Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
bartleby

Concept explainers

Question
Book Icon
Chapter 19, Problem 50Q
To determine

Thetime period for which the Sun will be a red giant.

Expert Solution & Answer
Check Mark

Answer to Problem 50Q

The Sun will be a red giant for 35millionyears.

Explanation of Solution

Given:

The luminosity of the Sun if it becomes a red giant is, L=2000L.

Formula Used:

The luminosity of the star is given by,

L=Et …… (I)

Here, E is the total energy that the star emits and t is the time.

Energy is emitted by the star by converting a fraction of total mass of the star and is given by,

E=fMc2

Here, f is the fraction of the total mass M and c is the speed of light.

Thus, the luminosity of the star is given by,

L=fMc2tLMt

The ratio of the luminosity of a star for two different cases is given by,

LL=( M t )( M t )=MMtt

Calculations:

Consider figure 19-9 of the book “Universe: Stars and Galaxies”; the main sequence lifetime of the Sun is 1.2×1010years.

The Sun consumes hydrogen at the rate of 600milliontons/second.

Therefore, the mass of hydrogen consumed by the Sun in 1.2×1010years is calculated as,

M1=(Rateofconsumption)(time)=(600milliontons/second)(1.2× 10 10years)={( 600 milliontons/ second × 10 6 tons 1milliontons × 10 3 kg 1ton )( 1.2× 10 10 years× 365days 1year × 24hr 1day × 60min 1hr × 60sec 1min )}=(6× 10 11kg/sec)(3.78× 10 17sec)

Solve further,

M1=2.27×1029kg

The standard value of the mass of the Sun is, M=1.99×1030kg.

Assume the amount of hydrogen in the Sun at present is 74% by mass of the Sun. Therefore, the mass of the amount of hydrogen in the Sun at present is calculated as,

Mp=(74%)M=( 74 100)(1.99× 10 30kg)=1.47×1030kg

The Sun is considered to be 5billionyears old. Therefore, the amount of hydrogen consumed by the Sun in 5billionyears is calculated as,

M2=(Rateofconsumption)(time)=(600milliontons/second)(5billionyears)={( 600 milliontons/ second × 10 6 tons 1milliontons × 10 3 kg 1ton )( 5billionyears× 10 9 years 1billionyears × 365days 1year × 24hr 1day × 60min 1hr × 60sec 1min )}=(6× 10 11kg/sec)(1.58× 10 17sec)

Solve further,

M2=9.48×1028kg

The initial amount of hydrogen present in the Sun is calculated as,

Mi=M2+Mp=9.48×1028kg+1.47×1030kg=1.56×1030kg

The mass of hydrogen left after the main sequence lifetime of the Sun is calculated as,

Mr=MiM1=1.56×1030kg2.27×1029kg=1.33×1030kg

The time period for which the Sun will be a red giant is calculated as,

tt=MMLLt1.2× 10 10years=1.33× 10 30kg2.27× 10 29kgL2000Lt=(35.15× 106years× 1millionyears 10 6 years)35millionyears

Conclusion:

Thus, for 35millionyears the Sun will be a red giant.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
We will take a moment to compare how brightly a white dwarf star shines compared to a red giant star. For the sake of this probler, lets assume a white dwarf has a temperature around 10,000 K and a red giant has a temperature around 5,000 K. As for their stellar radii, the white dwarf has a radius about 1/100th that of the Sun and a red giant has a radius around 100 times larger than the Sun. With this in mind, how does the luminosity of a red giant star compare to that of a white dwarf (Hint: do not try to enter all of these numbers into the luminosity equation fit won't go well); instead, remember that you are only interested in the ratio between the two, so all common units and components can be divided out)? Please enter your answer in terms of the luminosity of the red giant divided by the luminosity of the white dwarf and round to two significant figures. Also, please avoid using commas in your answer. A Moving to another question will save this response. Question 1 of 32 >» 31…
We will take a moment to compare how brightly a white dwarf star shines compared to a red giant star. For the sake of this problem, let's assume a white dwarf has a temperature around 10,000 K and a red giant has a temperature around 5,000 K. As for their stellar radiatin, the white dwarf has a radius about 1/100th that of the Sun, and a red giant has a radius around 100 times larger than the Sun. With this in mind, how does the luminosity of a red giant star compare to that of a white dwarf (Hint: do not try to enter all of these numbers into the luminosity equation {it won't go well}; instead, remember that you are only interested in the ratio between the two, so all common units and components can be divided out)? Please enter your answer in terms of the luminosity of the red giant divided by the luminosity of the white dwarf and round to two significant figures. Also, please avoid using commas in your answer.
A red giant star might have radius = 104 times the solar radius, and luminosity = 1730 times solar luminosity. Use the data given below to calculate the temperature at the surface of the red giant star. Data: solar radius R = 7 x 108 meters solar luminosity L = 4 x 1026 watts Stefan-Boltzmann constant a = 5.67 x 10-8 W m² K-4 (in K) A: 1226 OB: 1434 OC: 1678 OD: 1963 OE: 2297 OF: 2688 OG: 3145 OH: 3679
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Astronomy
Physics
ISBN:9781938168284
Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher:OpenStax
Text book image
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:9781337399920
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
Text book image
Stars and Galaxies (MindTap Course List)
Physics
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Cengage Learning
Text book image
Stars and Galaxies
Physics
ISBN:9781305120785
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
Text book image
The Solar System
Physics
ISBN:9781337672252
Author:The Solar System
Publisher:Cengage
Text book image
Horizons: Exploring the Universe (MindTap Course ...
Physics
ISBN:9781305960961
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning