14. Stars 1

Transcript: Since light has a finite speed, three hundred thousand kilometers per second, there’s an inevitable consequence called light travel time. In terrestrial environments light essentially travels instantly or appears to travel fast. The finite speed of light, three hundred thousand kilometers per second, has a consequence called light travel time. On the Earth, light essentially travels instantly. It takes light eight minutes to reach us from the Sun, so technically we are seeing the Sun as it was eight minutes ago. In the solar system it takes light hours to travel through the solar system. However, the distance to nearby stars is hundreds of thousands of times larger than the size of the solar system. Even the nearest star, Proxima Centauri, has a distance of 4.3 lightyears. This means we see Proxima Centauri as it was four and a third years ago. Polaris, the pole star, is at a much larger, distance 650 lightyears. Thus, we see Polaris as it was in the 1300s. If Polaris exploded we would not know about it until after 2600 A.D.

Transcript: Some stars in the sky, somewhat hotter than the Sun with temperatures of 5 thousand to 10 thousand Kelvin, have very low luminosities in the range of one-hundredth to one-thousandth the Sun’s luminosity. Application of the Stephan-Boltzmann Law shows that they must be physically small with sizes less than a tenth the size of the Sun, perhaps as low as one-hundredth the size of the Sun. These stars are called white dwarfs.

Transcript: Certain rare stars in the sky with either red or blue colors are extremely luminous, up to a million times the luminosity of the Sun. Application of the Stephan-Boltzmann Law shows that their sizes must be in the range of ten to a thousand times the size of the Sun. These exceptional stars are called supergiant stars. Some are hot and blue, and others are cool and red. Although in each case the color only refers to the outer nebulous atmosphere of the star, the centers are much hotter.

Transcript: A cool main sequence star with a temperature of about three thousand Kelvin lies on the main sequence with a luminosity of about a hundredth the luminosity of the Sun and a size about a quarter the Sun’s size, but there are stars with the same temperature, or color, as the Sun that are much more luminous, up to ten thousand times the luminosity of the Sun or even more. Betelgeuse and Antares are two well known examples. Application of the Stephan-Boltzmann Law shows that these stars must have sizes that are several hundred times the Sun’s size. These are called red giant stars.

Transcript: As was first seen nearly a hundred years ago, when luminosities and effective temperatures are gathered for hundreds of stars near the Sun, the result is not a scatter plot. Most stars in the H-R diagram lie on a diagonal line or track that runs from hot, luminous, and blue stars in the upper left corner down to cool, faint, and red stars in the lower right corner. Stars with these properties are called main sequence stars. The main sequence runs across the H-R diagram, and it represents all stars that get their energy from the fusion of hydrogen into helium.

Transcript: The H-R diagram is a plot of spectral class, or equivalently effective temperature, against stellar luminosity. The Stephan-Boltzmann Law tells us that luminosity goes as a high power of the temperature, the fourth power, and this is seen in the H-R diagram where the full range of the diagram is only about a factor of 20 in temperature but a factor of 108 or a hundred million in luminosity. Lines of constant radius can also be represented on the H-R diagram according the Stephan-Boltzmann Law. They are diagonal lines on the diagram which tell us the difference between giant stars, main sequence stars, and dwarf stars.

Transcript: As a way of exploring stellar properties and understanding how stars work, in the early twentieth century two astronomers, the Danish astronomer Ejnar Hertzsprung and the American astronomer and Henry Norris Russell, experimented with plotting spectral class for stars against their luminosity. They saw patterns in the ways stars appeared in this plot which led them towards an idea of how stars work. This is called the H-R diagram or the Hertzprung-Russell diagram, and it’s a key tool of stellar astronomy. In a typical H-R diagram the y-axis is luminosity, which runs from about 106 solar luminosities, or an absolute magnitude of -10, down to about 10-4 solar luminosities, an absolute magnitude of plus 15. The x-axis is temperature, photospheric temperature, or spectral class running from O stars, traditionally plotted on the left side, at temperatures of forty thousand Kelvin down to N stars with temperatures of twenty-five hundred Kelvin.

