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Astronomy

Figuring for Yourself

AstronomyFiguring for Yourself
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  1. Preface
  2. 1 Science and the Universe: A Brief Tour
    1. Introduction
    2. 1.1 The Nature of Astronomy
    3. 1.2 The Nature of Science
    4. 1.3 The Laws of Nature
    5. 1.4 Numbers in Astronomy
    6. 1.5 Consequences of Light Travel Time
    7. 1.6 A Tour of the Universe
    8. 1.7 The Universe on the Large Scale
    9. 1.8 The Universe of the Very Small
    10. 1.9 A Conclusion and a Beginning
    11. For Further Exploration
  3. 2 Observing the Sky: The Birth of Astronomy
    1. Thinking Ahead
    2. 2.1 The Sky Above
    3. 2.2 Ancient Astronomy
    4. 2.3 Astrology and Astronomy
    5. 2.4 The Birth of Modern Astronomy
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  4. 3 Orbits and Gravity
    1. Thinking Ahead
    2. 3.1 The Laws of Planetary Motion
    3. 3.2 Newton’s Great Synthesis
    4. 3.3 Newton’s Universal Law of Gravitation
    5. 3.4 Orbits in the Solar System
    6. 3.5 Motions of Satellites and Spacecraft
    7. 3.6 Gravity with More Than Two Bodies
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  5. 4 Earth, Moon, and Sky
    1. Thinking Ahead
    2. 4.1 Earth and Sky
    3. 4.2 The Seasons
    4. 4.3 Keeping Time
    5. 4.4 The Calendar
    6. 4.5 Phases and Motions of the Moon
    7. 4.6 Ocean Tides and the Moon
    8. 4.7 Eclipses of the Sun and Moon
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  6. 5 Radiation and Spectra
    1. Thinking Ahead
    2. 5.1 The Behavior of Light
    3. 5.2 The Electromagnetic Spectrum
    4. 5.3 Spectroscopy in Astronomy
    5. 5.4 The Structure of the Atom
    6. 5.5 Formation of Spectral Lines
    7. 5.6 The Doppler Effect
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  7. 6 Astronomical Instruments
    1. Thinking Ahead
    2. 6.1 Telescopes
    3. 6.2 Telescopes Today
    4. 6.3 Visible-Light Detectors and Instruments
    5. 6.4 Radio Telescopes
    6. 6.5 Observations outside Earth’s Atmosphere
    7. 6.6 The Future of Large Telescopes
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  8. 7 Other Worlds: An Introduction to the Solar System
    1. Thinking Ahead
    2. 7.1 Overview of Our Planetary System
    3. 7.2 Composition and Structure of Planets
    4. 7.3 Dating Planetary Surfaces
    5. 7.4 Origin of the Solar System
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  9. 8 Earth as a Planet
    1. Thinking Ahead
    2. 8.1 The Global Perspective
    3. 8.2 Earth’s Crust
    4. 8.3 Earth’s Atmosphere
    5. 8.4 Life, Chemical Evolution, and Climate Change
    6. 8.5 Cosmic Influences on the Evolution of Earth
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  10. 9 Cratered Worlds
    1. Thinking Ahead
    2. 9.1 General Properties of the Moon
    3. 9.2 The Lunar Surface
    4. 9.3 Impact Craters
    5. 9.4 The Origin of the Moon
    6. 9.5 Mercury
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  11. 10 Earthlike Planets: Venus and Mars
    1. Thinking Ahead
    2. 10.1 The Nearest Planets: An Overview
    3. 10.2 The Geology of Venus
    4. 10.3 The Massive Atmosphere of Venus
    5. 10.4 The Geology of Mars
    6. 10.5 Water and Life on Mars
    7. 10.6 Divergent Planetary Evolution
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  12. 11 The Giant Planets
    1. Thinking Ahead
    2. 11.1 Exploring the Outer Planets
    3. 11.2 The Giant Planets
    4. 11.3 Atmospheres of the Giant Planets
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  13. 12 Rings, Moons, and Pluto
    1. Thinking Ahead
    2. 12.1 Ring and Moon Systems Introduced
    3. 12.2 The Galilean Moons of Jupiter
    4. 12.3 Titan and Triton
    5. 12.4 Pluto and Charon
    6. 12.5 Planetary Rings
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  14. 13 Comets and Asteroids: Debris of the Solar System
    1. Thinking Ahead
    2. 13.1 Asteroids
    3. 13.2 Asteroids and Planetary Defense
    4. 13.3 The “Long-Haired” Comets
    5. 13.4 The Origin and Fate of Comets and Related Objects
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  15. 14 Cosmic Samples and the Origin of the Solar System
    1. Thinking Ahead
    2. 14.1 Meteors
    3. 14.2 Meteorites: Stones from Heaven
    4. 14.3 Formation of the Solar System
    5. 14.4 Comparison with Other Planetary Systems
    6. 14.5 Planetary Evolution
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  16. 15 The Sun: A Garden-Variety Star
    1. Thinking Ahead
    2. 15.1 The Structure and Composition of the Sun
    3. 15.2 The Solar Cycle
    4. 15.3 Solar Activity above the Photosphere
    5. 15.4 Space Weather
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  17. 16 The Sun: A Nuclear Powerhouse
    1. Thinking Ahead
    2. 16.1 Sources of Sunshine: Thermal and Gravitational Energy
    3. 16.2 Mass, Energy, and the Theory of Relativity
    4. 16.3 The Solar Interior: Theory
    5. 16.4 The Solar Interior: Observations
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  18. 17 Analyzing Starlight
    1. Thinking Ahead
