Disclaimer: I’m not an expert in spherical astronomy. But I wonder why you don‘t do such stuff with some funny astronomy software. Example: ♀ transit today 16:12:20 RA 16h 17.0m Dek. -24° 21'. Same procedure for ☾ and ♃.

I used Sky Safari Pro for these simple things.

I guess that you might prefer Stellarium as it can be scripted.

Best regards, Karl

Update: See also. But I guess you know this already. And I hope the math mentioned ibidem is O.K. 🤪😎