Milwaukee Astronomical Society

 

Beginner's Guide

Celestial Sphere

 

Understanding the Celestial Sphere

Big Dipper - 5 and 10 degree measuring sticks

The Big Dipper to measure degrees

A basic understanding of our celestial sphere is necessary to know the sky, how the stars move, why the moon and planets are only seen in only a relatively small path in the sky, and how we mathematically designate the locations of the stars.

But a fundamental concept you need to know is what is a degree ( ° ) as in geometry. A circle has 360 degrees. When we look up into the sky we're seeing half of the sphere (horizon to horizon) which is half of a circle so 180°. From the horizon to the zenith (the point directly overhead) is 90° (aka right angle). As you can see from the image of the Big Dipper, you can use 3 of its stars to gauge smaller angles, in this case 5 and 10 degrees. And to give you an idea of a single degree, the full moon in the sky is about ½°.

Earth's Grid - Latitude and Longitude - Wikipedia Commons

The Grid System of Earth

To understand celestial coordinates it is helpful to review the coordinate system we use for the Earth called the Geographic coordinate system. The reference lines we use are latitude and longitude. Latitude lines run east/west whereas longitude lines run north/south. Latitude lines are parallel and are natural because our rotating sphere dictates those lines. The axis of our rotation runs from the north pole to the south pole. Directly in the middle of that sphere we call the equator and that is designated as 0°. Latitude lines to the north are designated as degrees north (i.e., 15°N). An example of a line to the south would be shown 15°S.

Longitude lines go north to south. They are not parallel because they intersect at the north and south poles. But where is the zero line? Unfortunately there is no "natural" line. But we do have a zero line, 0°, and it's called the Prime Meridian (aka Meridian of Greenwich) because the line runs right through the Royal Observatory in Greenwich, London, England. It was the first one used and within a few years so many were using it as the reference, it was selected as the standard. Lines of longitude are designated either east or west based on their position relative to the Prime Meridian.

But we almost always need more precision than a single degree. Decimals can be used, but more often degrees are divided into minutes and seconds. Just like a clock there are 60 minutes in a degree and 60 seconds in a minute. Our MAS Observatory in New Berlin, WI, has coordinates:

Latitude: N42° 58' 07.57"
Longitude: W88° 08' 53.89"
' is the symbol for minutes, " for seconds.

 

Celestial Coordinates

Celestial Coordinates - Wikipedia Commons As the picture to the left shows, the celestial grid is very much identical to the terrestrial grid with latitudes and longitudes. It's as if the terrestrial grid has just been projected onto the sky. Celestial coordinates are designated with Declination and Right Ascension, often abbreviated as Dec and RA. Dec is analogous to latitude; RA to longitude. Every object in the sky has those two numbers which give its location.

Declination (Dec) values are almost identical to latitude values, but instead of the N or S indicators for north or south of the equator, the range goes from -90° (south celestial pole) to 0° to +90 (north celestial pole.)

Right Ascension (RA) values, however, are different because they're specified in hours, minutes, and seconds. The range of values goes from 0h 0m 0s to 23h 59m 59s - 24 hours. At the equator in the celestial grid, 1 hour of RA equals 15°. So 15° times 24 = 360°.


Area around the constellation Orion - Stellarium

Above is the area of sky around the constellation Orion with the grid lines and values shown. Look at the following star coordinates against that map to see how they match.

 Name  Bayer Design  Dec  RA
 Betelgeuse  α Orionis  +7° 24' 25"  5h 55m 10s
 Rigel  β Orionis  -8° 12' 06"  5h 13m 32s
 Aldebaran  α Tauri  +16° 30' 33"  4h 35m 55s

 

Celestial Sphere - North Polar Region - Stellarium

Sky looking directly North showing the RA and Dec lines.

Circumpolar 24 hour rotation in 20 seconds. Stellarium. MAS animation. When you look up into the night sky and watch the motions of the moon, planets, and stars, you see them rising in the east and continually moving to the west where they will set. But that doesn't adequately describe the stars that are far north on the celestial sphere. Here you will find the circumpolar stars. These stars never rise and never set so they are always above the horizon. The image to the right shows the circumpolar region looking straight north. The animation shows a complete rotation in just 20 seconds. It takes 24 hours for that to happen in the real sky. Click/Tap here or on the image for a larger view.

The circle of stars that are circumpolar depend on the observers latitude. In the picture we are showing the view from Milwaukee which is at 43°. That also means that the North Star (Polaris) is 43° above the horizon.

 

The Big Dipper Calendar and Clock

As you've just seen above, the stars that are circumpolar never set so they can be seen all year long and any time of night, assuming your horizon is good enough. The stars of the Big Dipper can be used as both a calendar and a 24 hour clock. Below we show 4 images of the sky looking directly north during the early evening of the 4 seasons.

Big Dipper in Winter - Early evening

Winter

Big Dipper in Spring - Early evening

Spring

Big Dipper in Summer - Early evening

Summer

Big Dipper in Autumn - Early evening

Autumn

The skies are about what you'd see at 9:00PM local time (note: not daylight savings) on January 20 (Winter), April 20 (Spring), July 20 (Summer), and October 20 (Autumn). The images above are for Milwaukee so it would be exactly what you'd see. But since the sky is always rotating, you can "see" the Big Dipper at this same location anytime of the year. Taking the Winter position shown, you will see that on December 20 at 11:00PM, November 20 at 1:00AM, October 20 at 3:00AM, etc. We put see in quotes because the Big Dipper will be at that position, but it will be daylight so you really can't see it.

