Equatorial Coordinate System Example Problem

Let's explore a problem using the equatorial coordinate system, which locates celestial objects with two angles: right ascension (RA), akin to longitude and measured in hours, minutes, and seconds along the Celestial Equator, and declination (Dec), akin to latitude, measured in degrees, arcminutes, and arcseconds above or below the celestial equator.

Consider an astronomer locating a star with these coordinates:

• Right Ascension (RA) = hms
• Declination (Dec) =

The goal is to determine the star's position relative to the vernal equinox and celestial equator, and check its visibility from an observatory at North on February 24, 2025.

Step 1: Understanding the Coordinates

Right Ascension (RA): hms indicates the star is 5 hours, 32 minutes, and 15 seconds east of the vernal equinox. Since h of RA equals (as h covers ), convert to degrees:

h
m	since m    and
s	since s    and
Total RA

Declination (Dec): means the star is 22 degrees, 45 arcminutes, and 10 arcseconds north of the celestial equator. In decimal degrees:

Total Dec

Thus, the star is at east of the vernal equinox and north of the celestial equator.

Step 2: Visibility from North

To assess visibility, check if the star rises above the horizon at latitude N. Key thresholds:

• Circumpolar limit (always visible):
• Southern limit (never rises):

With Dec = , which lies between and , the star rises and sets. Its visibility on February 24, 2025, depends on local sidereal time, but it's observable for part of the night.

Problem Twist: Altitude at Meridian

Calculate the star's altitude when it crosses the meridian (its highest point):

Altitude	latitude   declination

The star peaks at approximately above the southern horizon, making it well-placed for observation.

This example illustrates how equatorial coordinates pinpoint celestial objects and determine their observability. [1]

[1] This example was generated by Grok, an AI developed by xAI, on February 24, 2025.