Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 18, Problem 51E
If Betelgeuse had a mass that was 25 times that of the Sun, how would its average density compare to that of the Sun? Use the definition of
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Students have asked these similar questions
In the model shown in the table below, what fraction of the Sun's mass is hotter than 5,000,000 K?
R/R SunT (106 K) Density (g/cm³)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.006
0.60
1.2
2.3
3.1
4.9
5.1
6.9
9.3
13.1
15.7
0.00
0.009
0.035
0.12
0.40
1.3
4.1
13
36
89
150
M/M Sun L/L Sun
1.00
0.999
0.996
0.990
0.97
0.92
0.82
0.63
0.34
0.073
0.000
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.91
0.40
0.00
Assume that Hydrogen comprises 79% of the Sun's mass. How much mass is this? 1.57e+30 kg
Only about 11% of the initial Hydrogen in the Sun is in the core where it is hot enough to burn. What was the total mass of the inital H in the core of the Sun?
Hint: Use the answer above and the percent in the core to determine the total mass.
Using the results from above, how much total energy is available to the Sun via nuclear fusion over its lifetime? (HINT: only 0.71% of the total mass of the available H in the core is converted into energy)
Hint: E = m c^2
The radius of the Sun is 7x10⁸ m and its mass is 2x10³⁰kg.What is the density of the Sun
(density = mass/volume)? The density of water is 1000 kg/m³. What is the ratio of the Sun's density to that of water?
Chapter 18 Solutions
Astronomy
Ch. 18 - How does the mass of the Sun compare with that of...Ch. 18 - Name and describe the three types of binary...Ch. 18 - Describe two ways of determining the diameter of a...Ch. 18 - What are the largest- and smallest-known values of...Ch. 18 - You are able to take spectra of both stars in an...Ch. 18 - Sketch an HR diagram. Label the axes. Show where...Ch. 18 - Describe what a typical star in the Galaxy would...Ch. 18 - How do we distinguish stars from brown dwarfs? How...Ch. 18 - Describe how the mass, luminosity, surface...Ch. 18 - One method to measure the diameter of a star is to...
Ch. 18 - We discussed in the chapter that about half of...Ch. 18 - Is the Sun an average star? Why or why not?Ch. 18 - Suppose you want to determine the average...Ch. 18 - Why do most known visual binaries have relatively...Ch. 18 - Figure 18.11 shows the light curve of a...Ch. 18 - There are fewer eclipsing binaries than...Ch. 18 - Within 50 light-years of the Sun, visual binaries...Ch. 18 - Which is easier to observe at large distances-a...Ch. 18 - The eclipsing binary Algol drops from maximum to...Ch. 18 - Review this spectral data for five stars. Which is...Ch. 18 - Which changes by the largest factor along the main...Ch. 18 - Suppose you want to search for brown dwarfs using...Ch. 18 - An astronomer discovers a type-M star with a large...Ch. 18 - Approximately 6000 stars are bright enough to be...Ch. 18 - Use the data in Appendix J to plot an HR diagram...Ch. 18 - Use the diagram you have drawn for Exercise 18.25...Ch. 18 - Use the data in Appendix I to plot an HR diagram...Ch. 18 - If a visual binary system were to have two...Ch. 18 - Two stars are in a visual binary star system that...Ch. 18 - Describe the spectra for a spectroscopic binary...Ch. 18 - Figure 18.7 shows the velocity of two stars in a...Ch. 18 - You go out stargazing one night, and someone asks...Ch. 18 - If you were to compare three stars with the same...Ch. 18 - Are supergiant stars also extremely massive?...Ch. 18 - Consider the following data on four stars: Which...Ch. 18 - If two stars are in a binary system with a...Ch. 18 - It is possible that stars as much as 200 times the...Ch. 18 - The lowest mass for a true star is 1/12 the mass...Ch. 18 - Spectral types are an indicator of temperature....Ch. 18 - We can estimate the masses of most of the stars in...Ch. 18 - In Diameters of Stars, the relative diameters of...Ch. 18 - Now calculate the radius of Sirius’ white dwarf...Ch. 18 - How does this radius of Sirius B compare with that...Ch. 18 - From the previous calculations and the results...Ch. 18 - How much would you weigh if you were suddenly...Ch. 18 - The star Betelgeuse has a temperature of 3400 K...Ch. 18 - Using the information provided in Table 18.1, what...Ch. 18 - Confirm that the angular diameter of the Sun of...Ch. 18 - An eclipsing binary star system is observed with...Ch. 18 - If a 100 solar mass star were to have a luminosity...Ch. 18 - If Betelgeuse had a mass that was 25 times that of...