Transcript: A human lifetime is a blink of an eye compared to the age of the stars which can be hundreds of millions or billions of years. So how is it possible for astronomers to understand the life process of a star, to see their birth, death, and life? Consider an analogy of an intelligent ant living in a forest who lives a very short time but observes the diversity of nature. For instance, there are tall trees and short trees, saplings, fallen logs. Some of the falling logs have been helped by insects to decay back into Earth itself. Could a short living intelligent ant deduce the life cycle of the forest from sapling up to tall tree, to fallen log, and then back to Earth by observations over a short period of time? This is the situation astronomers find themselves in.

Transcript: Classification is often an important first step towards physical understanding. Imagine you lived in a small town and did a survey where you gathered information on every inhabitant, three pieces of information: their age, their height, and their weight. If you plotted height against weight you would notice an obvious trend, height and weight are correlated. Most people would fall on a particular track in a diagram of height plotted against weight. Some combinations are never seen; you would not have someone who is 3 feet high and 300 pounds nor someone who is 6 feet high and 60 pounds. The pattern will be telling you something. In this case the pattern reveals age because babies obviously grow into children who grow into larger people, and so height and weight are correlated with age. In the case of stars, a similar situation is applied because astronomers did not know the fundamental nature of stars when they first started observing them, and they used stellar classification to get a start.

Transcript: Stars are stable. For most of their lives, fusion provides the energy source. Even though the Sun and other stars are fusing hydrogen into helium, it does not mean that they are bombs. The Sun will be stable for billions of years. Stars also do not cool off. Energy flows continuously from the core where fusion occurs to the outer cooler regions. At every point within a stable star there’s an energy balance between two forces: the inward force of gravity and the outward pressure caused by energy release from nuclear reactions. This balance is called hydrostatic equilibrium.

Transcript: Mass is a fundamental property of a star, but it can be difficult to measure. It’s a question of how do you weigh a star in empty space? Typically astronomers make a model of the star based on the knowledge of its energy source, and this can lead to an estimate of its mass. By direct observation the best situation is the case of a binary star where we can use the orbit to estimate the mass by an application of Kepler’s laws.

Transcript: The Stephan-Boltzmann Law allows us to understand the state of stars with the same spectral type as the Sun but with very different luminosities. In this case the scaling reduces to radius going as the square root of luminosity. There are stars the same color as the Sun with 100 thousand times the Sun’s luminosity. By the Stephan-Boltzmann Law these stars must be three hundred times the size of the Sun. Conversely, there are stars the same color as the Sun with one-ten thousandths of the Sun’s luminosity, and these stars must be one hundredth the size of the Sun. Even without being able to measure stellar diameters directly we can use the physical scaling of the stellar model applied by the Stephan-Boltzmann Law to understand the true size of stars.

Transcript: The Stephan-Boltzmann Law allows us to estimate the size range of stars like the Sun that get their energy from fusion of hydrogen into helium. As a reference, the Sun has a luminosity of 3.8 times 1026 watts, a surface temperature of 5,700 degrees Kelvin, and a radius of 700 thousand kilometers. The Stephan-Boltzmann Law gives a scaling that radius is proportional to the square root of luminosity and the temperature to the minus two power. This means that there are stars 106 times more luminous than the Sun at a temperature of 40 thousand Kelvin that must have sizes of 20 solar radii. At the other end of the energy sequence, there are stars emitting one thousandth the luminosity of the Sun with temperatures of 2,500 Kelvin that are one-fifth the size of the Sun. Thus, there is a factor of a hundred in the size range of stars like the Sun that convert hydrogen into helium by fusion.

Transcript: The Stephan-Boltzmann Law says that the luminosity of a star is proportional to its surface area and the fourth power of the temperature. If the luminosity is in watts, the radius is in meters, the temperature is in Kelvins, then the constant of proportionality, the Stefan-Boltzmann constant, is 5.67 times 10-8. This means that a star with twice the area has twice the luminosity, twice the number of photons emitted per second, but a star with twice the temperature has 24 or sixteen times the luminosity, sixteen times as much light emitted per second. So hotter stars emit more light per second and more light per unit area.