    2. 17.1 The Brightness of Stars
    3. 17.2 Colors of Stars
    4. 17.3 The Spectra of Stars (and Brown Dwarfs)
    5. 17.4 Using Spectra to Measure Stellar Radius, Composition, and Motion
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  19. 18 The Stars: A Celestial Census
    1. Thinking Ahead
    2. 18.1 A Stellar Census
    3. 18.2 Measuring Stellar Masses
    4. 18.3 Diameters of Stars
    5. 18.4 The H–R Diagram
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  20. 19 Celestial Distances
    1. Thinking Ahead
    2. 19.1 Fundamental Units of Distance
    3. 19.2 Surveying the Stars
    4. 19.3 Variable Stars: One Key to Cosmic Distances
    5. 19.4 The H–R Diagram and Cosmic Distances
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  21. 20 Between the Stars: Gas and Dust in Space
    1. Thinking Ahead
    2. 20.1 The Interstellar Medium
    3. 20.2 Interstellar Gas
    4. 20.3 Cosmic Dust
    5. 20.4 Cosmic Rays
    6. 20.5 The Life Cycle of Cosmic Material
    7. 20.6 Interstellar Matter around the Sun
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  22. 21 The Birth of Stars and the Discovery of Planets outside the Solar System
    1. Thinking Ahead
    2. 21.1 Star Formation
    3. 21.2 The H–R Diagram and the Study of Stellar Evolution
    4. 21.3 Evidence That Planets Form around Other Stars
    5. 21.4 Planets beyond the Solar System: Search and Discovery
    6. 21.5 Exoplanets Everywhere: What We Are Learning
    7. 21.6 New Perspectives on Planet Formation
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  23. 22 Stars from Adolescence to Old Age
    1. Thinking Ahead
    2. 22.1 Evolution from the Main Sequence to Red Giants
    3. 22.2 Star Clusters
    4. 22.3 Checking Out the Theory
    5. 22.4 Further Evolution of Stars
    6. 22.5 The Evolution of More Massive Stars
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  24. 23 The Death of Stars
    1. Thinking Ahead
    2. 23.1 The Death of Low-Mass Stars
    3. 23.2 Evolution of Massive Stars: An Explosive Finish
    4. 23.3 Supernova Observations
    5. 23.4 Pulsars and the Discovery of Neutron Stars
    6. 23.5 The Evolution of Binary Star Systems
    7. 23.6 The Mystery of the Gamma-Ray Bursts
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  25. 24 Black Holes and Curved Spacetime
    1. Thinking Ahead
    2. 24.1 Introducing General Relativity
    3. 24.2 Spacetime and Gravity
    4. 24.3 Tests of General Relativity
    5. 24.4 Time in General Relativity
    6. 24.5 Black Holes
    7. 24.6 Evidence for Black Holes
    8. 24.7 Gravitational Wave Astronomy
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  26. 25 The Milky Way Galaxy
    1. Thinking Ahead
    2. 25.1 The Architecture of the Galaxy
    3. 25.2 Spiral Structure
    4. 25.3 The Mass of the Galaxy
    5. 25.4 The Center of the Galaxy
    6. 25.5 Stellar Populations in the Galaxy
    7. 25.6 The Formation of the Galaxy
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  27. 26 Galaxies
    1. Thinking Ahead
    2. 26.1 The Discovery of Galaxies
    3. 26.2 Types of Galaxies
    4. 26.3 Properties of Galaxies
    5. 26.4 The Extragalactic Distance Scale
    6. 26.5 The Expanding Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  28. 27 Active Galaxies, Quasars, and Supermassive Black Holes
    1. Thinking Ahead
    2. 27.1 Quasars
    3. 27.2 Supermassive Black Holes: What Quasars Really Are
    4. 27.3 Quasars as Probes of Evolution in the Universe
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  29. 28 The Evolution and Distribution of Galaxies
    1. Thinking Ahead
    2. 28.1 Observations of Distant Galaxies
    3. 28.2 Galaxy Mergers and Active Galactic Nuclei
    4. 28.3 The Distribution of Galaxies in Space
    5. 28.4 The Challenge of Dark Matter
    6. 28.5 The Formation and Evolution of Galaxies and Structure in the Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  30. 29 The Big Bang
    1. Thinking Ahead
    2. 29.1 The Age of the Universe
    3. 29.2 A Model of the Universe
    4. 29.3 The Beginning of the Universe
    5. 29.4 The Cosmic Microwave Background
    6. 29.5 What Is the Universe Really Made Of?
    7. 29.6 The Inflationary Universe
    8. 29.7 The Anthropic Principle
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  31. 30 Life in the Universe
    1. Thinking Ahead
    2. 30.1 The Cosmic Context for Life
    3. 30.2 Astrobiology
    4. 30.3 Searching for Life beyond Earth
    5. 30.4 The Search for Extraterrestrial Intelligence
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  32. A | How to Study for an Introductory Astronomy Class
  33. B | Astronomy Websites, Images, and Apps
  34. C | Scientific Notation
  35. D | Units Used in Science
  36. E | Some Useful Constants for Astronomy
  37. F | Physical and Orbital Data for the Planets
  38. G | Selected Moons of the Planets
  39. H | Future Total Eclipses
  40. I | The Nearest Stars, Brown Dwarfs, and White Dwarfs
  41. J | The Brightest Twenty Stars
  42. K | The Chemical Elements
  43. L | The Constellations
  44. M | Star Chart and Sky Event Resources
  45. Index

