The Big Dipper, Star Brightness and Movement

Actual photograph of the Andromeda Galaxy, thought to be similar to the galaxy we live in, the Milky Way Galaxy.

I recently had a fantastic idea for a new category on my blog: The Night Sky. I could discuss one particular constellation per post, and follow that each time with a few astronomical subjects. For the most part, I will stick to the constellations of the northern hemisphere (sorry Australian friends!!). This will be fun and not too technical for non-scientists and I will learn a bit too.

This idea embraces my central idea of wonder and suggests that people do something that could potentially enrich their life a lot: LOOK UP! There are moments when I can be a bit of an extroverted kook. I have stopped total strangers on the street just after dusk and, pointing to the sky, said “Hey! Look! There’s Jupiter!”. Sometimes people appear afraid of me, sometimes annoyed, and sometimes they stop and raise their eyes to the sky and say “Huh..”, nudged out of their personal reverie, and we are just two human beings who are momentarily connected by our similar place in the vast Universe. Did you know that the moon rises about 50 minutes later in the sky each night? Why would you? 150 years ago that was common knowledge because without the electric light people relied on the moon to help them see outside. On dark nights the sky shimmered; a vast sea of stars. It was easy to look up and wonder then. Maybe you’ve done the same when you’ve been out in the desert or anywhere far from the light pollution of the city on a clear night.

Too many people don’t know where they are. Unfortunately, this too often applies even to their place on earth. But when it comes to the solar system, our galaxy, or the Universe even more people don’t have a good understanding of what kind of world they are living in, let alone where.  Not long ago I took my niece out to a dark place in the countryside and we lay on the grass and looked up at the Perseid Meteor shower (August 9-14th each year), along with the summer constellations of the northern hemisphere and the international space station as it sailed by. She asked me lots of questions. Let’s go find out where we are!

Unlike what I will do in the future, I will start with some basic concepts, and with this knowledge in hand I will present the Big Dipper.

Star Brightness: Apparent Magnitude and Absolute Magnitude.

As I lay on the ground with my neice, she asked me why some of the stars were brighter than others. I was just about to answer when she said “Oh! I know…some are farther away than others.” Good thinking! That was one reason. There are two. “Can you guess the other reason?” She thought for a bit…”Because some are just bigger?” That was pretty close, but it is better to simply say that some are just brighter, for reasons we will explore at a later time. This means if all the stars were the same distance away, some would just shine brighter than others if viewed from the same distance. The distance that astronomers use for this is 32.6 light years (how far light would go in 32.6 years = 191,613,909,400,000 miles). The brightness of a star at this distance is called it’s “absolute magnitude”. Now if you consider that some bright stars are farther away and some dimmer stars are closer, this changes how bright they look to our eyes and this is called “apparent magnitude.” The star Vega, which is the fifth brightest star in the night sky of both hemispheres, and the second brightest star in the northern hemisphere, has been chosen to set the standard of apparent magnitude, and so Vega is set at zero. Brighter stars than Vega take on a negative apparent magnitude and dimmer stars a higher number. Each time you go one number higher you are 2.5 times dimmer–so a star with a magnitude of 3 is 1/6.25 as bright as a star with a magnitude 1 (1/1 x 1/2.5 x 1/2.5 = 1/6.25). In discussing the brightness of stars when I talk about the constellations I will be using apparent magnitude. This is how bright they would be under perfect conditions on earth and it is something we can all use to compare. All of you readers will not see these stars the same, however, because the conditions under which we are viewing them differ (disregarding the obvious fact of cloudy skies). Some of us live next to large cities with lights going all night long. This brightens the whole sky and is what is known as light pollution. This obscures all but the brightest celestial objects…hopefully, everyone can still see the moon. Then there is the atmosphere itself which can block out the star light depending on what is in it. Natural dust and unnatural pollution are two atmospheric elements that can do this. Water vapor is another and it has a surprisingly large effect refracting, or bouncing the light about, making it less distinct. Furthermore, both dust and water widen the ring of light pollution around a city. You will have to go farther away from any manmade light to get the clearest view. Warm air has the ability to contain more water vapor than cold, so the winter sky is usually best for star gazing. If I take Miranda out to the dunes again on a cold (northern Michigan cold!), clear night in winter we will be dressing very warmly as we settle into a snowbank for a very good view.