Transcript: The size of a star is a fundamental quantity, but it’s very hard to measure because stars are so far away. The Sun, our nearest star, is half a degree across on the plane of the sky, but if we move the Sun to a distance of one parsec its size would be about a hundredth of a second of arc. Atmospheric blurring of stellar images blurs them to 50 to 100 times larger than this, so when we see stars on an astronomical image it never reflects the true size of a star, just the blurring of the Earth’s atmosphere. At a distance of 10 parsecs where there’s significant numbers of stars, the size of a star would be a thousandth of an arcsecond, and to detect surface features we’d need even higher resolution. So only the very largest and nearest giant or super giant stars have ever been resolved by astronomical observation.

Transcript: Luminosity, distance, and apparent brightness are all related by the inverse square law of light. If we measure any two of these quantities we can estimate the third. For example, if two stars have the same apparent brightness but one is known to be three times more distant, say by parallax measurement, than the more distant star must be nine times more luminous. Or, if we have two stars of equal luminosity and one appears four times fainter than we know the fainter star is two times further away. Finally, if we have two stars at an equal distance, perhaps they’re in a cluster, than the star that appears five times brighter must be five times more luminous.

Transcript: Stellar luminosity is a fundamental property of stars. It’s the amount of energy radiated each second. Absolute brightness is another word for this. Really we’re talking about the energy radiated at all wavelengths which is technically called the Bolometric luminosity. Since most stars emit most of their radiation in visible light, visible or visual luminosity and Bolometric luminosity are usually almost equal. However, this is not true for very cool or very hot stars.

Transcript: The component of a star’s motion on the plane of the sky is called the tangential velocity, and it’s typically harder to measure than a radial velocity. We need the distance to the star, typically given by parallax, and the rate of angular motion across the plane of the sky. This is called the proper motion. For a typical stellar space velocity of 20 kilometers per second a star moves about 600 million kilometers in a year. This is a large amount of motion, but at a distance of a parsec it only corresponds to a half an arcsecond per year on the plane of the sky, barely detectable. For more distant stars it would be hard to detect. On the other hand we can be patient and make observations over more than one year. In this way proper motions have been detected for thousands of stars.

Transcript: The component of a star’s velocity to and away from the observer is called the radial velocity, and it’s measured using the Doppler Effect. In the Doppler Effect, when a source of waves is moving towards the observer the waves are bunched up in the direction of motion causing a blueshift. When the source of waves is moving away from the observer the waves are stretched out causing a redshift. The typical size of a radial velocity of a star in the solar neighborhood is about ten to twenty kilometers per second. As a fraction of the velocity of light, which is the way the Doppler Effect must be measured, this is a small percentage, less than one part in 104. So the measurement of radial velocity by the Doppler Effect requires a high precision measurement of less than 0.01 percent. If stars were moving randomly near the Sun, half of the stars would show blueshifts and half would show redshifts.

Transcript: The branch of astronomy that deals with the positions and motions of stars is called astrometry. The positions of stars are measured by taking images of the sky. We also need to know a stars distance, typically, which is most directly measured through the parallax technique, the application of geometry. Stars are so far away that their motions are difficult to detect, and in general stellar motion is composed of two components, each of which has to be measured using a separate technique. There is the radial component of the motion, or its component to and away from the observer, called the radial velocity, and then there’s the transverse velocity or its component of motion on the plane of the sky. To get the total space motion these two components are combined in quadrature using Pythagoras’ theorem.

Transcript: Most stars are very different in chemical composition from you, or I, or the material on the Earth. The Sun for example, of every 10 thousand atoms has 74 hundred hydrogen atoms, 24 hundred helium atoms, and 150 or so corresponding to all the other elements in the periodic table; for example, there are only three carbon atoms, two nitrogen atoms, and five oxygen atoms out of that 10 thousand. Contrast that with human material which of course is mostly water. Out of every 10 thousand atoms in the human body 62 hundred are hydrogen, 11 hundred carbon, 200 nitrogen, and 25 hundred oxygen; only two are helium. Humans have vastly more carbon, nitrogen, and oxygen than typical stellar material.

