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The Celestial Coordinate System and its Use - Part 1

By Winnie Jiang

Main Article

Think of your favorite celestial object. Is it rising and setting like the Sun and Moon? Is it circumpolar? Or is it unfortunately never rising? (If you don’t know its path, you’ll discover soon) The reason behind why your celestial object may follow a path like so can be explained by your location on Earth (Geographic Coordinate System) and the location of your object in the sky (Celestial Coordinate System).

Geographic Coordinate System:

Longitude and latitude are important components to knowing your location on Earth and they are divided like so:

Both units of longitude and latitude are in degrees (°) or sexigesimal degrees (°, ′, and ′′). The Equator has a latitude of 0° (in both degrees and sexigesimal degrees), where anything on the Southern hemisphere would have a negative latitude and anything on the Northern hemisphere would have a positive latitude. Interestingly, the Royal Observatory Greenwich in London England has a 0° longitude due to historical reasons, and 0° longitude is called the Prime Meridian.

Example:

Vacouver, Canada has a longitude and latitude of: 49.2827° N, 123.1207° W

North (N) and South (S) are used for latitudes relative to Earth’s equator. And East (E) and West (W) are used for longitudes relative to the Royal Observatory Greenwich’s longitude.

(https://bjc.edc.org/Jan2017/bjc-r/img/4-internet/world-map.png)

(https://bjc.edc.org/Jan2017/bjc-r/cur/programming/4-internet/2-gps-data/2-introgps.html?topic)

Your latitude and longitude can be easily checked by searching up online.

Now, onto Celestial Coordinate System:

Celestial Coordinate System:

Think of a sphere with infinite radius in space enveloping the Earth where its center is also the center of the Earth (the Celestial sphere) and that sphere also has a set of coordinates but with different names and have different initial points. That coordinate system is called, very creatively, the Celestial Coordinate System. In this system, latitude is named Declination (Dec) and longitude is named Right Ascension (RA).

(S&T / Gregg Dinderman)

(https://skyandtelescope.org/astronomy-news/observing-news/equinox-arrives-september22nd/)

Dec of 0° is the equator of the celestial sphere and RA of 0° is the point where the celestial equator and the ecliptic intersect and the point where Vernal Equinox happens.

Now it may be confusing all of a sudden, but let me explain.

The Ecliptic is the orbital path of the Sun as seen from the self-rotating Earth. Although the Sun is a set point (not really due to Newton’s 3rd law, but we can say it is for our sake), stationary observers on the self-rotating Earth will perceive the Sun as moving across the sky. And the Celestial equator is rather straightforward, it is simply the same as Earth’s equator but on the Celestial Sphere. As seen from the illustration above, the two paths intersect at two points, but what are the two points?

As defined, one of the point is the Vernal Equinox (the Sun is exactly above the equator, has an altitude of 90°, and the length of day and night on that day are the same) and one is the Autumnal Equinox (shares the same definition as the Vernal Equinox, has a different name because it happens in autumn 🤷)

After introducing the Geographic and Celestial Coordinate System, let’s get back to the position of celestial objects in your local sky.

Unfortunately, we can’t see through the ground nor stop the rotation of the Earth. Therefore, we can only see half of the sky at a time. That half of the sky is affected by your location on Earth and the time you are observing. Imagine drawing a tangent line on your specific latitude with respect to the surface of the Earth and the Celestial Sphere with a finite radius:

At an infinitely small duration of time, you are only able to view the part of sky within the green dotted line in the celestial sphere as shown above. But don’t worry, as Earth self-rotates and rotates around the Sun you will see more parts of the sky.

Now there’s also the concern of light pollution and treetops and other earthly obstructions, so it is optimal to view celestial objects with an altitude of at least 20°. Good thing is that due to the Earth’s movement, the position of celestial objects in your local sky will change. To calculate the highest position of a celestial object in your local sky (altitude of the celestial object above your horizon when your local meridian crosses RA of 0°) you can use the equation: Maximum Altitude = 90+Dec-Lat, where all units are the same in degrees.

How we arrived to the equation can be explained as this with the following illustrations:

Fig 1:

Green sphere represents the Earth, where the surrounding hollow blue sphere represents the Celestial sphere. The horizontal and vertical light green opaque ovals represent the 0° latitude plane and the 0° longitude plane respectively. The red opaque ovals represent the 0° altitude plane and the 90° altitude plane (the plane which lines up with the turquoise dashed line is the plane with 90° altitude since the turquoise line shows the zenith of the certain latitude). A star with a random declination (D) is placed on the celestial sphere where it aligns with the zenith of a random latitude (L).

Fig 2

In order to know angle A, the altitude of a star with a Dec of angle D, with the illustration of Fig 2, we are able to perform basic trigonometry to deduce the equation provided above. Knowing the angle between the zenith and the horizon is 90°, we need to calculate the angle difference between the declination of the star and the latitude, which is simply D-L. Then, adding 90 to the angle difference, we arrive at the maximum altitude formula of the star of a particular latitude: 90+Dec-Lat.

For example, for Vega (one of three stars of the Summer triangle with Dec of +38.78°), its maximum altitude at Toronto, Canada, (latitude of 43.65° N) is 90+38.78-43.65=85.13°.

To practice, you can use the Rotating Sky NAAP labs by the University of Nebraska-Lincoln

(https://astro.unl.edu/naap/motion2/animations/ce_hc.html).

Now, knowing the basics of the celestial coordinates, there are much more applications for it other than simply finding out the maximum altitude of your celestial object for observing. You can use it to find out when your object will rise and set, when it will reach its maximum altitude for optimal observing, and more. However, it may be more complicated to achieve the above, so technologies may be your best option. The application Stellarium is a great tool to find out the answers to the above. Nevertheless, I’ll come back with part 2 regarding the basics of the above.

To be continued…

Vocabulary

Circumpolar:

Above the horizon at all time with a certain latitude. (Oxford Languages)

Longitude:

The angular distance of a place east or west of the meridian at Greenwich, England. (Oxford Languages)

Latitude:

the angular distance of a place north or south of the earth's equator (Oxford Languages)

Sexagesimal System:

Numerical system which has a base of 60 instead of 10. For example, hours and minutes are divided into 60.

Newton's 3rd Law of Motion:

For every action (force) in nature there is an equal and opposite reaction. (NASA)

Altitude (In the passage's context):

The apparent height of a celestial object above the horizon, measured as an angle. (Oxford Languages)