2.2: The Sky Above
- Page ID
- 152347
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A Map of the Sky
Now that we have an idea of what our celestial neighborhood is like, let's examine how everything appears from the surface of the Earth. We know that we are surrounded by the stars of our galaxy in all directions and at a large range of distances. To demonstrate what we see from Earth, astronomers have created a spherical map, to track the locations of individual stars.
The Celestial Sphere
The first thing to do when using a map is to orient yourself in relation to objects on the map. However, the objects in this map are above you, so we first need to define where we are relative to the sky. Imagine that you are standing in an open plain with no buildings, mountains, tall trees, or anything around you to block your view. The sky above you is like a dome with you at the center, like in Figure \(\PageIndex{1}\). The person in this figure is standing on a flat surface and the sky is represented by the dome around them. The top of that dome, the point directly above your head, is called the zenith. Where the dome meets Earth is called the horizon.
If you lie back in an open field and observe the night sky for hours, you will see stars rising on the eastern horizon, similar to how the Sun and Moon rise in the east. The stars will then move across the dome of the sky over the course of the night eventually setting on the western horizon. Watching the sky turn like this night after night, you might eventually get the idea that the dome of the sky is really part of a great sphere that is turning around you, bringing different stars into view as it turns. The early Greeks regarded the sky as just such a celestial sphere. Some thought of it as an actual sphere of transparent crystalline material, with the stars embedded in it like tiny jewels. Our celestial sphere is a map, like the one in Figure \(\PageIndex{2}\).
We can put an imaginary stick through Earth's North and South Poles, representing our planet's axis. It is because Earth turns on this axis every 24 hours that we see the Sun, Moon, and stars rise and set every day. Today, we know that these celestial objects are not really on a dome, but at greatly varying distances from us in space. However, it is convenient to imagine the objects on a celestial sphere to help us keep track of objects in the sky. A planetarium is designed to replicate a celestial sphere by projecting a simulation of the stars and planets onto a white dome. Using the concept of the celestial sphere, you can also project your location on Earth onto it by finding your zenith. Once you have found your zenith, draw a great circle on the celestial sphere perpendicular to your zenith. That circle, in red in Figure \(\PageIndex{2}\), is your horizon. That means that, from your position on Earth, you can only ever see objects on the celestial sphere that are above your horizon. In this model, the rotation of the Earth is represented by the celestial sphere rotating clock-wise around the North Pole. This means that everything on the sphere, the Sun, Moon, and stars move from east to west. However, there will be some parts of the sphere that they will never be able to see because of their position on Earth, namely the parts of the celestial sphere near the South Pole.
As the celestial sphere rotates, the objects on it maintain their positions with respect to one another. A grouping of stars such as the Big Dipper has the same shape during the course of the night, although it turns with the sky. During a single night, even objects we know to have significant motions of their own, such as the nearby planets, seem fixed relative to the stars. Meteors, or shooting stars, flash into view for just a few seconds and move with respect to other objects on the celestial sphere. On a very dark night, satellites can also be seen moving, and sometimes blinking, relative to the stars. We can use the fact that the entire celestial sphere seems to turn together to help us set up systems for keeping track of which objects are in the sky and where they are located at a given time.
Celestial Poles and Celestial Equator
To help orient us in the turning sky, astronomers use a system that extends Earth's axis into the sky. Imagine a line going through Earth, connecting the North and South Poles. This is Earth's axis, and Earth rotates about this line. If we extend this imaginary line outward from Earth, the points where this line intersects the celestial sphere are called the north celestial pole and the south celestial pole. As Earth rotates around its axis, the sky appears to turn in the opposite direction around those celestial poles. We also (in our imagination) throw Earth's equator onto the sky and call this the celestial equator. It lies halfway between the celestial poles, just as Earth's equator lies halfway between our planet's poles.
In Figure \(\PageIndex{2}\) the person is standing in the Northern Hemisphere. If they are observing the stars over the night, they will see them moving from east to west. However, the stars near the north celestial pole do not rise or set. Instead they move in a circle around the pole. If the observer has a camera that can take long exposures, they can point it directly at the north celestial pole, leave it there for the night and get an image similar to the one in Figure \(\PageIndex{3}\). In this image, the camera has tracked the motions of the stars tracing circles around the celestial pole. The only difference is that the image in the figure is of stars around the south celestial pole.
Keep in mind that astronomers measure how far apart objects appear in the sky by using angles. By definition, there are 360° in a circle, so a circle stretching completely around the celestial sphere contains 360°. The half-sphere or dome of the sky then contains 180° from horizon to opposite horizon. Thus, if two stars are 18° apart, their separation spans about 1/10 of the dome of the sky. To give you a sense of how big a degree is, the full Moon is about half a degree across. This is about the width of your smallest finger seen at arm's length.
Now let's imagine how our location on Earth affects our view of the sky, as depicted in Figure \(\PageIndex{4}\). The apparent motion of the celestial sphere depends on your latitude, or position north or south of the equator. For more information regarding latitude, longitude, and the equator, see the section about Earth. Since the Earth's axis is pointing at the celestial poles, there are two points in the sky that do not appear to turn. If you stood at the North Pole of Earth, you would see the north celestial pole overhead, at your zenith. The celestial equator, 90° from the celestial poles, would lie along your horizon. As you watched the stars during the course of the night, they would all circle around the celestial pole, with none rising or setting. The exception is any stars directly above you, which would either not move at all or move in a very small circle. Only the northern half of the celestial equator is ever visible to an observer at the North Pole. Similarly, an observer at the South Pole would see only the southern half of the sky.
If you were at Earth's equator, you see the celestial equator pass overhead through your zenith. The celestial poles, being 90° from the celestial equator, must then be at the north and south points on your horizon. As the sky turns, all stars rise and set. They move up from the east side of the horizon and set on the west side. During a 24-hour period, all stars are above the horizon exactly half the time.
As an example, let's see what an observer somewhere between the equator and the North Pole would see. They are neither at Earth's pole nor at the equator, but in between them. The north celestial pole is neither overhead nor on the horizon, but in between. It appears above the northern horizon at an angular height, or altitude, equal to the observer's latitude. In San Francisco, for example, where the latitude is 38° N, the north celestial pole is 38° above the northern horizon.
For an observer at 38° N latitude, the south celestial pole is 38° below the southern horizon and never visible. As Earth turns, the whole sky seems to pivot about the north celestial pole. For this observer, stars within 38° of the North Pole can never set. They are always above the horizon, day and night. This part of the sky is called the north circumpolar zone. For observers in the Northern hemisphere, the Big Dipper, Little Dipper, and Cassiopeia are examples of star groups in the north circumpolar zone. On the other hand, stars within 38° of the south celestial pole never rise. That part of the sky is the south circumpolar zone.
At this particular time in Earth's history, the star closest to the north celestial pole is called Polaris, the pole star. It is the star that moves the least amount as the northern sky turns each day. In the southern sky, σ Octantis, also known as Polaris Australis, is closest to the south celestial pole, but unfortunately it is too faint to be observed without a telescope.


