Download Unit 13―The “Fixed” Stars

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Unit 13―The “Fixed” Stars
184. The Constellations. By now you have probably figured out that astronomers “sort of” use two different
coordinate methods for locating “things to study.” When measurements have to be taken down to minute position locations, their telescopes must be capable of turning to the precise location on the celestial sphere down to
minutes and seconds of arc. To view a meteor shower, a planet or a comet, knowing where in any constellation
the event is occurring often is enough. After all, the comet or planet is going to move throughout the course of
the night anyway so you merely get it into your cross hairs and start the telescope compensating for the rotation
of the Earth. If you need to examine a specific star, it might be known as beta-constellation-name. In that case,
since you are so familiar with that constellation you simply get the beta star in that constellation into your cross
hairs.
The following illustration is by no means a modern day photograph but just happens to illustrate what you have
to face night after night to have successful astronomical viewing. Trying to illustrate a brighter star by making
it bigger on the illustration demonstrates that sometimes the bright stars you normally “key on,” to get yourself
oriented, do not look the way they did the last time. By now, you should be familiar with several constellations
near the equator as they were illustrated in previous units. You should be able locate one familiar one because
of the positioning, or alignment, of a group of stars.
Got one? Now if you could only remember which constellations are to the immediate left or right of that one,
that is, higher and lower right ascension and by how much. Notice now that you just changed coordinate systems. In this illustration you might have trouble locating anything near the pole star as you are not used looking
at it this way. This illustration roughly approximates what you would be seeing while looking south and you
are used to facing north to view the polar constellations.
So no matter how modern we attempt to be in astronomy, we just cannot discard the ancients’ method for locating things, using the road map provided by the constellations. If you cannot quickly locate more than a dozen
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constellations easily and quickly in the sky while giving your friends a “nighttime tour,” you haven’t been doing
your homework for the course.
It is generally understood that the outline, and hence the included stars in any constellation, would not be exactly as they are if we could start over and redefine them as we might see them via later history. Unfortunately,
most of the early developments in astronomy were made by people living in the northern hemisphere and it was
natural to borrow what the ancients had already imagined so that astronomers could start talking to each other.
It is generally agreed that the constellations in the southern hemisphere are more “compactly designed” as they
were discovered and named at much later dates.
People in the U.S. insist on looking for the Big Dipper, instead of Ursa Major or the Big Bear, because of our
pioneer heritage. They have trouble seeing the Big Bear as they conveniently leave off the nose of the bear and
only see the straight line lip of the dipper. See if you can “put the nose back on the big bear.” The trouble with
doing that is that extra star is one of the fainter ones and it is “sometimes there and sometimes not,” depending
upon viewing conditions for that night. And so we will be shortly discussing more on apparent magnitude as
that is an integral part of “locating things” as well.
185. The number of stars. "As numerous as the stars of heaven" is a familiar figure of speech appearing in literature but very early on, and before Hubble made his contribution to the same question, astronomers naturally
asked the question, “How many stars are there?” Even before modern telescopes extended our abilities to see
and enumerate the stars, attempts were made to count the stars we could see with normal vision to see if the results tell us anything. Using the magnitude scale that has been around since ancient times, where the brightest
stars are assigned a magnitude of one and stars at the lower limit of what the human eye can see are assigned a
magnitude of six, studies were made of nearly 5,000 stars which is typical of what one can actually see from
one hemisphere. The resulting count looked like this.
Magnitude Count
1.0
11
2.0
39
3.0
142
4.0
463
5.0
1,483
6.0
4,326
Even with such simple data, while exhaustively obtained, can we even ask the question, “Does the data tell us
anything?” The first thing we see is that the number of stars increases with decreasing apparent brightness.
Until we know more about whether some stars are inherently bigger than others or some stars “burn” by a faster
process, we cannot be 100% certain, but a good first guess is the drop in brightness corresponds to increasing
distance from the Earth. That makes sense if you imagine that stars have some “mean distance” between them
and as we move farther out from our Sun on a three dimensional sphere of space there would be more stars at
each distance. Armed only with such observations, it is easy to see that the earliest investigations into the stars
did not give us any idea of how big the Universe might be.
As soon as modern day telescopes “arrived on the scene,” it became abundantly clear that there were many
more stars than the simpler viewing methods were showing. That means that with telescopes one could see
stars that were less bright than the unaided human eye can see, or stars dimmer than magnitude six.
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Review Question. Return to Unit 8 where telescopes were discussed. Put your finger on the exact explanation,
or portion of a diagram, that says that telescopes can “make the invisible visible.”
186. Classification by magnitudes. Stars that can only be made visible by means of a telescope are generally
called telescopic and those that can be visible to the unaided eye are called lucid. (Have you ever heard someone state, “Now let me make this lucidly clear?”)
