A star is observed to have the following equatorial coordinates:

• Right Ascension (RA): 5 hours 34 minutes 12 seconds
• Declination (Dec): 22^∘ 15′ 48′′

1. Convert the Right Ascension (RA) from hours, minutes, and seconds into decimal degrees.
2. Determine the star’s position in the sky relative to the Celestial Equator (is it north or south of the equator?).
3. If the local sidereal time (LST) at your location is 3 hours 45 minutes, calculate the hour angle of the star.

Solution

1. Convert RA to decimal degrees.

   RA = 5 hours 34 minutes 12 seconds.

   Since

   1 hour	= 15∘		because 24 hours = 360∘,
   1 minute	= 0.25∘		because 60 minutes = 15∘,
   1 second	= ≈ 0.0041667∘,

   we obtain

   5 hours	= 5(15∘) = 75∘,
   34 minutes	= 34(0.25∘) = 8.5∘,
   12 seconds	= 12(0.0041667∘) ≈ 0.05∘.

   Therefore,

   
2. Determine the star’s position relative to the celestial equator.

   The declination is

   

   Because the declination is positive, the star is north of the celestial equator.

3. Calculate the hour angle.

   The Local Sidereal Time is 3 hours 45 minutes. Converting to decimal degrees,

   3 hours	= 3(15∘) = 45∘,
   45 minutes	= 45(0.25∘) = 11.25∘.

   Hence,

   

   The hour angle is

   

   Equivalently,

   

   A negative hour angle means that the star is east of the local meridian; it has not yet crossed the observer’s meridian.

This example was generated by DeepSeek, an AI, on February 25, 2025.