MCC PHS 142 M01 Astronomy Homework Ch.16-17 Adj Prof Astronomy: Sam Wormley <email@example.com> Web: edu-observatory.org Background Material Textbook - Read Chapters 16-17 Textbook - http://highered.mcgraw-hill.com/sites/0073512184/student_view0/chapter16/ Textbook - http://highered.mcgraw-hill.com/sites/0073512184/student_view0/chapter17/ (take the Multiple Choice Quiz for for each chapter) Web - http://www.sjaa.net/eph/0612/Cannon.pdf Web - http://umbra.nascom.nasa.gov/images/latest.html Web - http://edu-observatory.org/eo/sun.html Web - http://edu-observatory.org/eo/aurora.html Web - http://edu-observatory.org/weather/weather_ia.html Web - http://www.phys.hawaii.edu/~jgl/nuastron.html Web - http://xxx.lanl.gov/abs/astro-ph/9805135 Web - http://xxx.lanl.gov/pdf/astro-ph/9805135 Web - http://science.nasa.gov/headlines/y2001/ast15feb_1.htm?list125479 Web - http://www.sec.noaa.gov/ Web - http://antwrp.gsfc.nasa.gov/apod/archivepix.html The Sun - Our Star The Sun is an ordinary G2 star, one of more than 100 billion stars in our galaxy. mass: 1.989e30 kg temperature: 5800 K (surface), 15,600,000 K (core) The Sun is by far the largest object in the solar system. It contains more than 99.8% of the total mass of the Solar System (Jupiter contains most of the rest). The Sun is personified in many mythologies: the Greeks called it Helios and the Romans called it Sol. The Sun is, at present, about 75% hydrogen and 25% helium by mass (92.1% hydrogen and 7.8% helium by number of atoms); everything else ("metals") amounts to only 0.1%. This changes slowly over time as the Sun converts hydrogen to helium in its core. The outer layers of the Sun exhibit differential rotation: at the equator the surface rotates once every 25.4 days; near the poles it's as much as 36 days. This odd behavior is due to the fact that the Sun is not a solid body like the Earth. Similar effects are seen in the gas planets. The differential rotation extends considerably down into the interior of the Sun but the core of the Sun rotates as a solid body. Conditions at the Sun's core (approximately the inner 25% of its radius) are extreme. The temperature is 15.6 million Kelvin and the pressure is 250 billion atmospheres. At the center of the core the Sun's density is more than 150 times that of water. The Sun's energy output (3.86e33 ergs/second or 386 billion billion megawatts) is produced by nuclear fusion reactions. Each second about 700,000,000 tons of hydrogen are converted to about 695,000,000 tons of helium and 5,000,000 tons (=3.86e33 ergs) of energy in the form of gamma rays. As it travels out toward the surface, the energy is continuously absorbed and re-emitted at lower and lower temperatures so that by the time it reaches the surface, it is primarily visible light. For the last 20% of the way to the surface the energy is carried more by convection than by radiation. Brightness and Color There are two basic things we can measure from stars, how bright they are, and what color they are (their color spectra). It is these two properties that tell us what kind of a star we are looking at. With successive measurements we can tell if a star is variable, if it has any measurable parallax and if it has a proper motion. The Pleiades, an Open Star Cluster The Pleiades star cluster, often called the "Seven Sisters", is undoubtedly the most famous galactic star cluster in the heavens, known and regarded with reverence since remote antiquity. The name is said to be derived from the Greek word meaning "to sail", from the tradition that the helical rising of the Pleiades was the sign of the opening of the navigational season in the Mediterranean world. In Native American legend the Pleiades are connected with the Mateo Tepe or Devil's Tower, that curious and wonderfully impressive rock formation which rises like a colossal petrified tree-stump to a height of 1300 feet above the plains of northeastern Wyoming. According to the lore of the Kiowa, the Tower was raised up by the Great Spirit to protect seven Indian maidens who were pursued by giant bears; the maidens were afterward placed in the sky as the Pleiades cluster, and the marks of the bears claws may be seen in the vertical striations on the sides of the Tower to this day. The Cheyenne had a similar legend. The brightest members of the Pleiades are accompanied by bright nebulosity; these are reflection nebulae--dust