Solution to Sidereal Time Problem in All Experts Redux

 The problem again:

The star Canopus (RA = 6h 20m) is observed to have a local hour angle = 45 deg on Feb. 10th for a given location.

What is the local sidereal time?

Find the local time of transit (L.T.T.)

Solution:

L..S.T.= HA + RA of object

Hour angle (HA) = 45 deg so convert to hours:

HA = 45 deg/ 15 deg/ h   =  3 h

RA of object =   6 h 20 m

Then: 

L.S.T. = 3 h   +   6h 20 m = 9 h 20 m

Local time of transit (L.T.T.) = Star's RA - Sun's RA

To get Sun's RA we note Feb. 10th is 39 days before March 21st (vernal equinox so 0 h) and assume non leap year.

Then Sun's RA = 0 h  - 39 d x (4 m/ day) =

0 h - 156 m = 0h - 2h 36 m 

So Sun's RA = 24 h -  2 h 36 m = 21 h 24 m

Then L.T.T. =   6 h 20 m - 21 h 24 m = - 17 h 36 m

Or: 24 h 00m - 17 h 36 m = 6h 24 m