Transcript: Spectroscopy is the key to chemical composition to determining what a star is actually made of. There are two issues. One is detecting the presence of an element, and the second is the amount of that element. The presence of an element is determined by measuring one or more spectral features that exactly match the wavelengths of features of the element as seen in a lab. This is the idea of a spectral fingerprint, unique to each element in the periodic table. The amount of the element depends on the strength of the lines. In general, wider and deeper absorption lines correspond to a larger abundance or more atoms of that particular element. The actual abundance needs a physical model for the star to be accurately determined.

Transcript: The sequence of stellar spectral classes is also a sequence of photospheric temperature. Going through the stellar sequence, we have O stars with temperatures of 30,000 Kelvin, they are white hot or even blue as seen in the sky, B stars which are also bluish with temperatures of 18,000 degrees Kelvin, blue-white A stars with temperatures of 10,000 Kelvin, white F stars, temperatures of about 7,000 Kelvin, yellowish-white G stars (the Sun is a G star) with temperatures of about 5,500 Kelvin, orangish K stars with temperatures of about 4,000 Kelvin, and the coolest stars of all, orange or reddish M stars with temperatures of only 3,000 Kelvin.

Transcript: The spectral lines that appear in a stellar sequence depend on temperature. Helium takes a larger temperature to ionize than hydrogen, and this effects the visibility of helium compared to hydrogen. Going from hotter stars to cooler stars: O and B stars show ionized helium and neutral helium, A and F stars show mostly neutral hydrogen atoms, G stars show neutral hydrogen and some ionized calcium, K stars show neutral metal atoms of various species, and the coolest M stars show neutral metals and molecular lines.

Transcript: The sequence of stellar spectral classes is another example of the historical baggage that astronomers carry around. It’s hard to remember, so generations of students have dreamt up mnemonics to help them remember the unusual sequence of letters. For example: Old Boring Astronomers Find Great Kicks Mustily Regaling Napping Students. Or try this one: Overseas Broadcast, A Flash Godzilla Kills Mothra, Rodan Named Successor. Or perhaps this one, oven Baked Ants, Fried Gently, Kept Moist Retain Natural Substance.

Transcript: The original spectral classification sequence formed by Annie Cannon was alphabetical based on the strength of the hydrogen absorption features, but it turns out that stellar temperature, a more fundamental quantity, has a complex and not direct relationship with the strength of the hydrogen features. And so the original sequence got reordered with time. The current spectral sequence of stars going from hotter stars to cooler stars goes O, B, A, F, G, K, M. There’s been an extension in more recent years to the classes R, N, and S.

Transcript: Since hydrogen is the most abundant element in the universe and in stars, its spectral transitions are fundamental to stellar classification. The ground state is numbered n = 1, an electron in the lowest energy level it can have. States then go up, n = 2, n = 3, increasing in number at higher excitations from the ground state and closer and closer spacings until the atom is ionized. Transitions in and out of the n = 1 state appear mostly in the ultraviolet part of the spectrum and are called the Lyman series. Transitions in and out of the n = 2 state appear in the visible part of the spectrum and are called the Balmer series. Among the Balmer series the most prominent line is H-alpha or hydrogen-alpha involving transition between n = 2 and n = 3 states.

Transcript: Over a hundred years ago dozens of women labored in the basement of the Harvard College Observatory paving the way for a modern understanding of stars. These women were paid 25 cents an hour, less than half of what a man would make for similar work, to do the painstaking and tedious work of classifying photographic stellar spectra. Large photographic plates had thousands of individual tiny spectra superimposed on them. The women observed these spectra through a magnifier glass, made notes of the wavelengths of the prominent lines, and calculated the positions and wavelengths of the lines. No computers existed at the time, so these calculations were very tedious. These women were not allowed to be staff members of Harvard College Observatory. They could not take classes, and they could not even earn a degree at Harvard University where they worked. Their work, however, was central to the understanding of stars by classification. Annie Cannon was the most prominent of these stellar classifiers or computers. In her working life she classified over 225 thousand stars, individually and by hand, and she made large and increasing contributions to the subject as she more deeply understood the nature of stellar spectra. The stellar classification scheme that she produced is still in use today.