As soon as telescopes started making more and more stars visible it became clear that 5,000 stars per hemisphere wasn’t even close to “the total number of stars.” The Milky Way appears as a nebula to the naked eye―a
cloud of light with no visible details. Telescopes quickly revealed that there were many more stars in the Milky
Way than one could even possibly count so, for a number of years, the Milky Way was thought to be “all that
there was” and hence must be the Universe.
Now that telescopes are revealing stars whose apparent magnitude is less than 6, and the ancients left us only
with a scale that runs from one to six, a method has to be established in order the classify stars as having a magnitude of 7, 8 or even 9. In our discussion of calendars it was noted how difficult it is to “erase” a standard that
has been around for centuries and start over once it was recognized that the original system was not easy to
adapt to new discoveries. To discard an old system means you essentially throw out all the useful data that goes
with it and that makes it difficult to compare current data with historic data without having to use very difficult
comparisons and do it on a repeated basis.
So, good or bad, it was decided to retain the original scale of magnitudes while extending it so that it could easily be used as a numerical scale even when using electronic devices that are measuring brightness, luminosities
and magnitudes of stars and such things. To do this, studies and mathematical analyses were made of the human eye to determine just how much luminosity, or radiant energy, was actually in the beam of light when the
average human eye says that the magnitude is, say, five. Even to determine this was complicated as the human
eye responds to different colors differently so color itself had to be included as well. To include color as part of
these measurements for the eye, the equivalence of black body radiation was used, such as the Sun, and that
starts with the assumption that most stars are black body radiators like the Sun.
The result of these analyses showed the ancients gave us a system where a linear change in magnitude of five
very closely resulted in a change of total radiant energy by a multiplicative factor of 100. This was a nice
round number and was close enough to ancient data that, at most, the ancient record of a magnitude might
change in only the decimal place. But we do not want to “jump” through data by factors of 5 on a magnitude
and so jump by whole factors of 100 on the energy or luminosity scale, but we need to know luminosity values
for single values of magnitude. That means we are looking for a number which when multiplied by its self five
times equals 100. That is called the “fifth-root of 100.” And the ancients stuck us with an “upside down” scale
where an increase in one scale comes from a decrease in another. The result of all of this is the appearance of a
negative exponent to handle one scale going up while the other goes down.
We can avoid all the units and constants involved in the resulting equations for comparing the magnitude of one
star to that of another and how that relates to the luminosity showing up in our photometers by comparing the
ratios of the two stars. If star Sm has an apparent magnitude of “m” and star Sn has an apparent magnitude of
“n,” the ratios of the luminosities of the stars (as showing up in our photometers) will be:
Sn/Sm = (100)(m-n)/5 = (10)(m-n)1/2.5
While the equation can seem difficult, assume (in the first equation) the star Sn is the star with the higher magnitude number than star Sm. Then (m-n) results in a negative exponent so the number already starts out less than
one or the luminosity is less for the star with the higher magnitude number. The appearance of “/5” is another
way to express “taking the fifth root” of the resulting number.
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The second version of the equation is presented as it will often appear in texts that way. We leave it to the more
mathematical inclined to notice that 102 is the same as 100 and (10)1/2.5 = 102/5. We told you that astronomers
use lots of exponents. A student of math might have guessed that when we flagged a linear range to be compared with a multiplicative range, that would involve the use of logarithms. Take the logarithm of both sides
of the equations and they look much simpler―the final equation from the original studies.
Easy Calculation: Now that we have a magnitude scale that allows us to classify stars deeper into space, suppose we determine that a new star has a magnitude of 10. Using the above equation, show that this new star has
a luminosity of 1/100th of a star with magnitude of 5 as it should. Note that in practice the equation is used in
reverse. The meter connected to our photometer is indicating the luminosity of the star. We then use the equation to determine what is the equivalent magnitude to assign to the star?
It may still seem strange to you that astronomers would continue to use and extend an “upside down” measuring
system, until you realize that the original hope was that the scale would be a “distance indicator.” While the
luminosity decreases with increasing magnitude, generally speaking, the distance to a star increases with increasing magnitude. We cannot be certain that it will be true in every case until we know more about how stars
actually produce their light.
In the meantime, the scale has a few convenient features that astronomers quickly learned to use. Convince
yourself that the fifth root of 100 is approximately 2.5119. That means when two stars differ by one unit of
magnitude, the one star is approximately 2.5 times brighter/dimmer than the other star. But then the system
runs into some other strange features. To be placed on this scale, Sirius, the brightest of the fixed stars (and of
course you can locate Sirius) would have a magnitude of -1 and Arcturus and Vega would have a magnitude of
0―but the scale still works with those values. Then it gets stranger when we attempt to apply it to something
other than the stars. The Moon has a magnitude of -12, Venus -3 and Neptune +8. Can you roughly read “distance” using the last three values? So it the system is not all that bad.
