# What constellation is closest to the Zenith with RA=12 and Dec =47.6?

I have several options, but I do not know how to calculate which option is closest to the zenith in title. Could you please help me with this? Thank you.

Canes Venatici,CVN,13.14763.+40.04187,M
Cygnus,CYG,20.61006,+42.53633,A
Lynx,LYN,8.01440,+46.23233,M
Perseus,PER,3.49832,+43.88451,A
Ursa Major,UMA,10.98253,+52.52900,A

• You might not have the question described correctly. According to djm.cc/constellation.html 12.00 +47.6 is in Ursa Major. I think if you provided geographic coordinates in latitude and longitude, then you can ask which constellation is closest to the zenith provided with the coordinates. If for example 47.6 were latitude, then the zenith would have a declination of 90-47.6=42.2 degrees, and that seems closest to the declination given for Cygnus.
– uhoh
Commented Jan 8, 2020 at 5:31
• @uhoh If 47.6 is a latitude, don't you also need a time to know the declination of the zenith? Commented Jan 8, 2020 at 7:48
• @usernumber Aha! yes indeed, you are way ahead of me! :-) but if it is a normal time, then you would need the time of year as well. However, if the 12 is a sidereal time then maybe it's good to go? See item #6 in astronomy.stackexchange.com/a/32621/7982
– uhoh
Commented Jan 8, 2020 at 8:38
• Please edit this and replace the picture with actual text. Pictures are not searchable.
– user1569
Commented Jan 10, 2020 at 8:07

The positions in Canes Venatici and Ursa Major are both within 1.5h of the target RA. In this case we can get away with a rough approximation to the angular separation between positions i and j: $$\theta_{ij} \approx \sqrt{\left(15 (\alpha_i - \alpha_j) \cos \frac{\delta_i + \delta_j}{2} \right)^2 + (\delta_i - \delta_j)^2}$$ where α and δ are RA and Dec.