We start with the stars. Even today, when we’re distracted by indoor living andartificial lights, many of us uncover the stars beautiful and also fascinating. Yet imaginehow castle must have actually captivated ours ancestors, who spent far an ext time under thestarry night sky!

For hundreds of years, world have wondered around the stars. What space they?How much away space they? What is the definition of their arrangement in the sky?How perform their areas in the sky adjust over time, and why?

This last concern turns out to be the easiest to answer, therefore it’s a natural placeto begin our examine of astronomy. As you’ll see, the answer end up informing us just alittle around the stars, but a good deal about the earth.

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The Stars from Utah

Here’s a time-exposure photograph that vividly illustrates the movement of the stars v a portion of our sky:


Stars increasing in the east, as perceived from Ogden, Utah. The camera was an installed on atripod and the shutter was left openfor ten minutes, to present the stars’ evident motion. The foreground mountainswere illuminated by city lights.

As time passes, the stars rise in the east (just choose the sun). But notice thatthey rise diagonally, not straight up. The diagonal goes from phibìc (left) tosouth (right). After ~ a couple of hours, these exact same stars will show up high in the southerly sky.

Turning to challenge south, we watch that the stars there are relocating from left (east) to right(west):

Ten-minute time exposure facing south and slightly west, from the same ar as theprevious photo. The stars are moving from left (east) to ideal (west) acrossthe field of view. Despite the annoying light pollution, you deserve to barely do outpart that the Milky Way, best of center.

By currently you deserve to probably guess that stars set in the western sky, again alonga diagonal:


Ten-minute time exposure encountering west, native the same location as theprevious 2 photos. The stars are setup along a diagonal, from southern (left)to north (right). The bright star in ~ the lower-right is Arcturus.

And in the north, the motion is many interesting. Stars increase in the northeast andset in the northwest, moving in counter-clockwise circles about a point that"s high over the north horizon:


Half-hour time exposure encountering north and slightly west, indigenous the same ar as theprevious three photos. The stars space tracing counter-clockwise circles, centeredon a point near the prominent North Star (Polaris). Notice the huge Dipper in ~ thelower-left.

The magestic movements of the night sky were intimately acquainted to ancient people. This particular day thisfamiliarity has been lost (except through astronomy geeks), so you"ll have to make a special effort to remember and visualize the patterns. It help to was standing under the night sky and suggest with her hands, tracing out the courses of differentstars. In summary:

Other stars rise in the southeast and follow shorter, reduced arcs throughout thesouth before setting in the southwest.

Besides direct observation, girlfriend can get accustomed come these activities by playing v theSky motion Appletthat I"ve created for this purpose. A selection of other helpful resources are listed atthe bottom of this page.



Orion the Hunter is among the brightest and also most acquainted constellationsof the night sky. The heat of 3 stars near the middle is dubbed Orion"s Belt.

Notice likewise that as the stars move through the sky, they stay in the very same patterns.That is, the evident “distance” between any kind of two stars never changes. A given patternof stars may move throughout the sky and turn sideways or also upside-down, however it won"tgrow larger or smaller, or adjust its form in any type of other way.

The permanence that the stellar patterns urges us to mentally attach the dotsto do pictures, dubbed constellations. Different cultures have done this in differentways, and also you might enjoy comprising your very own constellations once you"re the end underthe stars. To far better communicate, however, professional astronomers have actually agreed top top a setof 88 main constellations, many of which originated v the ancient Greeks.Some of the official constellations are easy to recognize, while others space obscureand difficult. Finding out the constellations is valuable if you want to navigate or telltime through the stars, or recognize where to look in the sky for a details star or otherinteresting object.

If you desire to find out the constellations, you have the right to start v the Sky movement Appletand then move on to several of the resources provided at the bottom the this page.

Measuring Angles

When we talk about the noticeable "distance" between two clues in the sky, we"re reallytalking about an angle, measured in between the 2 imaginary present runningfrom her your eye the end to those points:


The angle between two clues in the sky is defined as the angle in between two imagine lines to run from you the end to those points. For the two stars shown, theangle is around 16 degrees.

The larger the angle, the farther personal the 2 points appear come be in the sky.The actual distance between two stars is much harder to determine, as we"ll latersee.

Here"s a photograph of the big Dipper, with few of the angles in between stars labeled:


The bowl of the huge Dipper is around 10° vast and 5° deep. The entire handle is16° long, and also the totality Dipper is 26° long.

Similarly, the broad of Orion"s Belt is a tiny under 3°, andthe four star-trail photos over each span a width of around 60° from next to side.

