Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Question
Chapter 19, Problem 48Q
To determine
The total mass of Hydrogen that the Sun will convert into Helium during its main-sequence lifetime.
The fraction in which this can be represented.
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Students have asked these similar questions
For a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W).
(Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)
Most stars (Main sequence) generate light
through the same mechanism. Because of this,
there is an empirical relation between their
mass, M, and their Luminosity, L. This relation
could be written in the form
L/Lsun = (M/Msun,
This relation is shown in the log-log diagram
below. Find the value of a and round it to the
nearest integer.
10
104
102
10-2
10-4
0.1
1.0
2.0
0.2
0.5
5.0
10.0
20.0
Mam (solar masses)
Luminosty (solar units)
Using solar units, we find that a star has 4 times the luminosity of the Sun, a mass 1.25 times the mass of the Sun, and a surface temperature of 4090 K (take the Sun's surface temperature to be 5784 K for the sake of this problem). This means the star has a radius of.................... solar radii and is a .................... star (use the classification).
Chapter 19 Solutions
Universe: Stars And Galaxies
Ch. 19 - Prob. 1QCh. 19 - Prob. 2QCh. 19 - Prob. 3QCh. 19 - Prob. 4QCh. 19 - Prob. 5QCh. 19 - Prob. 6QCh. 19 - Prob. 7QCh. 19 - Prob. 8QCh. 19 - Prob. 9QCh. 19 - Prob. 10Q
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- = 2000 K and a radius of R, A young recently formed planet has a surface temperature T Jupiter radii (where Jupiter's radius is 7 x 107 m). Calculate the luminosity of the planet and 2 determine the ratio of the planet's luminosity to that of the Sun.arrow_forwardThe mass-luminosity relation describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 4 M⊙ would have a luminosity of ______ L⊙. If a star has a radius 1/2 that of the Sun and a temperature 4 that of the Sun, how many times higher is the star's luminosity than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125) If a star has a radius 2 times larger than the Sun's and a luminosity 1/4th that of the Sun, how many times higher is the star's temperature than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125) If a star has a surface temperature 2 times lower than the Sun's and a luminosity the same as the Sun, how many times larger is the star than the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)arrow_forwardLet's calculate how much mass will be lost by the Sun 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 that it is only the core of the star that is hot enough for fusion). During nuclear fusion, the Sun converts about 0.7% of the core hydrogen mass into energy. The total mass of the Sun is 2 × 1030 kg. How many kilograms of mass will be converted to energy during the main sequence stage of the Sun's life? What is the ratio of this lost mass to the Earth's mass (6 × 1024 kg)? In other words, how many Earths of mass will be turned into energy?arrow_forward
- This star has a mass of 3.3 MSun. What is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.arrow_forwardA star has a period of P = 37 days. It has a radius of 5.7 times the radius of the sun. Calculate it's equatorial speed Vrot. Answer: Okm/s Om/s Check A star has a radius of 5.7 times the radius of the sun and a mass of 18 times the mass of the sun. It rotates at 0.7 of the critical speed W, the speed at which it's surface at the equator is actually in orbit. Recall Vrot is calculated at the equator and W= Vrot/Vorb Calculate it's period P. Answer: Odays Ohours Oseconds Checkarrow_forward12: A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) Answer: 36.854 13:This star has a mass of 3.3 MSun. what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr. Please answer question 13 thank you.arrow_forward
- Jupiter radiates more energy than it receives from the Sun by 8.7 x10-10 LO. Jupiter's radius is 7.1 x109 cm and its mass is 1.9 ×1030 g. Compute its dynamical and thermal timescales. (b) Can we assume that Jupiter is in hydrostatic equilibrium? (c) Could gravitational contraction have powered Jupiter's luminosity for its entire 4.5 Gyr lifetime? (d) Use conservation of energy to estimate the rate at which Jupiter's radius is shrinking to power this radiation. You may ignore the factor of order unity that arises from Jupiter's unknown density distribution.arrow_forwardA 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: 3679arrow_forwardQUESTION 16 Use the figure shown below to complete the following statement: A low-mass protostar (0.5 to 8M the mass compared to our sun) remains roughly constant in decreases in until it makes a turn towards the main sequence, as it follows its evolutionary track. Protostars of different masses follow diferent paths on their way to the main sequence. 107 Luminosity (L) 10 105 10 107 10² 101 1 10-1 10-2 10-3 Spectral type 0.01 R 0.001 Re 60 M MAIN SEQUENCE 40,000 30,000 20 Mau 10 Mgun 5 Mun 0.1 Run Ren radius; temperature luminosity; radius 3 Min. 05 BO temperature; luminosity Oluminosity: temperature radius: luminosity 1 M 10,000 6000 Surlace temperature (K) 1,000 Rs 2 M STAR L 0.8 M B5 AO FOGO КБ МБ -10 +10 3000 Absolute visual magnitude andarrow_forward
- Let us imagine that the spectrum of a star is collected and we find the absorption line of Hydrogen-Alpha (the deepest absorption line of hydrogen in the visible part of the electromagnetic spectrum) to be observed at 656.5 nm instead of 656.3 nm as measured in a lab here on Earth. What is the velocity of this star in m/s? (Hint: speed of light is 3*10^8 m/s; leave the units off of your answer)arrow_forward1 Solar constant, Sun, and the 10 pc distance! The luminosity of Sun is + 4- 1026 W - 4- 1033ergs-1, The Sun is located at a distance of m from the Earth. The Earth receives a radiant flux (above its atmosphere) of F = 1365W m- 2, also known as the solar constant. What would have been the Solar contact if the Sun was at a distance of 10 pc ? 1AU 1 1.5-+ 1011arrow_forwardIs the Sun on the zero-age main sequence? Explain your answer.arrow_forward
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