Transcript: Astronomical spectroscopy began with Newton dispersing the Sun’s light with a prism. In 1817, Joseph Fraunhofer dispersed the Sun’s light with much higher resolution and saw the spectrum crossed by narrow, dark absorption features. These features exactly corresponded to the wavelengths of lines from hydrogen in the laboratory, showing that the Sun was made of hydrogen. Fraunhofer had an interesting personal history. He was an orphan and as a child was working as an indentured servant in a lab and workshop of a man in Germany. A gas explosion caused the death of his mentor and the destruction of the lab. Fraunhofer wandered from the rubble dazed and confused and with no job and no home. His story was played in the local papers, and he got a new mentor and a start in life and became one of the foremost astronomers of his time. In the 1870s, photography advanced to the point where people could make photographic spectra, and at that point stellar classification moved forward rapidly. In the modern age, Charge Coupled Devices or CCDs are used to record spectra of stars and other astronomical objects. These digital electronic detectors can produce high quality spectra of hundreds of thousands of objects, and so every spectrum is categorized by several types of features: the emission features and absorption features corresponding to the elements that make up the gas of a star and the continuum which peaks at a wavelength determining the temperature of the photosphere according to Wien’s Law.

Transcript: In 1872, Henry Draper was the first man to photograph stellar spectra. This was a huge advance on previous practice which just relied on naked eye observations or visual observations where the features in the spectrum had to be described and then transcribed or written down. Draper started on a long project to photograph all the bright stars in the night sky and classify their stellar spectra. He died before the project could be finished, but he left in his will money to Harvard College Observatory to continue and finish the project. Edward Pickering led the project, but most of the work was done by a small set of female computers who actually, by eye, classified tens of thousands stellar spectra in the most tedious and painstaking way imaginable. The first classification was based on the strength of the hydrogen absorption features in the stellar spectrum. Class A of stars had the deepest hydrogen features, class B the next deepest, C the less deep, and so on up to letter P. Most of the features in the spectra were from hydrogen and some were from helium. All other features due to other elements were lumped together in the category called metals which is clearly a misnomer because many of the elements heavier than helium are not actually metallic.

Transcript: Distance is a fundamental stellar property. Without knowing distance it’s impossible to measure the luminosity or absolute brightness of a star, and so without measuring distance it’s impossible to know the true nature of a star seen in the sky whose flux is measured whether it’s a giant star, a main sequence star, or a dwarf. Parallax is difficult to measure from the ground. Typical image sizes from ground-based observatories are about an arcsecond or fraction of an arcsecond. Image positions can be measured to about a tenth of that, and so that only allows the possibility of measuring parallaxes of a few tenths of an arcsecond which limits us to distances of a few parsecs, the nearest dozen or so stars. From space the image sizes go down by a factor of ten or twenty to 0.1 arcseconds or 0.05 arcseconds. The position accuracies can be measured ten times better than that to a hundredth of an arcsecond or less which opens up a distance range of a hundred parsecs. There are twenty-five thousand stars within a hundred parsecs. In 1989 ESA launched the Hipparcos satellite which used a highly elliptical orbit and several years of observations to directly measure the parallax of a hundred thousand stars. Thus we have the distances of a large stellar population sample within a few hundred lightyears of the Sun.

Transcript: The way astronomers observe and calibrate the apparent brightness of something is through the technique of photometry. Photometry allows astronomers to measure the number of photons per second coming from an astronomical source in some specified wavelength range or pass band that’s defined by a filter. A filter is simply a colored piece of glass sitting above the CCD detector in a telescope that isolates a narrow range of wavelength. CCD detectors are sensitive to a wide range of wavelengths, and so the pass band must be specified by a separate optical element. Most photometry is done at optical and near infrared wavebands, so some of these wavebands are beyond the sensitivity of the human eye. The traditional wavebands are named after letters that do not follow the alphabet, they exist for historical reasons. In the optical bands we have U, B, V, R, and I at 350, 450, 550, 700, and 850 nanometers, and in the near-infrared the J, H, and K pass bands at 1.25 microns, 1.65 microns, and 2.2 microns. Relative brightness in absolute units is then determined by measuring bright stars where the absolute brightness has been measured by spacecraft.