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- If the sun expanded to a radius 5000 times its present radius, what would its average density be (in g/cm3?)arrow_forwardIf the radius of the sun is 7.001×105 km, what is the average density of the sun in units of grams per cubic centimeter? The volume of a sphere is (4/3)π r3. The sun is a sphere with an estimated mass of 2.00×1030 kg. What exactly is the conversion process for this?arrow_forwardWhich aspects of the Sun’s activity cycle have a period of about 11 years? Which vary during intervals of about 22 years?arrow_forward
- Now suppose that all of the hydrogen atoms in the Sun were converted into helium. How much total energy would be produced? (To calculate the answer, you will have to estimate how many hydrogen atoms are in the Sun. This will give you good practice with scientific notation, since the numbers involved are very large! See Appendix C for a review of scientific notation.)arrow_forwardShow that the statement that 92% of the Sun’s atoms are hydrogen is consistent with the statement that 73% of the Sun’s mass is made up of hydrogen, as found in Table 15.2. (Hint: Make the simplifying assumption, which is nearly correct, that the Sun is made up entirely of hydrogen and helium.)arrow_forwardWhy do you suppose so great a fraction of the Sun’s energy comes from its central regions? Within what fraction of the Sun’s radius does practically all of the Sun’s luminosity originate (see Figure 16.16)? Within what radius of the Sun has its original hydrogen been partially used up? Discuss what relationship the answers to these questions bear to one another. Figure 16.16 shows how the temperature, density, rate of energy generation, and composition vary from the center of the Sun to its surface.arrow_forward
- The Sun’s luminosity (or power) is 4 x 1026 Watts (=J/s). How many kilograms of hydrogen must be fused every second to maintain this luminosity? (hint: work backwards from the energy per second to the mass released to the amount of hydrogen required, using the results from the previous question.) The Sun’s mass is ~2x1030 kg. If 10% of this is Hydrogen available in the core, how long will the Sun be able to continue fusing hydrogen at this rate? This is considered the Sun's "lifetime". If the Sun is 4.6 billion years old (and assuming it's power output is constant), how many years does it have left?arrow_forwardThe average density of the sun is 1. 4 g/cm3 What do you expect the density to be at 0.25 of Rsun? 2) The average density of the sun is 1.4 g/cm3. The following resource claims that the sun's core has a density of 150 g/cm3 and a radius of 25% of the sun's radius. Assume the core has a constant density and calculate it's mass. What fraction of the sun's mass is in the core according to that resource?arrow_forwardUse Wein's law to determine the wavelength corresponding to the peak of the black body curve (a) in the core of the Sun, where the temperature is 10^7, (b) in the solar convection zone (10^5), and (c) just below the solar photosphere (10^4K). What form (visible, infrared, X-ray, etc.) does radiation take in each case?arrow_forward
- Can you solve the problem, according to the information provided?arrow_forwardif the sun expanded to a radius 200 times its present radius what would its average density ne in (g/cm^3?)arrow_forwardIf the temperature at the centre of the sun is 15,000,000 K and the temperature of the photosphere is 5,800 K, what is the ratio of the temperature at the centre of the Sun compared to the photosphere? Express your final answer in the fully factorised form x : 1, where x is a number that you should determine to an appropriate number of significant figures and write it using scientific notation.arrow_forward
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