22 minutes error in my calculations for some reason.
I think the root of the error is the 2h44m that I calculated for the sun's position. According to Stellarium the sun's right ascension on that day is 21h38m. Meaning it is 2h22m behind not 2h44m. And that's why I get that 22 minutes error. But I don't understand how it can be 2h22m because Feb/10 is 41 days away from March/21. That means 41x4 = 164 minutes = 2h44m.
What am I missing here?
The sun's position is irrelevant to when a star will be in its meridian; the Sun's coordinates in the RA/dec grid does change over the year. A star's position is fixed in that system and it will be always at the exact same sidereal time that it culminates (as that's the definition of sidereal time).
The difference of the sidereal day to the mean solar day is ~3:56 minutes (366 earth revolutions in a sidereal year, 365 in a solar year), thus a star culminates (and rises and sets) that much earlier each day.
If you compare it to the true solar time (which determines when the Sun is in the meridian) as you try, you also have to account for the difference of the mean solar time and the true solar time due to the eccentricity of Earth's orbit; this phenomenon visible as the analemma (which basically visualizes the equation of time) accounts for a difference of the true noon which varies by about +-20 minutes throughout the year - and can explain the differences you see.
This means that the Sun culminates at different times throughout the year. On March 21st it may be 12:00h. But that is not exactly true 2 month earlier or later, it might be 11:40h or 12:20h.
I think the explanation in the video as linked in your comment as &quot;hours behind the sun&quot; can be a bit mis-leading, and is only exactly true for that one exact date (and defines how the two coordinate systems align with respect to eachother) - but he ignores the equation of time and assumes the mean solar time to be used while his words &quot;behind the sun&quot; imply true solar time. For the task at hand, where to visually find a certain constallation, that is good and accurate enough, though - so not wrong, just mathematically you will have to consider effects he graciously left out.