To measure up the angles between stars and also other clues in the sky, astronomers useprotractors and comparable instruments, frequently attached come a telescope for precise pointing. To obtain an approximate measurement, however, youcan use tools that are constantly with you: your hands. The width of her fist, heldat arm"s length, is about 10°, while the width of your tiny finger tip, alsoheld in ~ arm"s length, isabout 1°. These angle don"t depend lot on her size, due to the fact that people through biggerhands also tend to have longer arms. Following time you see the huge Dipper, hold out yourfist and also check the the Dipper"s key is about one fist wide. To estimate largerangles you have the right to use both hands to counting multiple fists. It"s also helpful to rememberthat the angle between the horizon and zenith (straight overhead) is 90°, as isthe angle between two surrounding cardinal direction such as north and east, or eastand south.


Angle approximates using fist and fingers, v arm outstretched.

Question: How plenty of fists, stack one on top of another, would it taketo with from the horizon to zenith?

Check her answer: 9Right. Now use her actual fists to check this!No, remember that a right angle is 90 degrees.

The price of Rotation

Now look ago at the east- and also west-facing star trace photosat the peak of this page. The stars in this photos are complying with circular arcs thatbegin in the east, pass high across the southern sky, and end in the west.You, the observer, are at the approximate facility of these circular arcs, so friend candirectly measure up the angle v which these stars move, by holding up your hands(to the real sky, no the photo!). If you make this measure carefully, you"ll findthat in 10 minutes, each of this stars moves with an angle of 2.5°. The price ofmotion is steady, so simple multiplication or department allows us to calculation theangle for any other time period: 5° in 20 minutes, 7.5° in 30 minutes,15° in one hour. End a full 24-hour day, the edge of rotation would certainly be

15° × 24 = 360°.

The stars therefore complete a complete circle (360°) in 24 hours.(Of course, you typically can"t see the stars during daylight, yet they"re still thereand still complying with their circular paths,as you deserve to confirm v a telescope or by getting over earth"s atmosphere.)

Question: How many minutes would it take because that a star to move just one degree?(Calculate the answer carefully—don"t just guess.)

Check her answer: 4That"s correct!No, remember the the stars move 15° in 60 minutes.

The price of angular movement is the exact same in other parts the the sky, although friend can"t simply measurethe angles through your hands because you"re not at the center of the circles. In the northernsky, however, you deserve to measure the angles straight by laying a protractor down on a photograph. Here"s a longer time exposure the star trails near the north Star:

In the northern sky, every stars relocate at the same rate approximately the common centerof their circles. During this 75-minute time exposure, the stars rotated by approximately 19°.

If you use the info in this picture to calculate the timefor a one-degree rotation (or 15° or any type of other angle), you should getapproximately the exact same answer as above.

Question: how would you usage the data indigenous the preceding photograph to calculatethe time required for a one-degree rotation?

multiply 19 by 75. No, even a 19° rotation takes just 75 minutes. Divide 19 by 75. No, remember which is the angle and which is the time. Division 75 by 19. Yep! and also round the answer to the nearest minute.

This computer-simulated multiple-exposure photo (made with Sky motion Applet)shows Orion in the southern skies at the same time on 7 successive nights. Each night,after completing a complete circle, the stars have shifted rightward by about one degree.

To it is in precise, though, I must tell you that all of the angle quoted above are onlyapproximate. In fact, the takes a little less 보다 an hour for the stars tomove by 15°, and also therefore the takes a small less than 24 hours for thestars to complete an entire circle. In fact, the takes just 23 hours and also 56 minutes,or 4 minutes much less than a full day. During those last 4 minutes the stars willmove by second degree, so in precisely 24 hours, the stars actually move by361°, not 360.

These extra 1° rotations include up over the weeks and months, so that after a fullyear, at any kind of given time that night, you"ll check out the stars in the exact same positions as before.(Since a year is 365 days, no 360, you deserve to probably guess the the extra per-day rotationis in reality slightly less than 1°. If friend really desire to be an accurate aboutthese things, you likewise need come take into account leap years—but let"s no bother.)

So, together the periods pass, us see various groups that stars in a given direction, atany given time of night. In January you deserve to watch Orion increasing in the eastern just after sunset,but by March, Orion will certainly be high in the south, heading westward, by the time the sky isdark. Meanwhile the shining star Arcturus will be climbing in the east, a sign that feather is coming. If you find out to identify the influential stars and constellations, theywill give you a solid sense of the passage of the seasons. Night owls and early riserscan also enjoy a preview of the stars the evening observers will check out in thecoming months.

The Celestial Sphere

To simplify their expertise of the activities of the sky, ancient people invented amechanical model to explain these motions. Us still usage this design today because it"s soconvenient—even despite it"s wrong. If you deserve to visualize the model, girlfriend won"t have actually tomemorize a whole bunch of different facts around how the stars move.


The stars show up to be attached come a large celestial sphere, spinning aboutthe celestial poles, and around us, when every 23 hours and also 56 minutes.

