Contents
- Preface
1Science and the Universe: A Brief Tour
2Observing the Sky: The Birth of Astronomy
7Other Worlds: An Introduction to the Solar System
13Comets and Asteroids: Debris of the Solar System
14Cosmic Samples and the Origin of the Solar System
18The Stars: A Celestial Census
20Between the Stars: Gas and Dust in Space
21The Birth of Stars and the Discovery of Planets outside the Solar System
27Active Galaxies, Quasars, and Supermassive Black Holes
- AHow to Study for an Introductory Astronomy Class
- BAstronomy Websites, Images, and Apps
- CScientific Notation
- DUnits Used in Science
- ESome Useful Constants for Astronomy
- FPhysical and Orbital Data for the Planets
- GSelected Moons of the Planets
- HFuture Total Eclipses
- IThe Nearest Stars, Brown Dwarfs, and White Dwarfs
- JThe Brightest Twenty Stars
- KThe Chemical Elements
- LThe Constellations
- MStar Chart and Sky Event Resources
- Index
Figuring for Yourself
Figuring for Yourself
The text says a star does not change its mass very much during the course of its main-sequence lifetime. While it is on the main sequence, a star converts about 10% of the hydrogen initially present into helium (remember it’s only the core of the star that is hot enough for fusion). Look in earlier chapters to find out what percentage of the hydrogen mass involved in fusion is lost because it is converted to energy. By how much does the mass of the whole star change as a result of fusion? Were we correct to say that the mass of a star does not change significantly while it is on the main sequence?
The text explains that massive stars have shorter lifetimes than low-mass stars. Even though massive stars have more fuel to burn, they use it up faster than low-mass stars. You can check and see whether this statement is true. The lifetime of a star is directly proportional to the amount of mass (fuel) it contains and inversely proportional to the rate at which it uses up that fuel (i.e., to its luminosity). Since the lifetime of the Sun is about 1010 y, we have the following relationship:
where T is the lifetime of a main-sequence star, M is its mass measured in terms of the mass of the Sun, and L is its luminosity measured in terms of the Sun’s luminosity.
- Explain in words why this equation works.
- Use the data in Table 18.3 to calculate the ages of the main-sequence stars listed.
- Do low-mass stars have longer main-sequence lifetimes?
- Do you get the same answers as those in Table 22.1?
You can use the equation in Exercise 22.34 to estimate the approximate ages of the clusters in Figure 22.10, Figure 22.12, and Figure 22.13. Use the information in the figures to determine the luminosity of the most massive star still on the main sequence. Now use the data in Table 18.3 to estimate the mass of this star. Then calculate the age of the cluster. This method is similar to the procedure used by astronomers to obtain the ages of clusters, except that they use actual data and model calculations rather than simply making estimates from a drawing. How do your ages compare with the ages in the text?
You can estimate the age of the planetary nebula in image (c) in Figure 22.18. The diameter of the nebula is 600 times the diameter of our own solar system, or about 0.8 light-year. The gas is expanding away from the star at a rate of about 25 mi/s. Considering that distance = velocity time, calculate how long ago the gas left the star if its speed has been constant the whole time. Make sure you use consistent units for time, speed, and distance.
If star A has a core temperature T, and star B has a core temperature 3T, how does the rate of fusion of star A compare to the rate of fusion of star B?