Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 19, Problem 46Q
To determine

(a)

Escape speed from the present-day Sun.

Expert Solution
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Answer to Problem 46Q

The escape speed from the present-day surface of the Sun is approximately 619kms-1.

Explanation of Solution

Given:

(Gravitational Constant)=6.673×10-11m3kg-1s-2

Mass of the Sun(MSun)=2×1030kg

RadiusoftheSun=696,000×103m

Let Vesc1 be the escape speed from the present-day surface of the Sun.

Formula used:

Escape speed is given by the formula

Vesc=2GMSunR

Where, V is the escape velocity, G is the gravitational constant, M is the sun and R is the radius.

Calculation:

Vesc1=2×6.673×10-11m3kg-1s-2×2×1030kg696,000×103m=619,278.40ms-1619kms-1

Conclusion:

The escape speed from the present-day surface of the Sun is approximately 619kms-1.

To determine

(b)

Escape speed from the Sun after it became a red giant.

Expert Solution
Check Mark

Answer to Problem 46Q

The escape speed from the Sun after it became a red giant is approximately 61.9kms1.

Explanation of Solution

Given:

(Gravitational Constant)=6.673×10-11m3kg-1s-2

Mass of the Sun(MSun)=2×1030kg

RadiusoftheSun=696,000×103m

Let Vesc2 be the escape speed from the surface of the Sun after it became a red giant.

Formula used:

Escape speed is given by the formula,

Vesc=2GMSunR

Calculation:

Substitute the values:

Vesc2=2×6.673×10-11m3kg-1s-2×2×1030kg696,000×105m=61,927.84ms161.9kms-1

Conclusion:

The escape speed from the present-day surface of the Sun is approximately 61.9kms-1.

To determine

(c)

The reason for mass of a red giant star loses easily rather than a main-sequence star.

Expert Solution
Check Mark

Answer to Problem 46Q

The escape speed from a red giant star is much lower than the escape speed from a main-sequence star.

Explanation of Solution

Introduction:

According to the calculations, the escape speed from the Sun at present-day is approximately 619kms-1 and the escape speed from the Sun after it became a red giant is approximately 61.9kms-1. Escape speed determines the lowest speed that a mass required in order to permanently escape the gravitational field of a certain planet or a celestial body.

The results imply that after the Sun became a red giant, the speed that a mass requires to escape into the outer space is approximately10 times lower than the speed required to escape the present day Sun, which is still a main-sequence star. Hence, more mass from a red giant star would escape from it to the outer space than a main-sequence star.

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Students have asked these similar questions
One way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?
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
When the Sun becomes a red giant, it's luminosity will be 2000 times its current value. The solar flux at Earth will also increase by a factor of 2000. Neglecting the greenhouse effect, the surface temperature of the earth is determined by thermal equilibrium: the flux of radiation absorbed equals the flux of radiation emitted. This means the Earth's surface flux must also increase by a factor of 2000.  If the current average surface temperature is 58 degrees F, what will the average surface temperature be when the Sun is a red giant.  Express your answer in units of degrees Fahrenheit.  [Hint: Recall that the Stefan-Boltzmann law says that the flux F emitted by a blackbody is related to its surface temperature T (measured in Kelvins) is F=σT4  . Use this law in the form of a ratio, expressing T in Kelvins. Then convert back to Fahrenheit.]
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