The model is merely that the stars are all attached come the within of a giant rigid celestial spherethat surrounds the earth and spins roughly us once every 23 hours, 56 minutes. The rotate carrieseach star approximately in its observed circular path, if a special allude in the northern sky,at the center of the circles, continues to be fixed. The sphere"s rigidity accounts for how the shapesof the constellations never ever change, and its enormous size accounts because that howthe constellations never prosper or shrink, as they would certainly if a particular point on planet weresignificantly closer to one next of the round than the other.

To much better describe areas in the sky, we offer names to the assorted parts the the celestialsphere. The fixed point in the north sky is referred to as the phibìc celestial pole, andis located only about a degree away native the renowned North Star (which renders tiny circlesaround it). Ninety levels from the pole is the celestial equator, a good circle thatruns from straight east to straight west, pass high above our southern horizon. Mintaka,the rightmost star in Orion"s Belt, wake up to lie nearly exactly top top the celestial equator, therefore youcan think the the celestial equator as tracing the path of this star. Another important greatcircle is the meridian, which runs from directly north to straight south, passingstraight overhead. As the round turns, the meridian stays fixed in the sky. The pointstraight overhead is called zenith.

The Stars from other Locations

I"ve explained the stellar motions as they show up from my residence in Ogden,Utah, at a latitude the 41° phibìc of the equator. What around other locations?Moving eastern or west provides no difference, other than to determine when you view things.If friend live aside from that east, you"ll see any kind of given star increase and collection sooner; if girlfriend live fartherwest, each star rises and also sets later. Us compensate because that these differences, in an almost right way, by setup our clocks according to different time zones.

Moving north or south is much more interesting. The farther phibìc you go, the higher in thesky you"ll check out the north celestial pole and also the stars about it—and the lower all the stars will show up in the south.In fact, the angle between your north horizon and the phibìc celestial pole is preciselyequal to your latitude.

For example, in Ogden the phibìc celestial pole is 41° over my north horizon, but if you"re in Anchorage, Alaska, the edge is 61°. At the earth"s north pole,you would view the north celestial pole right overhead, and the celestial equator wouldlie follow me yourhorizon, so you would never see any kind of stars increase or set; lock would simply move in counter-clockwisecircles if you"re encountering upward, or horizontally come the ideal if you"re facing the horizon.Stars listed below your horizon (that is, southern of the celestial equator) would constantly be concealed from your view.

On the other hand, if friend travel southern to Mexico City, you"ll watch the phibìc celestial pole only19° over your northern horizon. The huge Dipper will no longer always be visible, settingin the northwest and rising in the northeast instead. However in the southerly sky, you"ll watch stars thatare never ever visible in Utah, consisting of the famed Southern Cross.

Farther south, at earth"s equator, the north celestial pole lies on the northernhorizon, and also the celestial equator passes straight overhead. Indigenous here, together the constellations risein the east, they show up to head straight up, quite than along a diagonal.In the west, they head directly down together they set. Also morestars are visible in the southern sky, make clockwise half-circles around a suggest on thesouthern horizon, the southern celestial pole.

From the southern hemisphere, friend can"t see the north celestial pole in ~ all. The south celestialpole, however, will appear over your southerly horizon, by one angle equal to your southerly latitude.Stars climbing in the east will head upward and also to the left, toward the northern sky.The celestial equator will additionally pass v the northern sky, lower and lower as you headfarther south.


This several-hour-long time exposure, taken from tropical north Australia,shows the clockwise motion of the southernstars roughly the southern celestial pole. The trails of the southerly Cross begin at the height of the image, through the peak of the overcome initially above the edge. Picture by David Miller/DMI.


The old Greeks conceived the universe as a large sphere that stars,surrounding the much smaller spherical earth. In this contemporary plasticmodel, however, the dimension of the planet is considerably exaggerated in comparison to the celestialsphere.

Finally, if friend visit earth"s southern pole, you"ll watch the southern celestial pole straight overhead,with the stars make clockwise circles roughly it. The celestial equator will certainly lie on her horizon,with the stars moving parallel to it, from ideal to left. You always see the same half of the celestialsphere, fully distinct from the half that friend would check out from earth"s phibìc pole.

The explanation for all these results is just that the earth"s surface ar is curved. Therefore whenyou travel to a different location, your horizon tilts with respect come the stars. Today every college child is taught that the earth is (approximately) a sphere. Also in ancient times, however,astute travelers realized the the transforms in the stars as you take trip north or south have to becaused by the curvature the the earth. The ancient Greeks even reasoned the the earthmust be a sphere, and thus pictured the universe as a pair that spheres: an massive celestialsphere, carrying the stars around us when a day, and the much smaller spherical earth, fixedat the facility of the universe.


The picture at right mirrors Orion close to the western horizon. The picture was nottaken native Utah.

Question 1: Is Orion climbing or setting?

increasing No, you"re facing west. Setup Stars practically always set in the west. Counts on where photograph was bring away No it doesn"t!