clouds near the stars which reflect their light. Eta Tauri or Alcyone, the central star and brightest member of the Pleiades, is nearly 1000 times more luminous than the Sun, and probably about 10 times greater in size. The apparent magnitude is 2.87, spectral type B7e III; the absolute magnitude is about -2.6. In contrast, the faintest known members are less than 1/100th the solar luminosity. Between these extremes we find the usual Main Sequence containing all intermediate types and spectra, down to faint red dwarfs of the 16th magnitude. When a cloud of pre-stellar material condenses it forms fragments which contract under their own gravity until the interiors are hot enough for nuclear reactions to take place. From that moment on the objects are real stars. Large masses collapse rapidly--in about 100,000 years; smaller ones less rapidly--in about 10 million years in the case of a star like the Sun. The energy of a star comes from the inner core of about 20% of the star's mass, where hydrogen is transformed into helium with the release of energy which is radiated upwards to the surface of the star. This is the first phase of a star's life. Theory predicts and observation confirms that the luminosity of a star increases with its mass. The luminosity and surface temperature also go hand in hand: the higher the temperature the greater rate of radiation per unit area. A graph showing luminosity against surface temperature for stars in the first phase of their existence is a very smooth curve. It is usually plotted in the form of absolute magnitude V A against color (B-V) which is also a measure of its surface temperature, with the most luminous stars (lowest magnitudes) at the top and the color increasing (redder, cooler stars) to the right. This curve, called the standard main sequence, has been built up from observations of stars in nearby clusters whose distances are known. All stars, from the time of their birth until the core has used up its hydrogen supply, lie on this curve. The color-magnitude diagram of the Pleiades obviously coincides with the standard main sequence when shifted by the distance modulus of 5.52 mag. The Pleiades cluster lost it most luminous stars because of its age (65 million years). Only the first 25 stars are used here because of space, and perhaps, your tolerance. The observed color-magnitude information for the Pleiades extends several magnitudes fainter than these and contains about 250 members with measured photoelectric magnitudes. Color-magnitude diagrams of star clusters have to be corrected for interstellar extinction, that is, for the dimming of starlight by dust in the space between stars. Dust is concentrated in the galactic plane, and, since open star clusters lie in that plane, all but the nearest of them are affected by extinction. In the early days of galactic research it was noticed that cluster distances, estimated from the apparent magnitudes of member stars, were systematically larger than distances estimated from the apparent cluster diameters, assuming that all open clusters more or less the same linear dimensions. The apparent diameter of a cluster decreases inversely as the distance, while the apparent brightness of a star decreases inversely as the square of the distance. The observation that cluster stars appeared dimmer than expected was one of the pointers to the existence of obscuring material in the intervening space. The effect of extinction is to make the stars appear dimmer and redder than they really are. The color-magnitude diagram of the Pleiades, a nearby cluster, does not suffer from interstellar extinction. The method of finding the distance of a cluster by matching the main sequence is a reliable one, because the use of a large number of stars smooths out photometric errors in the individual points. Investigations of the distances of open star clusters have played an important part in tracing the spiral arms of the Galaxy. Modern research on color-magnitude diagrams is concerned not only with age and distance but also with small variations in the evolution of stars in clusters of different chemical composition. A remarkable fact about the Pleiades Cluster is that the entire star-swarm is enveloped in a faint diffuse nebulosity of vast extent (Tennyson s "silver braid") which appears to shine by reflected light. This cosmic cloud is elusive visually, but shows much