We have repeatedly mentioned that part of the scientific method is to let your data “talk to you.” That means
examining whatever data you have and see if it is giving you some additional information because of patterns
exhibited in the data. From there you verify the pattern you discovered by a more mathematical treatment that
would confirm the pattern. It is quickly noticed by an observer, that in the table above, where we have listed
magnitude against a count of stars, the number of stars for each successive magnitude is approximately 3 times
the number of stars for the preceding magnitude. Check that out to see how closely that observation fits the data.
We could do a complicated mathematical treatment and hypothesize that the “magnitude” scale is revealing an
increasing scale of radial “distance”, then estimate the number of stars per unit volume of space and, since the
volume of a sphere which is 4/3piR3, use that to see how the star count would increase with an increase in magnitude―but that would very complicated. Why not use the scale the simple way it was intended to be used in
the first place?
Start with the assumption that the figure for a magnitude 6 of 4,326 is a fairly accurate count for the number of
stars that would be found on the edge of sphere of radius/magnitude 6. Recall that a larger sample volume produces a more reliable value. Why is that again?
Calculation: Using that figure, your calculator and that hypothesized factor of three for each magnitude increase, (a) show that the number of stars at the radius/magnitude of 10 would be 0.35 million stars, or 3.5x105.
Clear your calculator and only enter the decimal value and track the powers of ten separately. (b) Calculate the
number of stars at a magnitude of 20, the approximate limit of ground based telescopes at the start of the 20th
century, would be 2.0x1010 = 20 x 109 or about twenty billion stars.
So even before Edwin Hubble started showing us how big the universe really was, astronomers were aware that
there are many more stars out there than we could ever look at or study and the calculations you just made were
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for the number of stars at one fixed radius. To get a better number for the total number of stars one would have
to add up the stars within the entire sphere of radius/magnitude 20. With that many stars at magnitude 20, the
limit for ground based telescopes and most of those could be confirmed to lie within the Milky Way Galaxy, it
is easy to see why at the start of the 20th century it was assumed that the Milky Way was “all that there was” or
it was the entire universe.
187. Distances of the stars. It is clear that astronomers must find a way to accurately determine the true distances to stars in order to really understand them. You should review Unit 10 where we discussed parallax and
how it was the first start in obtaining accurate measurements for distances to the stars. However, it was clearly
limited in its use to only the nearest stars which for lack of a better name might be called The Sun’s Nearest
Neighbors. Using parallax measurements, the distances to thousands of stars were determined and published in
the 1800’s and just some of that data appears in the table below. We have limited the following table to those
stars with the most recognizable names.
To make the comparison simple in table form, the “distances” for the stars might be thought of as a “sort of”
astronomical unit, where instead 93x106 miles the unit used was 93x1012 or a million regular AU. So, to obtain
the true distance to Alpha Centauri the distance listed there of .27 would be multiplied by 93x1012 miles, or
25x1012 miles, so minute differences in distances in the table correspond to a thousand or a million real AU differences. The right ascension is given in hours, declination in degrees and parallax in arcseconds. Even in the
1800’s they had ways to present complicated numbers in a simpler way.
The Sun’s Nearest Neighbors
STAR
Α Centauri
Magnitude RA h Dec ° Parallax ″ Distance
.7
14.5
-60°
0.75
0.27
Proxima Cent.
5.4
14.5
-62°
0.76
0.24
61 Cygni
5.0
21.0
+38
0.40
0.51
η Herculis
3.6
16.7
+39
0.40
0.51
-1.4
6.7
-17
0.37
0.56
Procyon
0.5
7.6
+5
0.34
0.60
γ Draconis
4.8
17.5
+55
0.30
0.68
σ Draconis
4.8
19.5
+69
0.25
0.82
η Cassiopeiæ
3.4
0.7
+57
0.25
0.82
Altair
1.0
19.8
+9
0.21
0.97
10 Ursa Majoris
4.2
8.9
+42
0.20
1.03
Castor
1.5
7.5
+32
0.20
1.03
β Cassiopeiæ
2.3
0.1
+59
0.16
1.28
70 Ophiuchi
4.4
18.0
+2
0.16
1.28
µ Cassiopeia
5.4
1.0
+54
0.14
1.47
ϑ Eridani
4.4
3.5
-10
0.14
1.47
Sirius
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STAR
Magnitude RA h Dec ° Parallax ″ Distance
ι Ursa Majoris
3.2
8.9
+48
0.13
1.58
β Hydri
2.9
0.3
-78
0.1
1.58
Fomalhaut
1.0
22.9
-30
0.13
1.58
Br. 3,077
6.0
23.1
+57
0.13
1.58
ϑ Cygni
2.5
20.8
+33
0.12
1.71
β Coma
4.5
13.1
+28
0.11
1.87
π Herculis
3.3
17.2
+37
0.11
1.87
Aldebaran
1.1
4.5
+16
0.10
2.06
Capella
0.1
5.1
+46
0.10
2.06
B. D. 35°, 4,003
9.2
20.1
+35
0.10
2.06
Gr. 1,646
6.3
10.3
+49
0.10
2.06
γ Cygni
2.3
20.3
+40
0.10
2.06
Regulus
1.2
10.0
+12
0.10
2.06
Vega
0.2
18.6
+39
0.10
2.06
We immediately notice a few things in the table that require an explanation. Alpha Centauri is slightly closer to
our Sun than Proxima Centauri as indicated in its slightly larger distance number and slightly larger parallax
number as we would suspect. Yet Alpha Centauri is a more luminous (less apparent magnitude) star and yet it
is farther away. Clearly the apparent magnitude scale is not going to be a good distance indicator.
