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Monday Feb. 28 Syllabus and Class Notes Are At: Go to Courses, AST301 – Introduction to Astronomy – Lacy Monday Feb. 28 Syllabus and class notes are at: www.as.utexas.edu go to courses, AST301 – Introduction to Astronomy – Lacy Reading for this week: Chapter 9 If you want help on anything covered in the course, come to discussion session Thursday at 6:00 in RLM 15.216B. Tests are in homework return boxes. Go get yours. Topics for last week and today Describe how astronomers measure temperatures of stars. How do astronomers use parallax to measure the distances to stars? Why does parallax vary inversely with distance? Describe and explain the relationship between a star’s apparent brightness (or flux), its absolute brightness (or luminosity), and its distance from us. Describe and explain the relationship between a star’s luminosity, its radius, and its temperature, and how this relationship is used to measure radii of stars. Sketch an H-R diagram, showing the location of main sequence stars, red giants, and white dwarfs. Explain how astronomers measure masses of stars. Describe how the luminosities of main sequence stars are related to their masses. Exam Answers 1. For this question assume the Earth and Mars both have circular orbits around the Sun. The radius of Mars' orbit is about 1.5 AU. a) What is the closest the Earth comes to Mars? (Drawing a picture might help.) 1.5AU – 1AU = 0.5 AU b) What is the greatest distance between the Earth and Mars? 1.5AU + 1AU = 2.5AU c) The angular diameter of Mars when it is closest to us is about 20seconds of arc. (That's 1/180 degrees.) About what is its angular diameter when it is farthest from us? It is 5 times farther away then (2.5/0.5), so it appears 5 times smaller, or 4 seconds of arc. d) At about what time of day or night is Mars highest in the sky when it is closest to us? It is opposite the Sun, so highest at midnight. e) In which place (closest to us or farthest) does Mars have the greatest apparent magnitude? It is brightest when closest, but the magnitude system is backwards, so its magnitude is largest when it is faintest, or most distant. 2. When talking about eclipses, I didn't realize there will be a partial eclipse of the Sun, visible in Austin, on April 8. a) What will the phase of the Moon be on the night of April 8? New (so it won’t be up at night). It is between the Earth and Sun. b) Based on this information, give a date this year when a lunar eclipse might be visible from someplace on Earth. Two weeks earlier or later. (Or 6 lunar months +/- 2 weeks.) c) Why are lunar eclipses much more often visible from a given place than solar eclipses? Anyone on the dark side of the Earth can see a lunar eclipse. You have to be in the Moon’s small shadow to see a solar eclipse. 3. Explain why the Sun passes more nearly overhead in Austin in June than it does in December. You could use the celestial sphere explanation or a drawing of the Earth in its orbit in June and December. The drawing of the Earth in its orbit shows that someone standing in the northern hemisphere of the tipped Earth has his head tipped toward the Sun in June more than in December. In the celestial sphere picture, the Sun is closer to Polaris in June, so follows a more northerly path across the sky. See the drawings on the board. 4. Newton's second law is a = F / m (or F = ma). a) Define each of the quantities in this formula. (Say what word each letter stands for, and also define the words.) a: acceleration – the rate of change of speed or direction of motion F: force – a push or pull on an object m: mass – a measure of the amount of matter in an object 2 b) Newton's law of gravity is F = G M1 M2 / d . Use this law to figure out how the force of gravity on a spaceship orbiting the Earth one Earth radius above the surface of the Earth compares to the force of gravity on that spaceship while sitting on the surface of the Earth. Give a number (it is x times bigger or smaller) and an explanation. The force varies as 1/d2, where d is the distance from the center of the Earth to the center of the spaceship. In orbit the spaceship is twice as far from the center of the Earth as on the surface, so the force on it is 1/22 = _ times as strong. 5. Betelgeuse (the star in Orion's right shoulder) has a surface temperature of about 3000K and emits light most strongly at a wavelength of about 1000 nm. Rigel (Orion's left knee) has a temperature of about 12,000K (4 times hotter than Betelgeuse). a) At about what wavelength does Rigel emit light most strongly? It is 4 times hotter, so it emits at 4 times shorter wavelength, or 250 nm. b) If the two stars have the same size, which emits the most light power, and how many times more power does it emit? (You can leave your answer to this question in the form of a formula that you could punch into a calculator.) Rigel emits 44 times as much light power (or luminosity). c) How does the energy of a photon from near the peak of Rigel's spectrum compare to the energy of a photon from near the peak of Betelgeuse's spectrum? Rigel is 4 times hotter, so its typical photons have 4 times more energy. 6.a) What particles make up a hydrogen atom? One proton and one electron. b) How does a helium atom differ from a hydrogen atom? It has two protons, two neutrons, and two electrons. Topics for this week Explain how astronomers measure masses of stars. Describe how the luminosities of main sequence stars are related to their masses. Describe the process of formation of a protostar from a molecular cloud. Describe the concept of hydrostatic equilibrium. Describe the concept of thermal equilibrium. Describe how a star changes if it is not in thermal equilibrium, and how this keeps the Sun’s luminosity stable. Describe how the mass-luminosity relation can be used to calculate the lifetimes of main sequence stars. Temperature-Luminosity diagrams Astronomers measure the temperatures and luminosities of many stars and plot them on a diagram called the Hertzsprung-Russell (or H-R) diagram. For historical reasons they plot temperatures increasing to the left (not right) and luminosities increasing upward. They find that stars cluster in 3 groups. Star survey results Many stars fall on a diagonal line running from the upper left (hot and luminous) to the lower right (cool and faint). The Sun is one of these stars. But some fall in the upper right (cool and luminous) and some fall toward the bottom of the diagram (faint). If all stars had the same size, where would they fall on the diagram? What can we say about the stars in the upper right? What can we say about the stars toward the bottom? Masses of Stars The gravitational force of the Sun keeps the planets in orbit around it. The force of the Sun’s gravity is proportional to the mass of the Sun, and so the speeds of the planets as they orbit the Sun depend on the mass of the Sun. Newton’s generalization of Kepler’s 3rd law says: P2 = a3 / M where P is the time to orbit, measured in years, a is the size of the orbit, measured in AU, and M is the sum of the two masses, measured in solar masses. Masses of stars It is difficult to see planets orbiting other stars, but we can see stars orbiting other stars. By measuring the periods and sizes of the orbits we can calculate the masses of the stars. If P2 = a3 / M, M = a3 / P2 This mass is actually the sum of the masses of the two stars. If we observe the motions of both stars we can find out the mass of each star. Mass – Luminosity Diagram We can plot the masses and luminosities of stars on a diagram like the H-R diagram. Red giant and white dwarf stars follow no pattern, but main sequence stars fall along a line with luminosity increasing with mass. Groups of four Choose a discussion leader and a scribe. Read the graph: What is the luminosity in solar luminosities of the Sun? What is the luminosity of a 10 solar mass main sequence star? (Make an estimate.) What is the relation between mass and luminosity? L α Mx What is x? (Make an estimate.) Mass-Luminosity Relation 1 solar mass 1 solar luminosity 10 solar masses 1000-10,000 solar luminosities Increasing the mass by a factor of 10 makes the luminosity increase by a factor of 1000-10,000, or 103-104. The rule must be L α M3 or L α M4. L α M3.5 is often used. Why are more massive stars more luminous? You should find out this week..
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