 

Ecliptic Path

Celestial Sphere - Wikipedia Commons

Celestial sphere with Earth's celestial pole up with Ecliptic path at angle. Wikipedia Commons.

Earth's orbit and the ecliptic path - Wikipedia Commons

The plane of Earth's orbit projected in all directions forms the reference plane known as the ecliptic. Wikipedia Commons.

Ecliptic - Path along the stars the Sun makes in a year. Wikipedia CommonsWe hope we have shown the motions of the stars and how we designate the coordinates to be relatively straightforward. But we need to add some complexity because you need to understand the ecliptic path.

The ecliptic is the plane of Earth's orbit around our Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. Simple enough. However, this path does not correspond with the celestial equator because the Earth is tilted in its orbit by 23.4°.

The equinox's and soltice's. Wikipedia Commons.The consequence of this is the seasons because the Sun's position to the equator changes constantly. We experience summer when the Sun is well above the celestial equator, when the Earth's northern hemisphere is pointed toward the Sun. Conversely, when the Sun is well below the equator, when the Earth's southern hemisphere is pointed toward the sun, we experience winter.

The ecliptic path crosses the equator at two times during the year: at the start of Spring on March 21st called the Vernal Equinox, while the other time is at the start of fall on September 21st called the Autumnal Equinox. The term equinox is derived from the word equal because at these two solar positions, day and night are the same length.

The Autumnal Equinox is where we start Right Ascension, the equivalent of the Prime Meridian (Meridian of Greenwich on Earth. That point is 0h (0 hours). Therefore, the Vernal Equinox (i.e., Spring) is 12h.

Moon and planets along the ecliptic path - Stellarium
Moon, Jupiter, Uranus, Saturn, and Venus. Stellarium
Moon and Planets along the ecliptic path. Stellarium
Moon, Mars, and Jupiter. Stellarium
The Ecliptic Path is also basically the plane of our Solar System. Not just the Sun, but all the planets travel close to this path. The above Stellarium screen shots show the ecliptic path and the moon and various planets. Note that they all lie relatively close to the ecliptic.

 

Precession of the Equinoxes

Earth as a gyroscope - Wikipedia Commons Before you can completely understand celestial coordinates, you need to have some understanding of the precession of the equinoxes which will add a little more complexity. The more modern term is axial precession and as you hopefully will see is a better description.

As you've seen the Earth's axis is not straight up and down as it orbits the sun but is tilted at a 23.4° angle. The north axis of our planet points at the north celestial pole which is a point very near Polaris (aka, the North Star). The path the sun makes through the sky is called the ecliptic path and it's therefore tilted 23.4°s to the celestial equator and the spots it crosses the equator are called the equinoxes.

But the spinning Earth is also a gyroscope and our 23.4° axis wobbles (as demonstrated in the animation) over time and that period is 25,772 years. Therefore, our current "North Star" Polaris has not always been that and won't be again until another 25,772 years.

Precession over 26,000 years. Stellarium. The diagram at the right shows the circle of the precession with marks to show the polar position at 2000 year intervals. The center of the circle is the North Ecliptic Pole. You can clearly see that the current celestial pole is very near Polaris. But over time you'll see other stars that will become the "North Star" as this position changes. In 12,000 years (14,000 AD) the very bright star Vega will be the north star. Also, because Earth's pole will be pointed in the opposite direction, we'll have a complete reversal of seasons! So when we're now having summer, it will be winter.

Granted that movement isn't very fast and to the naked-eye will take over a hundred years for it to be detected. So why does this matter? Because we don't just observe the sky without optical aid. A telescope magnifies and this motion can thus be easily seen in just years. But the effect also causes the ecliptic path to move. It has historically been called the precession of the equinoxes because it was noticed that those points slowly moved westward. And the reason that matters is we use the Autumnal Equinox as our reference for 0hr in right ascension.

 

J2000.0

Stellarium info on Betelgeuse showing the effect of precession. What this precession means is celestial coordinates are not static and they change continuously. So time becomes a very important variable. When you see celestial coordinates you'll often see "J2000.0" along with them. It means these were the precise coordinates of an object on January 1, 2000 and using a reference point like this is called an epoch. Celestial coordinates given without an epoch can be problematic.

When you're viewing the simulated sky in Stellarium if you click/tap on a given star it will bring up an extensive info panel. The image at the right is a screenshot for the star Betelgeuse in the constellation Orion. In the info you will see these two lines:

RA/Dec (J2000.0) 5h55m10.35s/+7°24'25.7"
RA/Dec (on date) 5h56m22.64s/+7°24'38.0"

The first date is for the epoch and that's J2000.0. The second one is for the date which in this example was December 12, 2021. When you're viewing a screen with the time running, you'll see these figures updated continuously.

 

Does It Matter?
These days to the amateur astronomer this is not a big deal because of computers. If you're using a GoTo mounted telescope, the catalog of objects will almost certainly be in J2000.0 coordinates. The computer applies an equation to update them to the current date before it slews to the object. If you were using the older setting circles you might have to apply precession values because the telescope would not be precisely pointed at your desired object. And for visual observers who locate their objects by starhopping there is no concern.