Sirius is so bright it has a magnitude of -1 and yet is farther away than Alpha Centauri. Fomalhaut is another
extreme example. Its extra 1.3 distance listed, compared to Alpha Centauri, corresponds to an additional distance of 1.3 x 93 x 1012 miles and yet it has a high luminosity (lower apparent magnitude). Obviously the luminosity of any star is not simply a function of distance. Our calculations using magnitude as distance worked for
a large collection of stars but certainly did not apply to every star within the collection.
Scanning the list of recognizable constellations, it is immediately noticed that the alpha star for many of them
do not appear in the listing and yet the alpha star is the brightest star in any constellation. The answer in all cases was the same―the parallax for the alpha star was so small it could not be measured. So how can it be brighter and yet so far away?
Where stars are listed from the same constellation, their distances do not correspond to being located near to
each other and so their apparent grouping into constellations is more of a function of their accidental, visual
alignment as viewed from Earth. So clearly the Celestial Sphere, with all the stars stuck to it, is merely a convenient illusion to make locating them simple for us.
Follow up sightings with the newer telescopes produced at the start of the 20th century produced at least one answer as to how farther stars can be brighter―Alpha Centauri was proven to be a double star, two stars rotating
around a common center of gravity, now called Alpha Centauri A and B. So the value listed above is too low
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(remember the inverted scale). Two stars in same place can suggest the amount of mass present can be part of
the contribution to brightness, maybe even if the mass is contained all in one star.
If astronomers had not carefully made observations night
after night starting in the 1700’s, recording declination
and right ascension down to the tiniest value, illustrations
could not have been published like this one at the beginning of the 20th century. Plotting century old data for Alpha Centauri, they were able to show that there were two
stars, one brighter than the other, and they orbited around
a common center of gravity.
They were able to determine that we see the orbiting
plane at an angle and that the major and minor axis of the
ellipse has a ratio of 47:40 and the orbital dimensions are
slightly larger than the orbit of Uranus, or comparable to
the size of our solar system. They estimated the orbital
period at 81 years. The more recently determined value
is 79.9 years. Not bad, considering some of the data they
used is more than 200 years old for us today.
If you will merely stare at the “two body equation” on page 15 of Unit 4, it is clear that to determine the masses
of two bodies rotating around you would have to know all the geometric distances involved and their periods in
order to determine the masses of the two bodies. As indicated above, they had all that and determined the combined mass of the two stars was twice that of the Sun with approximate percentages 110% and 90% of the total
mass. So the masses of some stars can be determined by simply “watching” and recording them.
188. Motion of the Stars. The movement of the stars Alpha Centauri A and B is a good introduction to something else we now need to get accustomed to when talking about the fixed stars―they move. It is only because
their motions seem very slow as measured on the celestial sphere that we could treat them as fixed for our purposes of navigating through the stars. Just as we needed to do when studying the motion of the planets, we need
to determine what part of the motion of any star is only an apparent motion on the celestial sphere caused by the
various motions and precession of the Earth and how much of their motion is a real motion as observed from
our solar system as a whole. The general motion of the so called fixed stars is small enough that we only see
them as short linear segment and such observed motions are called allineations since they appear linear. Out of
such observations we need to determine what part of that motion is inherent with the star itself and that is called
its proper motion.
Ancient astronomers did record many allineations among the stars but were unable to explain them, probably
because it was not at all clear what this celestial “sphere” was all about and what it was made from, so we
would like to think they left us a “message” for us to solve later. Stated another way, we suspect that the ancients were slowly discovering what we now call proper motion but had not yet put the concept together.
Hipparchus 125 BC and Ptolemy 130 AD observed and recorded many allineations among the stars. For example, they found that the three stars, ϑ Persei, α and β Arietis (constellation of Aries near Taurus), stood in a
straight line directly on a great circle. Check your star maps to determine that this is no longer true.