The Proper Motion of Stars

Another question my niece asked me is whether the stars move. This has a few answers. Of course, due to the earth’s rotation, the stars move across the sky at night in the same way the sun does during the day. This will be a topic for Night Sky Lesson Two. Then, there is also the fact that the night sky faces a different arena of stars on the opposite side of the sun in the summer as opposed to winter, so if you look up at the sky in the summer and again in the winter, they will indeed look like they moved. In each of these cases, however, it is the earth that moved and not the stars. To those ancient people so familiar with the night sky, they recognized that some stars looked “fixed”. They could predict from year to year where they would be at the same time on the same day. There were a few stars though, that seemed to follow more or less the track of the sun, and that “wandered” about back and forth relative to the stars that formed the constellations. These turned out to be planets. This also merits a full discussion later!

But what about the stars that are actually other suns light years away? Do they move relative to each other? As difficult as it is to tell, in fact impossible to the naked eye in the period of one short human lifetime, the answer is yes, they are all moving about relative to each other, and in some cases quite fast! This is the movement I think my niece meant, and it is called “proper motion.”

But to backtrack slightly, first you should know that all the stars that are visible to the naked eye at night are contained in the same galaxy, your home galaxy, the Milky Way. From the outside, the Milky Way would look quite a bit like the Andromeda Galaxy whose picture, taken from a telescope, is shown at the beginning of this essay. Here are some cool facts about your home galaxy: it is 100,000 light years across (!), 1000 light years deep and it contains approximately [~] 300 billion stars. At the center is a black hole, a very small (I use the term loosely because “space” is actually different there) region with unfathomable density; with a mass of 40,000 suns using one measure and 4 billion suns using another. All the ~ 300 billion stars revolve about this super massive center. The earth, which is half way from the central black hole to the outside rim, takes about 250 million years to go around once. So, when you look up (insert smiley face) and see a smear of dim light across the sky on a very clear night, what you are seeing is the residual light from all those 300 billion stars that dance in a circle with us.

Wait. What were we talking about? Oh yes, the “proper motion” of the stars. OK, so although all the stars in the Milky Way are moving generally together in a circle, they are not moving perfectly in sinc. This is something akin to the planets moving about the sun at different rates; each planet takes a bit longer to go around the sun the farther out it is. But also, groups of stars may have formed with different momentum to begin with, or are affecting each other by the gravitional forces between them. Astronomers can measure how fast the stars are drifting relative to each other and in which direction. Over millions of years this would make quite a difference. Some stars would have moved out of view, some would have moved into view, and some would have simply moved to a different place. If you were to go back, say 200 million years, in earth’s history to the time of the dinosaurs, the stars of the night sky would appear unfamiliar. You might even connect the stars in your mind and make your own constellations. I’m betting one might be a Tyrannosaurs Rex!

The Big Dipper

The Big Dipper (as it is called in the United States; “the Plough” I believe in the United Kingdom) is, along with Orion, the most obvious constellation in the northern hemisphere night sky. Of course, the stars in a constellation are not necessarily related to each other, but with our human penchant for pattern recognition, the ancient people who looked up at the sky made pictures in the stars and it helped them find their way. The Big Dipper is actually the upper back and tail of a larger constellation called Ursa Major, or a Big Bear. This is harder to spot, however, so for this discussion we will limit ourselves to the very obvious Big Dipper. The seven stars of this constellation, shown in my homemade drawing below, are familiar to most people because they are all reasonably bright to the naked eye, and they are close enough to being overhead that they are usually somewhere in view (although that may be in the early morning hours to northern hemisphere viewers in the winter; this is not a constellation that is usually visible from the southern hemisphere).