peculiar detail on long-exposure photographs. The spectrum of this nebulosity is identical to the spectra of the involved stars, a fact first discovered by V. M. Slipher at Lowell Observatory in 1912. The brightest portion of this nebulosity envelops the star Merope, and extends about 20 arcmin to the south; it was first noticed by Professor W. Temple with a 4-inch refractor observing at Venice on October 19th, 1859. He described it as resembling a faint stain of fog, like the effect of "a breath on a mirror". Seeing Merope s nebulosity is one of those benchmark tests that amateurs use to judge the quality of good optics. To the average eye the Pleiades Cluster appears as a tight knot of 6 or 7 stars, but some observers have recorded 11 or more under excellent conditions. Miss Agnes Clerke tells us that "Maestlin, the tutor of Johannes Kepler, perceived 14 stars", and mapped eleven Pleiades previously to the invention of the telescope; Carrington and Denning counted fourteen; Miss Airy marked the places of twelve with the naked eye". Personally, I can consistently see seven of the brightest eight and often think I can see Pleione next to Atlas in the "handle" of this "baby dipper". It would be interesting to see how many Pleiades you can see. You probably need to train your eyes. There are no shortcuts! The Battle Between Thermal Processes and Gravity In the Mysteries of Deep Space video we will watch, one astrophysicist keeps saying that gravity always wins. Gravity tries to collapse the star, but as long as there is nuclear fuel the star holds itself up against the pull of gravity. This is a very important concept! As long as there is nuclear "burning" going on the star holds itself up against gravity. Our sun has been doing this for about five billion years, and will do so for another four or five billion years, until it starts to run out of hydrogen to fuse into helium. For a few more hundred million years, it will fuse helium into carbon. After that there is no more nuclear fuel for our sun and gravity will win! Just about everything that happens in the universe can be considered a battle between thermal processes and gravity. All matter (and energy) is attracted to all other matter. Gravity is ceaselessly trying to pull matter together. Because of the motion of atoms (kinetic theory of gas), as atoms are crowded together, the temperature increases*, and so increases the pressure*. *This is not true for degenerate matter (white dwarfs). In the case of stars, gravity (sometimes aided by compression from a supernova shockwave or other perturbation) causes large clouds of gas (and dust) to collapse under their own weight, forming stars. The increasing density, and consequently the increasing temperature becomes so great in the centers of the collapsing gas that thermonuclear reactions get started. The increased heat given off from the thermonuclear reactions cause enough outward pressure to halt the collapse caused by gravity. Observations with the Hubble Space Telescope show us that star formation is a very violent process producing jets of ejected material traveling up to a third the speed of light. The Hubble Space Telescope has also observed many stars with dark planetary disks a few light years in diameter. These disks will likely evolve into systems of planets, and other left over material such as cometary material and asteroids. Eventually the stars come to equilibrium between heat production and gravity--a balance between the outward pressure from radiation (heat, light, etc.) and the inward pull of gravity. Stars have different evolutionary paths on the Hertzsprung-Russell (H-R) diagram based on their mass. And they have very different final fates depending on their mass. A picture is worth a thousand words. Look at the diagram on reproduced on the last page. That is the whole history of our sun plotted in terms of surface brightness as a function of surface temperature, an H-R diagram. Our sun lasts a little more than ten billion years with most of its life in thermal equilibrium on the "Main Sequence". Homework Problems Note the answers to the odd (Conceptual Questions, Problems and Figure-Based Questions) are in the back of your textbook. It is strongly suggested that you do some of those in every chapter so you have immediate feedback as how well you are understanding the material. There are online multiple choice