That would have meant that in their day all three stars had the same right ascension. Today the right ascension
of the three stars in their order above is 2h 44m, 2h 07m and 1h 54m. So the three stars would no longer be
viewed as lining up in a nice vertical line. Additional proof for proper motion was provided in 1718 by Edmund
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Halley, who noticed that Sirius, Arcturus and Aldebaran were over sixty minutes away from the positions
charted by Hipparchus roughly 1850 years earlier.
Knowing the individual motions of stars as well stars
moving in a group can be helpful. The velocity of stars
moving together as a group is sometimes called their
drift. It was known for some time that most of the stars
in Ursa Major have a proper drift motion generally towards our Sun drifting at a speed of 18 km/sec or 40,000
mph.
Two of the stars, the alpha star (Dubhe) on the lip of the
dipper and the eta star (Alkaid) on the handle tip, are
“rouges” of sort in they follow their own separate velocities as illustrated. So sometimes in the far future the constellation will look as in the bottom illustration. I wonder
what they will call the constellation then.
In determining velocities of stars, it can quickly become a compounded problem when trying to determine the
direction of the velocities in three dimensions. Imagine tracking the motion of a star on the celestial sphere.
How would you determine its velocity in the two dimensions across the sphere? Then what about its velocity
towards or away from Earth? It turns out the latter is the easiest to determine without having to spend months
or years getting the data.
You should review the Doppler Effect in Unit 8. Suppose you recorded the bottom spectrum from a star you are studying. The top
spectrum is how the same element shows up in a laboratory experiment.
Review Question: You notice that the spectral lines from the star have been shifted towards violet. Does that
mean the star is coming towards or away from Earth? In general terms, how would you calibrate the spectrograph on your telescope to be a “velocity meter?”
The velocities of stars in the other two directions could not have been completed except for determining the
right ascension and declination of many stars going back many years as well as centuries. Note again how little
the stars ϑ Persei, α, and β Arietis have moved from having the same right ascension in a 2,000 year period. So
we still think in terms of the background of “fixed stars,” except we have to “adjust” where they are fixed every
century or so.
189. Motion of the Sun. It is amazing that at the start of the 20th century, long before they had computers,
astronomers were doing “statistical analyses” of the volumes of star data they had and tried to see if “the average of everything” told them anything at all. Just like our previous attempts to use magnitude to see, on the average, how many stars there are at each magnitude and therefore how many possible stars might exist, astronomers found that the average observed velocity of all stars that had been measured, without considering direction, was 19 kilometers per second. Then the next question to ask would be “What velocity should the Sun have
so that the average velocities of all stars would be equal to zero?” That supposedly would subtract out the motion of the Sun and produce the true proper motion of the stars. They came up with a figure of 11 kilometers per
second for the Sun and concluded that the remaining 8 kilometers per second, or so, was the proper motion of
most stars.
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The difficulty in determining motion starts with the simple fact that all motion is a relative quantity and until
you know which object is located where you have no true sense of who, or what, is actually doing the moving―the observer or the object being observed. Until Edwin Hubble and other astronomers showed that our
Sun is part of just one galaxy out of many such galaxies, the varied motion of different stars made little sense.
Once we knew our Sun was on an outer arm of a rotating galaxy, with an orbital velocity as indicated, the
motion of some stars started to make sense. Most of
the stars that early telescopes could see were also part
of this galaxy and they “travelled with us” and so the
number of seemingly “fixed stars” made sense. The
rouge stars are merely located on a different arm and
their motion currently is “different than the rest.” Once
the speed of our Sun relative to the galaxy was determined to be 20 kilometers per second, now much of the
motion being observed was that of the Sun itself.
For additional galaxy photos go to http://hubblesite.org/
We stated that the 20 kilometers per second was “relative” to the galaxy itself. More recent numbers you may
locate account for the fact that the galaxy itself is moving and so the Sun’s speed relative to other frames of reference will have higher values. “Relative to the galaxy” is important phrase to explain what early astronomers
were actually measuring at the time. So when the Sun’s velocity is close to the value that has been observed for
many moving stars then some of those stars are not moving as fast as we thought and are more “fixed”
again―that is until Edwin Hubble started measuring the high receding velocity of the more far distant stars that
were not visible to the earlier telescopes and then the whole universe was now “on the move.”
At this point you may feel that the velocity measurements for all these stars didn’t tell us anything. Why do
some stars seem to have a proper motion producing an increase in right ascension while others seem to move in
an opposite direction? Any star on an inside orbit from our Sun would seem to move away (get ahead) in a direction opposite to one on an outer arm (fall behind). And what about the two stars in Ursa Major that seem to
be travelling toward our Sun? Are they trying to crash into our Sun? They may be attracted by the large
amount of mass in the center of the galaxy and, relative to our solar system they are merely “passing by.” So
notice again, the difficulty of knowing what you are actually seeing until you “have the bigger picture.”
