# 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
Jan 8 '20 at 5:31
• @uhoh If 47.6 is a latitude, don't you also need a time to know the declination of the zenith? Jan 8 '20 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
Jan 8 '20 at 8:38
• Please edit this and replace the picture with actual text. Pictures are not searchable.
– user1569
Jan 10 '20 at 8:07

## 2 Answers

With Stellarium, it appears that the point with coordinates RA=12, DEC=47.6 is in Ursa Major.

In the screenshot from Stellarium below, the constellation boundaries are in red. Ursa Major is at the bottom, Canis is on top. The blue grid is the equatorial coordinates.

This answer assumes that the observer's geographic latitude is 47.6°N and their local sidereal time is 12h, putting their zenith at the coordinates in the headline.

Among the other five positions, the declinations are all within 8° of +47.6°, while the right ascensions are all over the place. We can narrow the choices by comparing right ascensions to 12h: the positions in Cygnus and Perseus are over 8h away, and the position in Lynx is about 4h away,

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.

A precise solution would involve vector calculations similar to this answer.