My homemade drawing of the Big Dipper. The stars circled in red belong to the Ursa Major Moving Cluster; note they are moving in almost the same direction and speed and are close to the same distance from earth.

In this picture, along with the name of each star and it’s distance from earth, I have included the apparent magnitude and the direction of their proper motion, since these were the two astronomical subjects I discussed above. To make sure you are following along, which star is brightest to your naked eye? Yes, that would be either Dubhe or Alioth which both have the lowest number (lower = brighter) magnitudes at 1.8. Megrez would be the most difficult to spot. But don’t take my word for it! Go outside and look for yourself! Now, I have also drawn arrows to show the direction of the proper motion of each star and the length of the arrow indicates how fast it is moving (direction + magnitude shown as an arrow is called a vector). The Big Dipper is especially interesting when it comes to it’s proper motion. Look at my drawing. Can you see a pattern there?

This constellation has two outstanding points of interest in my opinion.

First, let’s look at Mizar in the middle of the handle. There is much more than meets the eye here. In fact, this star was once literally used to judge the acuity of a person’s vision. That is because if one’s eyesight is very good this one star can actually be seen to be two. A star named Alcor lies just to the east behind Mizar, with a rather dim absolute magnitude of 3.99. That is not the whole story, however. It turns out that Mizar is actually four stars. Two binary star systems (two stars gavitationally linked and that are orbiting each other) that are themselves revolving around each other. Then, Alcor is itself a binary star system. For much of history it was assumed that Alcor and Mizar were too far apart to be gravitationally linked. It has recently been discovered though, that they also revolve about each other. In case you are counting, that reveals that the one star “Mizar”  is actually six stars with three levels of binary revolution. If you ever purchase a telescope this famous night star would be a good place to aim it at. You are unlikely to resolve the four stars that make up the main part of Mizar, or the two that make up Alcor, but you will definitely see that Mizar and Alcor are separate. In fact, go outside and see if you can see these two “stars” without the telescopic. You should be able to tell if you need contacts. If so, try binoculars.

Both Mizar and Alcor are Arabic names as are a great many of the names of the northern hemisphere’s stars. Arab culture valued math and astronomy highly during the period when it was ascendant (roughly during Europe’s Dark Ages) and the night sky had high visibility in the desert regions where Islam spread rapidly. The conquering Muslim armies learned to use the night sky to orient themselves very effectively. Side note: any word for a star or in mathematics that starts with “al” is likely to be Arabic. Think “algebra” or “algorithm”.

My second point of interest concerns the proper motion of the stars of the Big Dipper. I hope you noticed in my masterpiece drawing that five of them are drifting, rather slowly, in the same direction. These are the stars of the “Ursa Major Moving Group.” Because they are moving in the same direction, at the same speed, are all approximately 80 million light years from earth, and by their light they seem to be composed of the same compliment of elements, they are assumed to have a similar origin. They formed inside the same nebula (a region of interstellar gas and dust) about 500 million years ago and stars that do this constitute what is called a “star cluster.”  They have drifted apart a bit since their birth, and now occupy an area of space approximately 18 by 30 light years. They are the closest such star cluster to the earth. So interestingly, this is a contellation where a majority of the stars really are related to each other!

Now I have a really cool video to share that illustrates the concept of the proper motion of stars within the Big Dipper. Consider the earth 100,000 years ago: the last Ice Age had just begun 10,000 years prior; homo sapiens (that’s man) had just arrived in the Middle East from Africa. At year zero is you and I. Now go 100,000 years into the future: no new human has been born for 50,000 years; all human conscousness has been transported to hard drives that live inside robots (the richest humans could afford to do this and they promptly exterminated the other flesh bound humans). Hey, make up your own future! Anyway, unrelated to the goings on down on earth, the Big Dipper would have changed like THIS. Notice how you can pause the movie and move it back and forth in time. If you ask me, my future human-robots will not have a Big Dipper anymore. They will have a pine tree.

Appropriately, I will end this essay with….good night. Have wonderful dreams.