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Even stars that do NOT seem to move relative to each
other can raise interesting questions about the origin of
things. One of the most studied clusters of stars is the
Pleiades and, yes, they do travel (drift) as a group so
they must have had a common origin.
How big must the nebula have been to form this many
stars when our solar nebula only formed one star? And
should we NOT expect to find any planets there as
radiation pressure from that many stars certainly
would have blown much of the remaining nebula
away, or one of the stars might have absorbed any proto-planet via gravitational attraction.
High resolution photographs of the Pleiades shows there is still some nebulosity in the cluster. Is that part of
the nebula that produced them or is that another nebular region they moved into? Are all such clusters associated with nebulae? You can see why a “nebular origin” becomes the thinking for our solar system and the
creation of stars in the first place.
190. Earliest Attempts to Classify Stars. I often joke with my biologist friends by saying that by the end of
the 19th century, astronomers were discovering things so fast and furious they did not have time to really figure
out what they were seeing and so they did what “you folks” do all the time when you discover a new “critter”―give it a name and hope someone else will study it later and figure out what it really is.
With more experimental efforts given to analyzing the spectrum of light coming from stars, rather than measuring their distances and velocities, astronomers thought they had discovered a “pattern” and started with three
names, or titles, to describe this pattern. They were probably misled by statistics which sometimes leads you to
the truth and at other times can be deceitful. Two thirds of the stars in the neighborhood of the Sun exhibit the
same spectral pattern as the Sun with its yellow-orange coloration. Probably they then assumed this was the
“normal thing” and labeled such stars as Solar.
Stars such as Sirius, the dog star, (why is it so called?) shine with a white intensity and a greater amount of the
blue end of the spectrum. When other stars, such as β Aurigae, exhibited a similar spectrum, they came up
with a name to explain such “deviants” stars as Sirian. Then noticing a large number of stars showing a spectrum deep into red, they name a third class of stars as simply Red. So, with the three names of Sirian, Solar and
Red, it started to look like they were learning something about the “differences” in stars.
We will save the modern classification of stars until the next section but this classification did not last very long
when further investigations showed that a star can glow white hot, like Sirius, for two completely different reasons and stars can glow deep red for more than one reason. They probably thought that they had found an “age
pattern” in that stars that are just starting out are young and shine brightly. Mature stars settle down and glow
yellow-orange. Old stars glow dim red like a bonfire that is about to go out. Further experiments eventually
showed that things are not this simple.
191. Double Stars. Here we mean a true double star system, or binary stars, where the stars are actually orbiting each other as if one is the satellite of the other. Sirius is known to be a true double as are θ Tauri,
α Capricorni and Vega. One thing that can be learned by studying double star systems is to obtain an estimate
of their age and their masses.
Just as we described in Unit 9, where the Moon is orbiting the Earth, as long as portions of one, or both, of the
objects are not solid, there is the possibility for “tidal action” which has one object doing work on the other.
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That means the object must lose kinetic energy, slow down in velocity and assume a larger orbit relative to the
other object. Since stars are anything but solid, we can assume that double stars that are in a very tight orbit
around each other are a young system. Hence, the distance between the stars is an estimate of their age. The
age of the Sirius double star system is estimated at 200 to 300 million years. Hmm! Since that is much younger
than even the Earth-Moon system, maybe young stars are of the Sirian type.
On the other hand, one of the double stars is very tiny, now classified as a white dwarf, and yet it also glows
with that very white spectrum. Clearly then, the amount of mass in a star does not determine its color. Or can
it? In 1760 a paper was presented at the Royal Society in London which claimed that the astronomer Claudius
Ptolemy in 150 AD had described Sirius and five other stars as “reddish” like Betelgeuse and other stars that we
still see as reddish. Was Ptolemy mistaken or can a star change its color with time? More on that topic in the
next unit!
In Unit 4 page 15, we showed an equation that Newton derived that applied to two bodies that orbit around each
other and of course that is what we have in a binary star system. The full equation looks complicated as:
G(m1 + m2)P2 = (d1 + d2)3 = R3
Now as long as we deal with ratios, the gravitation constant G can be ignored as it divides out of any ratio. After solving many astronomy mathematical problems you can almost start doing then in your head. Let’s make
things really simple and consider everything to be in Earth-Sun units. Applying the equation to the Earth and
Sun we imagine m1 + m2 to be “one earth-sun mass” and R3 to be (1 AU)3. So if we compute the same ratio of
R3/P2 for a binary star we would know how massive the two stars are compared to the Earth-Sun system. If
some time later we wanted to know the answer in kilograms, we could simply use the known values for the
Earth and Sun.