quizzes for each chapter of your textbook. Goto http://www.mhhe.com/fix then click on Your book Student Edition Choose a chapter Multiple Choice Quiz You are expected to do all of your own homework. Statistical patterns showing copying or collaboration will result in no credit for the homework assignment for all participants involved. The Code of Academic Conduct for Iowa Valley Community College District is found in the Student Handbook. Physical Science classes require the use of mathematics. If you don't know algebra, you sould NOT be taking this class. If you need to review, look at Introduction to Algebra http://www.math.armstrong.edu/MathTutorial/ WolframAlpha is way faster than a scientific calculator. http://www.wolframalpha.com There is little excuse for turning homework in late. You have a whole week between classes to read the chapters and do the homework. Homework one week late - half credit. Two or more weeks late - no credit. Do the homework during the week, not in class! You got homework questions, email me 24/7. firstname.lastname@example.org Even if you don't have a homework question, email me anyway! Problem 1: In addition to position, astronomers can record the visual brightness of a star, V. They can also record the brightness of a star through filters, in our case a bue filter, B. Apparent Magnitude, V, of a star, is how bright the star is to our eyes and instruments. The Absolute Magnitude is defined to be how bright a star would appear to us if it were at a distance of 10 parsecs (32.6 light years). Note that the distance of the Pleiades is 127 parsecs. So to convert the Apparent Magnitudes of the Pleiades to Absolute Magnitudes we must use the conversion formula: Absolute Magnitudes = Apparent Magnitude, V, - 5 log (distance in parsecs/10). So at 127 parsecs, 5 log (127/10) equals 5.52. So we will subtract 5.52 from all the V values. "B" stands for the visual magnitude of a star looking through a blue filter. Taking the difference between the unfiltered visual magnitude of a star and its visual magnitude through a blue filter gives us a measure of the star's color temperature, in this case a value called Color Magnitude (B-V). Complete the following table filling in the missing entries for V - 5.52 and B-V. V B V - 5.52 B-V ----------------------------------------------------- 2.87 2.78 Alcyone -2.65 -0.09 3.64 3.56 Atlas -1.88 -0.08 3.71 3.60 Electra -1.81 -0.11 3.88 3.81 Maia 4.18 4.12 Merope 4.31 4.20 Taygeta 5.09 5.01 Pleione 5.45 5.38 Celaeno 5.76 5.71 Asterope 6.29 6.31 etc. 6.82 6.84 6.99 7.02 7.35 7.45 1.83 +0.10 7.66 7.87 7.85 8.05 8.12 8.34 8.27 8.63 8.37 8.67 8.69 9.15 9.25 9.80 9.45 9.97 9.88 10.42 10.13 10.75 10.48 11.12 4.96 0.64 10.83 11.63 5.31 0.80 Problem 2: Make a graph Absolute Magnitude (V - 5.52) versus Color Magnitude (B-V) for the 25 brightest Pleiades from the above data. Hint: Use the date from the two right hand columes to make you plot. Choose Absolute Magnitude (V - 5.52) as the vertical axis and Color Magnitude (B-V) as the horizontal axis. Label the axes "Absolute Magnitude" and "B-V". Do NOT connect your data points. Problem 3: Explain why the absorption lines of an element have the same wavelength as the emission lines of that element? Problem 4: Why are the Balmer lines weaker in the spectra of G stars than they are in the spectra of A stars? Problem 5: How does the brightness of a giant star compare with the brightness of a main sequence star of the same spectral class? If different, by how much? Problem 6: Star A is 7 magnitudes brighter than star B. How does the apparent brightness of Star A compare with Star B? Hint: Give a numeric answer. You will need the mathematical definition of "magnitude". Problem 7: The time it would take for the Sun to consume all its hydrogen (if the Sun's luminosity remained constant) would be about 100 billion years. Why is this an unrealistic estimate of the lifetime of the Sun? Problem 8: Explain why the solar neutrino telescope (detector) in South Dakota is located one mile beneath the Earth's surface and why it can operate around the clock. Problem 9: Why is nearly all of the Sun's energy produced in the inner 1.5% of its volume? Problem 10: What does the differential rotation of the Sun have to do with the solar sunspot cycle? Problem 11: Using your planisphere, what constellation is along the southern horizon at Midnight on your birthday?