Transcript: It’s amazing to think that the Sun, which dominates the daytime sky and brings warmth and life to the Earth, is fundamentally the same as the stars in the night sky. Galileo started this thinking with his observations using the telescope to show that the stars in the night sky have a huge range of apparent brightness. Perhaps the Sun is just the very brightest of these stars. In the late seventeenth century Christiaan Huygens estimated the distance to the stars by emitting sunlight through a pinhole and adjusting the pinhole until the light that entered was the same as from the bright star Sirius. It was one-twenty-seven-thousandth of the Sun light implying to Huygens that Sirius was twenty-seven thousand times further away than the Sun. Newton used a similar reasoning by using Saturn as a mirror reflecting sunlight and comparing its brightness to the bright stars. Also, the inverse square law could be used to estimate that the brightest stars may be as much as 100 thousand times further away than the Sun. These are all crude estimates that make fundamental assumptions about the nature of the stars relative to the Sun.

Transcript: The first direct estimate of stellar distances used geometry. In 1838, Friedrich Bessel measured the parallax of the bright star 61-Cygni. This is the seasonal shift in the apparent position of the star on the sky relative to more distant stars as the Earth travels its orbit of the Sun. The shift was only 0.6 seconds of arc, a very small effect, which is in part why it took two hundred years of telescopic observations before parallax to any star was measured. Here, however, was finally a direct measure of the distance to the stars showing that the stars were indeed hundreds of thousands of times further away than the Sun itself. The formal equation that gives the distance to the stars in terms of parallax is that the distance in astronomical units is roughly two hundred thousand divided by the parallax angle in arcseconds, or the distance in parsecs equals one over the parallax angle.

Transcript: The magnitude scale is defined in such a way as a magnitude difference of five magnitudes corresponds to a factor of a hundred in apparent brightness. Two and a half magnitude difference corresponds to a factor of 10 in apparent brightness. Lower numbers in the magnitude scale are brighter, which is of course the opposite of a scale set by the number of photons per second. Zero on the magnitude scale is defined by the bright star Vega. The magnitude scale can be illustrated by some magnitude differences and corresponding brightness ratios of typical situations. Two bright stars that are identical, seen at the same distance, have a magnitude difference of zero; their brightnesses are equal. Magnitude difference of one, or a factor of 2.5 in apparent brightness, is the minimum difference visible by eye between stars in the night sky. Magnitude difference of 4, or a brightness ratio of 40, corresponds to the limit of the naked eye relative to binoculars. Magnitude difference of 5, or a factor of 100, is a range between the brightest and the faintest stars in the sky. A factor of 104, or 10 magnitudes, is the ratio between the full moon and Mars. Fifteen magnitudes, or a factor of 106 in apparent brightness, is the ratio between the brightest star and Pluto. Twenty magnitudes, or 108 in apparent brightness, is the limit between binocular vision and the Hubble Space Telescope, and twenty-five magnitudes, 1010 in apparent brightness ratio, is the ratio between the Sun and the brightest star in the night sky.

Transcript: Apparent magnitude or apparent brightness must be specified at a particular wavelength. Stars have different colors or different energy distributions, so the apparent brightness depends on the wavelength of observation. Traditionally, astronomy is done by eye, and the detector was the visual detector which is the wavelength sensitivity of the human eye peaking somewhere in the green part of the visual spectrum. This is called visual apparent brightness or visual magnitude. Professional astronomers have, however, more carefully defined the wavelength scales that they use when measuring astronomical objects. They’ve used filters to isolate relatively small ranges of wavelengths, and they define magnitudes or apparent brightness in terms of those narrow wavelength ranges.

Transcript: Apparent Brightness in astronomy is the number of photons per second collected at the Earth from an astronomical source. It depends on three things: First, the collecting area of the device used to observe the source of light. In the case of a telescope, the aperture of collecting area is much larger than the eye, so the apparent brightness is greater. It depends on the distance to the source; apparent brightness varies according to the inverse square law. If the source is two times closer, the apparent brightness is four times larger. If the source is three times closer, the apparent brightness is nine times larger, and so on. And it depends on the intrinsic brightness of the source, which is to say how many photons per second the source actually emits. Apparent brightness can be quoted as photons per second or can be given relative to the Sun or another bright star, in which case it’s a ratio with no units.