Easy Calculation: Suppose we observed the Alpha Centauri binary system mentioned above as having a period of 79.9 years and a mean orbital radius of 25.1 AU―something we can do by observing them in a telescope. Use your calculator to compute the value R3/P2 to show that the total mass in the binary system is about
2.5 Earth-Sun masses. Since most of that mass resides in the Sun, then the combined mass of the Alpha Centauri system is at least twice as large as the Sun. So we are already into methods for finding the mass of stars
and they start looking big.
Now that you know how simple that can be, you might repeat that calculation for addition binaries and see how
close your calculation agrees with the total mass of the binary compared to the Earth + Sun masses.
Mean Orbit
AU
Period
Years
Mass
AU
α Centauri
25.1
79.9
2.47
70 Ophiuchi
23.19
88.3
1.6
15
40.82
2.03
19.6
50.09
3
BINARY STAR
Procyon
Sirius
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192. Spectroscopic binaries.
Suppose you had your spectrometer analyzing the star you are studying and night after night the spectrum always recorded as spectrum number 1. Then one night, without warning, your spectrometer began recording the
spectrum labeled 2. This lasted for a number of days. Then, abruptly as it first changed it changed again and
the spectrum appeared as the one labeled 3. That clearly is a totally different spectrum than number 1. After a
time you started seeing spectrum number 2 again and eventually back to spectrum number 1.
By observing this anomaly over a long period of time you observe the consistent periodic changes in the spectra
as 1, 2, 3, 2, 1, 2, 3 and so on―always noticing that spectrum 2 appears BETWEEN changes from 1 into 3 and
the reverse of this. You eventually can determine its “periodicity” by simply timing the changes in the spectra.
You quickly notice that it always passes through spectrum 2 in going from 1 to 3 and 3 to 1 and the time that
spectrum 2 last is about the same in both directions. Clearly you have two stars revolving about each other.
Binary stars that are discovered in this way are known as spectroscopic binaries. Once the dual stars are recognized they sometimes can both be located visually and then they become known, finally, as visual binaries. One
of the very first binaries discovered in this way was announced in 1890. Since then, many such binaries have
been located.
The bright star Capella is an excellent example of working with spectroscopic binaries and how much you can
determine about them using mostly the spectroscope attached to the telescope. At intervals less than a month,
the lines of its spectrum were alternately single and then double when the two stars were aligned. It seemed that
their orbits were somewhat “edge on” as when each star’s spectrum was seen as a single, the shifting of the
spectrum toward the red or violet seemed to be the same amount, indicating the velocities of the two stars moving either away from us or towards us were about the same for both stars, namely 37 miles per second. That
could only be true if the masses of both stars were equal.
Historic Note: The following double star systems were first located as spectroscopic binaries―Polaris, Capella, Algol, Spica, β Aurigae and ζ Ursa Majoris,
Quick Calculation: Use Kepler’s Third Law (see Unit 4 page 7) to get an approximation to the distance between the two stars in the spectroscopic binary Capella, given that their orbital period is 104 days. Show that
their separation is about 0.44 AU. That is about ½ the distance from the Earth to the Sun. At that distance of
separation, it is no wonder the stars would be difficult to visually separate being about as close to each other as
Venus is from the Sun.
Update: In more recent times, Capella has been documented to have at least two sets of binary stars in its system. Imagine you were staring into a telescope to make the initial measurements of Capella. Capella is now
known to be 42.2 light years away. That means the light that entered your eye was emitted from Capella 42
years ago. What were you doing 42 years ago when the light that was to intrigue your measurements started
heading your way 42 years ago and just got here now?
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193. Dark Stars. For a time, astronomers thought they had discovered a new class of stars, which were temporarily named Dark Stars. Stars like Procyon were observed to do periodic loop-the-loop motions which violate
the laws of physics unless it is orbiting with a companion star. Since the second star could not be seen, astronomers merely assumed the existence of stars that do not emit light. Since the true nature of Jupiter was not
fully developed, the thought of declaring it a planet, rather than a dark star, wasn’t conceived. In Unit 11, we
discussed how Jupiter seems to be source of a great deal of internal energy that produces storms on its surface,
so Jupiter can be thought of as an “almost star”―if it had more mass it would become one. Then when more
powerful telescopes came on the scene and some of the dark stars were finally visible, the concept of dark stars
seemed premature. But then, that does raise the question “What is a star and what is a planet?” How much
energy does the planet have to generate on its own before it is a star and not a planet?
Without exhibiting a looping pattern, other stars were observed to slow down in its allineations and then speed
up again. Of course, that is not allowed by the Laws of Physics unless the motion is caused by the presence of a
second, unseen object. We could be seeing any orbital plane edge on and at all times we simply see the combined luminosity of the several stars. Methods like this are now being used on distant stars in hope of catching
a companion of a large, truly dark second object, which for lack of a better term, would be called a Jupiter-like
planet. In addition, if the Jupiter-like planet were in a small orbit around the star, the mere mass of the planet
would produce some anomaly like this in the motion of the star, maybe only a periodic “wiggle.” You should
follow modern progress with these efforts on the news and the internet.
