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[parent] convert equatorial coordinates into decimal degrees (Example)

A star is observed to have the following equatorial coordinates:

  • Right Ascension (RA): 5 hours 34 minutes 12 seconds
  • Declination (Dec): 22 deg 15 arcmin 48 arcsec
  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
  • Convert hours, minutes, and seconds to decimal degrees:
    $\displaystyle 1 \,$   hour $\displaystyle = 15^\circ \quad ($since $\displaystyle 24 \,$   hours$\displaystyle = 360^\circ)$    
       minute $\displaystyle = 0.25^\circ \quad ($since $\displaystyle 60 \,$   minutes$\displaystyle = 15^\circ)$    
       second $\displaystyle = 0.0041667^\circ \quad ($since    seconds$\displaystyle = 0.25^\circ)$    
  • RA in decimal degrees:
    $\displaystyle 5 \,$   hours $\displaystyle = 5 \times 15^\circ = 75^\circ$    
    $\displaystyle 34 \,$   minutes $\displaystyle = 34 \times 0.25^\circ = 8.5^\circ$    
    $\displaystyle 12 \,$   seconds $\displaystyle = 12 \times 0.0041667^\circ \approx 0.05^\circ$    
    Total RA $\displaystyle = 75^\circ + 8.5^\circ + 0.05^\circ = \boxed{83.55^\circ}$    

2. Determine the star's position relative to the celestial equator:

  • Declination (Dec) = 22 deg 15 arcmin 48 arcsec
  • Since the declination is positive, the star is north of the celestial equator.

3. Calculate the hour angle (HA):

  • Local Sidereal Time (LST) = 3 hours 45 minutes
  • Convert LST to decimal degrees:
    $\displaystyle 3 \,$   hours $\displaystyle = 3 \times 15^\circ = 45^\circ$    
    $\displaystyle 45 \,$   minutes $\displaystyle = 45 \times 0.25^\circ = 11.25^\circ$    
    LST $\displaystyle = 45^\circ + 11.25^\circ = \boxed{56.25^\circ}$    
  • Hour Angle (HA) = LST - RA
    HA $\displaystyle = 56.25^\circ - 83.55^\circ = \boxed{-27.3^\circ}$    
  • A negative hour angle means the star is east of the meridian (not yet crossed the observer's meridian).

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



"convert equatorial coordinates into decimal degrees" is owned by bloftin.
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Cross-references: Celestial Equator, position

This is version 8 of convert equatorial coordinates into decimal degrees, born on 2025-02-26, modified 2025-02-26.
Object id is 956, canonical name is ConvertEquatorialCoordinatesIntoDecimalDegrees.
Accessed 139 times total.

Classification:
Physics Classification: 95.10.-a (Fundamental astronomy)
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