Transcript: We can use relative brightness to show how bright various objects in the night sky are compared to the limits of technologies we use to observe the sky. In units where Vega, the bright star, is one unit of apparent brightness, the Sun is 40 billion times brighter. The full moon is 100 thousand times brighter than Vega, and for reference a 100 watt light bulb at a distance of 100 meters is 27,700 times brighter than Vega. Venus at its brightest is about 60 times brighter than the star Vega, Mars 12 times brighter, and Jupiter about 4 times brighter. The bright star Sirius is 3.5 times brighter than Vega. The limit of observation in cities with the naked eye, in units where Vega is one, is 0.025. That is, that we can see 40 times fainter than Vega. In a remote rural area the limit may be ten times less than that, 400 times fainter than Vega. Neptune on the same scale in the same units is 0.0008, a thousand times fainter than the bright star Vega. The limit of binoculars is about 6 timse 10-6 in these units, 100 thousand times fainter than the bright stars, and the limit of the Hubble Space Telescope in the same relative units is 3 times 10-12. The Hubble Space Telescope can see about a trillion times fainter than the brightest star in the sky.

Transcript: The apparent brightness of the Sun is a factor of 1010 or 10 billion times brighter than the brightest stars in the night sky like Vega, or Canopus, or Sirius. If we assume that the Sun and the stars are intrinsically the same type of object, that is they emit the same number of photons per second, we can use the inverse square law to say what the relative distance is to the stars and the Sun is. It must be a factor of the square-root of 1010 or 105. The stars are therefore roughly 105 or 100 thousand times further away than the Sun is from us. That’s 105 times 108 or 1013 kilometers, 10 trillion kilometers, or about a third of a parsec. Thus, this simple assumption gives us a rough estimate of the huge distance to the stars. We can compare the Sun and the stars directly through the medium of an equivalent light bulb of 100 watts. The Sun is like a 100 watt light bulb at a distance of 3 inches from your eye, very intense, don’t ever try that, whereas the brightest stars in the night sky are like 100 watt light bulbs at a distance of about 9 kilometers. That is a reading light at a distance of 5 miles. This gives a sense of the enormous range of apparent brightness between the Sun and even the nearest stars.

Transcript: Apparent brightness does not express a star or other source of light’s true energy output. Astronomers are more interested in absolute brightness or equivalently absolute magnitude or luminosity. For example, we can consider a situation where the apparent brightness of a 100 watt light bulb at a distance of 100 meters is actually the same as the apparent brightness of a dim, 1 watt nightlight at a distance of 10 meters, and both of those are the same at apparent brightness as an arc lamp of 10,000 watts at a distance of a kilometer. The three are obviously hugely different situations in terms of the intrinsic emission of light, and yet the apparent brightness of all three is the same. This is the situation astronomers find themselves in. Stars are not all 100 watt light bulbs, nor do they have their brightness written on them. And so astronomers try to use absolute brightness but find that it’s a very poor reflection of true brightness or distance.

Transcript: A parsec is a distance unit appropriate to the study of stars. It’s the distance that produces a parallax shift of one arcsecond. In other words, it’s the distance where the angle subtended by the star as seen from the Earth’s orbit six months apart, spanning the orbit, is one second of arc. One parsec equals 3.26 lightyears, so a parsec is slightly larger than a lightyear. Astronomers also use multiples of the parsec, a thousand parsecs, which is a kiloparsec, and a million parsecs, which is a megaparsec. The most useful thing about the parsec unit is that it corresponds to the typical distances between stars in the Milky Way Galaxy.

Transcript: The vast distances to the nearest stars encourage astronomers to use a new unit of distance. Whereas meters and kilometers work well on the Earth, and the astronomical unit is the appropriate unit for scales within the solar system, the distance scale to the stars is given as a lightyear. A lightyear is the distance that light travels in one year. It’s equal to about 6-million-million miles or 1016 meters. It’s defined as the speed of light, three hundred thousand kilometers per second, times the number of seconds in a year. Notice two things. The lightyear is not a metric unit. Occasionally astronomers use none metric units when they are convenient for the scales they’re dealing with, and also a lightyear is a unit of distance, not a unit of time.