Figuring for Yourself

32.

In Appendix J, how much more luminous is the most luminous of the stars than the least luminous?

For Exercise 17.33 through Exercise 17.38, use the equations relating magnitude and apparent brightness given in the section on the magnitude scale in The Brightness of Stars and Example 17.1.

33.

Verify that if two stars have a difference of five magnitudes, this corresponds to a factor of 100 in the ratio (b2b1);(b2b1); that 2.5 magnitudes corresponds to a factor of 10; and that 0.75 magnitudes corresponds to a factor of 2.

34.

As seen from Earth, the Sun has an apparent magnitude of about −26.7. What is the apparent magnitude of the Sun as seen from Saturn, about 10 AU away? (Remember that one AU is the distance from Earth to the Sun and that the brightness decreases as the inverse square of the distance.) Would the Sun still be the brightest star in the sky?

35.

An astronomer is investigating a faint star that has recently been discovered in very sensitive surveys of the sky. The star has a magnitude of 16. How much less bright is it than Antares, a star with magnitude roughly equal to 1?

36.

The center of a faint but active galaxy has magnitude 26. How much less bright does it look than the very faintest star that our eyes can see, roughly magnitude 6?

37.

You have enough information from this chapter to estimate the distance to Alpha Centauri, the second nearest star, which has an apparent magnitude of 0. Since it is a G2 star, like the Sun, assume it has the same luminosity as the Sun and the difference in magnitudes is a result only of the difference in distance. Estimate how far away Alpha Centauri is. Describe the necessary steps in words and then do the calculation. (As we will learn in the Celestial Distances chapter, this method—namely, assuming that stars with identical spectral types emit the same amount of energy—is actually used to estimate distances to stars.) If you assume the distance to the Sun is in AU, your answer will come out in AU.

38.

Do the previous problem again, this time using the information that the Sun is 150,000,000 km away. You will get a very large number of km as your answer. To get a better feeling for how the distances compare, try calculating the time it takes light at a speed of 299,338 km/s to travel from the Sun to Earth and from Alpha Centauri to Earth. For Alpha Centauri, figure out how long the trip will take in years as well as in seconds.

39.

Star A and Star B have different apparent brightnesses but identical luminosities. If Star A is 20 light-years away from Earth and Star B is 40 light-years away from Earth, which star appears brighter and by what factor?

40.

Star A and Star B have different apparent brightnesses but identical luminosities. Star A is 10 light-years away from Earth and appears 36 times brighter than Star B. How far away is Star B?

41.

The star Sirius A has an apparent magnitude of −1.5. Sirius A has a dim companion, Sirius B, which is 10,000 times less bright than Sirius A. What is the apparent magnitude of Sirius B? Can Sirius B be seen with the naked eye?

42.

Our Sun, a type G star, has a surface temperature of 5800 K. We know, therefore, that it is cooler than a type O star and hotter than a type M star. Given what you learned about the temperature ranges of these types of stars, how many times hotter than our Sun is the hottest type O star? How many times cooler than our Sun is the coolest type M star?

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