Question 2: native what latitude was this picture taken?

40° north to compare to the Utah photo above. 20° north Yep! Trails space 20° native vertical. 20° south The stars are setting from the south. 40° southern The stars are setting from the south.

Question 3: around how long was the camera shutter open?

1 minute just how long are the trails? 2 minutes How wide is Orion"s Belt? 5 minute Good! 10 minute Stars relocate 2.5° in 10 min.

The dimension of the Earth

Once friend understand exactly how the earth"s curvature renders the stars transition as you travel,you can easily determine the earth"s circumference. Every you have to do is travel directly north or southfor part measured distance, and also measure the angular shift of stars near the meridian. Due to the fact that the north Staris always really close to the meridian (and straightforward to discover to recognize), it"s more than likely the most convenient recommendation star.

The just real an obstacle with this measure is the you have to travel pretty far beforethe transition becomes noticeable. If you"re careful, though, you can measure an angular change of onedegree whenever you travel directly north or south by around 70 miles. So, because that instance, if youtravel indigenous Ogden come Provo (70 miles south), you"ll check out the phibìc Starget reduced in the sky by 1°. By the exact same token, stars in the southern sky will acquire higherby 1°. (Of course, it"s tough to measure up a shift of just 1°, for this reason it"s best to travel fartherthan 70 miles and also measure the proportionally larger angles.)

Now imagine continuing your trip southward. For every 70 miles traveled, the stars shiftby 1°. After ~ 700 miles, the stars would transition by 10°. Together you cross the equator, the NorthStar would disappear listed below your horizon, however you could proceed to measure the move in the brand-new starsthat you check out in the south. At some point you would involved the south pole, then proceed past it,now traveling northward, back to the equator, climate to the phibìc pole, and also finally roughly to yourstarting point. The stars have actually now change by a full 360-degree circle, ago to your originalpositions. And to attain this, girlfriend would need to travel a total distance that approximately

The earth"s circumference is therefore around 25,000 miles. The circumferencearound the equator is also about 25,000 miles, despite this is a tiny harder to measure.You may find it simple to remember that at the equator, every of the 24 (idealized) time zones is about1000 mile wide.

Question: walk you inspect my calculation of the earth"s circumference? If not, examine it now! Whichstatement ideal describes mine accuracy?

The calculate is precisely right. Nope. Execute the calculation! The calculation is wrong since I made a mistake. ~ above purpose? no likely. Ns rounded off the answer since "70 miles" isn"t exact to start with. Indeed.

Exercise: use this value of the one to calculation the diameterof the planet in miles, rounded come the nearest thousand.

Check your answer: 8000Yep!No, psychic the an interpretation of "pi", which is around 3.

The an initial person well-known to have actually done this calculation was the old Greek astronomerEratosthenes. Instead of using the north Star for reference he provided the noon sun, which isalso on the meridian. There"s some problem over just how accurate his calculations actually were,but the crucial thing is the he offered a valid method to calculate earth"s size, much more than 2100 year ago. (If you weretaught as a son that everyone before Columbus assumed the earth was flat, you to be lied to.Columbus was ridiculed no for believing the planet to it is in a sphere, but for grossly underestimatingits size, reasoning he could sail all the means to Asia prior to running the end of provisions. The wasextremely fortunate to hit land long before he would have reached east Asia.)

Which is yes, really Moving?

Throughout this conversation I"ve defined the activities of the starswith respect come our horizon. It"s organic to assume that our horizon, and hence the earthbelow it, is important fixed, and therefore the the stars truly move roughly in substantial circlesonce each day.

But if girlfriend think around it, we deserve to account for all the same monitorings if us assume thatthe stars are solved in space, and also the earth spins around once every day (in the opposite direction).The an initial person well-known to have said this possibility was another ancient Greek,Heraclides. Yet the idea didn"t catch on for an additional 1900 years, since it seemed so obviousto everyone that the planet doesn"t move. (After all, simply look at it! does the planet look like it"smoving? therefore there!)

Today, of course, we recognize that Heraclides to be right. It yes, really is the earth that spins incircles, no the stars. I"ll explain later how we recognize this, andhow it"s possible for the earth to turn attremendous speed without our feeling it. Meanwhile, you have my permission to say that the stars "rise" and also "set" and also "move" with the sky—as lengthy as you keep "with respectto our horizon" in the earlier of your mind.

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Additional Resources

There are lots of great resources the end there the can aid you learn about stellarmotions, constellations, and also the celestial sphere:

Here"s an amazing photograph showing star trails (from Australia) in every direction in ~ once.You have the right to find much more star trace photos here,here,here,here,and here.If you"re interested in the background of old Greek astronomy and the two-sphere design of theuniverse, there"s no far better treatment 보다 Thomas Kuhn"s book, The Copernican Revolution.