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°. 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 Medidian (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 Meridan.

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. 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 terrestial grid with latitudes and longitudes. It's as if the terrestial 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 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 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  Greek 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

Circumpolar Rotation - Wikipedia CommonsWhen 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. They are always in the sky. The image above shows circumpolar region looking striaght north. The animation at the right shows the same region and its rotation in just 6 seconds. It takes 24 hours for that to happen in the real sky.

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.

 

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 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. 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 Meridan 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 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.

 

Naming the Stars

Ursa Major. Wikipedia Commons. There are 3 major ways stars are named: proper name, Bayer designation, and Flamsteed designation. But for a handful of stars, they also have informal names, the one you've probably have heard of is the North Star. It's proper name is Polaris, the Bayer designation is α Ursa Minoris, and the Flamsteed designation is 1 Ursa Minoris.

 

Proper Names

Proper star names are straighforward. For example, the brightest star in the sky is Sirius. Another one you might have heard is Betelgeuse. Look at the figure of the constellation Ursa Major with contains the seven stars of The Big Dipper. Each of those stars has a proper name: Dubhe, Merak, Phecda, Megrez, Alioth, Mizar, and Alkaid. But there are a lot of stars in the sky. There are almost 10,000 stars visible to the naked-eye! This presents several problems: 1) we have to come up with names, 2) it's hard to keep any of these stars even remotely remembered, and 3) it's hard to put them on a star atlas for the sheer amount of space they take up. Is it important to know all those names? No, except for the very brightest stars in the sky. And we have other more convenient ways to name them.

 

Bayer Designation
Orion - Wikipedia CommonsYou will often see Greek letters used on star atlases to indicate stars. They use the lower case Greek alphabet: α, β, γ, δ, ε, ζ, η, θ, ι, κ, λ, μ, ν, ξ, ο, π, ρ, σ, τ, υ, φ, χ, ψ, and ω. These letters get appended with the given constellation. For example: the first star in the Big Dipper has the proper name of Dubhe. The Bayer designation is α Ursa Majoris. The second star, Merak is β Ursa Majoris, and so on. You should be able to immediately see this saves space on an atlas. If more letters are needed, the Bayer system then goes to A, b, c, d, ... (Small "a" is not used because it could be confused with α.

Note: you can also use the 3 character constellation abbreviation. So α Ursa Majoris = α UMa.

In general the stars of any given constellation are assigned Greek letters in descending order of brightness. So the brightest star in a constellation would be labeled α, the next brightest β, etc. Though this general rule is pretty good, there are some exceptions. Ursa Major is a good example. As they simply lettered them in order and not by brightness. Betelguese in the constellion Orion is labeled α Orionis, but Rigel (β Orionis) is brighter. And as you can see from the example of Orion, the Greek letters can be replicated. However, whenever that is done a numeric superscript is used to make it unique.

 

Greek Alphbet
  Upper   Lower   Name
  Α   α   Alpha
  Β   β   Beta
  Γ   γ   Gamma
  Δ   δ   Delta
  Ε   ε   Epsilon
  Ζ   ζ   Zeta
  Η   η   Eta
  Θ   θ   Theta
  Ι   ι   Iota
  Κ   κ   Kappa
  Λ   λ   Lambda
  Μ   μ   Mu
  Ν   ν   Nu
  Ξ   ξ   Xi
  Ο   ο   Omicron
  Π   π   Pi
  Ρ   ρ   Rho
  Σ   σ   Sigma
  Τ   τ   Tau
  Υ   υ   Upsilon
  Φ   φ   Phi
  Χ   χ   Chi
  Ψ   ψ   Psi
  Ω   ω   Omega

 

Flamsteed Designation
The third major way of labeling stars in a constellation is with Flamsteed numbers. Unlike Bayer designations which are assigned generally in brightness order, Flamsteed goes in order of Right Ascension. On a star atlas you probably will see few Flamsteed numbers. That is because even though the star will have a number, atlases always use Bayer designations when available.

 

 

Star Brightness Scale

The brightness of stars and other celestial objects is measured by magnitudes. We call this apparent magnitude because these are the brightness as seen from Earth. The premise of the system was introduced in ancient Greece where the brightest stars were magnitude 1 and the faintest stars that could be seen naked-eye were magnitude 6. That was obviously not very precise so it was updated, but in a way that tried to match the old system. A star of 1st magnitude (1.0) is 100 times brighter than a star of the 6th magnitude (6.0). What means a 1 magnitude difference in brightess is about 2.5 (more precisely 2.512) times. This is therefore a logarithmic scale.

Magnitude Scale

As you can see, the brightest objects are negative numbers. Sirius which is the brightest star in the sky is magnitude -1.44. The planets Jupiter and Mars at their brightest are near -3 while Venus gets near -5. The full moon is -12.7 and the sun is -26.7. Obviously at the dim end of the scale there is no limit. The Hubble Space Telescope has a limit of about the 31st magnitude.

We show various limits on the diagram, but keep in mind they are all approximate. For example, all city sky views are not the same. But we give them as a way to compare.

 

Brightness Difference By Magnitude
  One Magnitude = 2.5X   Six Magnitudes = 251X
  Two Magnitudes = 6.3X   Seven Magnitudes = 631X
  Three Magnitudes = 15.9X   Eight Magnitudes = 1585X
  Four Magnitudes = 39.8X   Nine Magnitudes = 3981X
  Five Magnitudes = 100X   Ten Magnitudes = 10000X
  One Magnitude = 2.5X   Six Magnitudes = 251X
  Two Magnitudes = 6.3X   Seven Magnitudes = 631X
  Three Magnitudes = 15.9X   Eight Magnitudes = 1585X
  Four Magnitudes = 39.8X   Nine Magnitudes = 3981X
  Five Magnitudes = 100X   Ten Magnitudes = 10000X

 

Star Colors

Stars come in more colors than just white, though that's what they look like to the casual observer. The reason is they are not very bright which means you are mostly using the rods of your eyes and they don't discern color. But they are your good light detecting sensors. If you've ever wondered why color mostly disappears as it gets dark even though you can still see, that's the reason. On the other hand the cones of your eyes which are concentrated in the center are not very light sensitive, but they discern color. During the day your pupils are contracted so light doesn't fall on the rods.

But for the brighter stars in the sky you can detect a little color. And you can enhance that by using binoculars and especially a telescope where they become much brighter so more light falls on your color sensitive rods.