194. Variable Stars. Exhaustive studies of stars that might have a dark companion were important as such a
dark companion could be swinging in front of the star and temporarily change its apparent magnitude. Not
knowing how to prove, or disprove this, might have delayed the discovery that some stars change their magnitude on their own and it is not caused by an orbiting companion.
A star Omicron Ceti, also known as Mira, meaning “wonderful,” is so extreme in its range of brightness that it
was almost obvious that it is producing that change on its own without requiring a companion. It is one of the
brightest of the known variable stars but when it reaches its low luminosity it becomes invisible to the naked
eye or a magnitude greater than 6.
In 1596, astronomer David Fabricius made the mistake of using Mira as a point of reference to track the motions of the planet Mercury. It looked like a good choice as Mira at the time was a magnitude 3 star. Three
weeks later his reference star disappeared from view. He thought he had seen a Nova, or new star, pop on the
scene and perhaps blew itself up. Mira has since been observed to have a period in its luminosity of 332 days.
The changes are known not to be in a completely steady rhythm, or as one modern astronomer put it, “Mira has
good days and bad days.” The lack of a steady rhythm in its luminosity suggests immediately that we are not
seeing the steady rhythm of objects orbiting each other but the changes in luminosity are generated within the
star itself.
195. The Algol Variables. Once the presence of variable stars were noted, the first attempts to classify them
was naturally based on the periods in which their luminosity changes. Mira has a long period of nearly a year.
Algol is probably the most famous of variable stars especially because of its very short period with great regularity―quite different than Mira. Its period is easy to measure with great accuracy at 68.8154 HOURS and in
that time changes from a 2.3 to a 3.5 magnitude star. When its light curve is plotted against the time in hours,
the result is not what one would expect from “rotating objects.” The curve is more of “crash and recover” or
something inherent in the makeup of the star itself. Variable stars then are starting to tell us something about
how stars are “put together” and how their structure determines their behavior.
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The light curve of Algol
196. The Cepheid Variables. As we discussed in Unit 8, astronomer Henrietta Swan Leavitt discovered a
special class of variable star now known as a Cepheid Variable, after the star Delta Cepheid she had exhaustively studied. She started first with nearby samples of such stars so that their distances could be measured by the
usual means such as parallax. Once their true distances were known, she was able to show that their periods
were directly related to their final, maximum luminosities they would achieve―essentially that the stars that are
going to achieve a larger luminosity take a longer time to get there. Hence, merely measuring their periods
would tell us how luminous the star would be if we were in the vicinity of that star, or its absolute magnitude.
Then measuring its apparent magnitude we could determine its distance.
So the first time we had a true distance indicator as long as we could find a Cepheid Variable in that cluster or
region of any galaxy. From there, Edwin Hubble and others were able to use Cepheid Variables to determine
the size and shape of the Milky Way, that the Andromeda Galaxy was not a part of the Milky Way and that the
Universe was now very, very much bigger than we ever thought.
197. Novae or New Stars. We cannot end this unit without mentioning another “misnaming” of a variable star
that appeared so seldom in history that it was the most difficult to really understand. Throughout history, astronomical sightings have been reported of seeing a star-like object that has never been seen before and hence, for
that reason only, was labeled a “new star.” The most famous report was from Tycho Brahe who reported that a
new star appeared in the year 1572. He reported that it was so bright that it could be seen in the daytime. It was
visible for 16 months and then disappeared from sight.
Nothing quite that spectacular has been reported since, but a new star, temporarily named Nova Aurigae appeared in December 1891 and was gone by April 1892 and Nova Perseus appeared in February 1901. This one
fluttered in brightness and finally was gone to the naked eye by September 1902. That one is interesting as it
still can be viewed by telescope as a ninth or tenth magnitude star.
Perhaps we should start thinking of a new star more of a star that is “ending its days.”
Summary: We started this unit by examining stars that move. By studying their motions we became aware of
changes that occur in these stars. These changes led to a bigger picture of our position in the neighborhood of
stars and eventually how big the universe really is. With further study of the makeup of the stars themselves
perhaps we will eventually know how this “star stuff” is put together and ultimately how the universe itself was
created.
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If you do a search on the Internet specifying videos and include in your search both the name of the video and
the channel that produced the video, if the video is more than two years old you can often watch it on YouTube,
or elsewhere, as a complete, 45 minute video without commercials. Some have become outstanding classics
and you might purchase them on DVD before they are no longer marketed.
How the Universe Works―Science and Discovery Channels
Beyond the Solar System―Science and Discovery Channels
Journey to the Edge of the Universe―National Geographic
Hubble’s Amazing Universe―National Geographic
Cosmic Clusters―History Channel
The Edge of Space―History Channel