UNIVERSE (LOOSELEAF):STARS+GALAXIES
6th Edition
ISBN: 9781319115043
Author: Freedman
Publisher: MAC HIGHER
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Chapter 16, Problem 22Q
To determine
The density of material within
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Assume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius.Assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of 6.2 *1011 kg/s, how long will it be before the hydrogen is entirely consumed? The Sun’s mass is 2.0 * 1030 kg.
If 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?
a) At solar maximum sunspots might cover up to 0.4% of the total area of the Sun. If the sunspots have a temperature of 3800 K and the surrounding photosphere has a temperature of 6000 K, calculate the fractional change (as a percentage) in the luminosity due to the presence of the sunspots.
b) A star of the same stellar class as the Sun is observed regularly over many years, and a time series of its bolometric apparent magnitude is collected. What would be the signal in this time series which indicated that the star had a magnetic dynamo similar to the Sun? Briefly describe two or three possible sources of other signals which could confuse the interpretation of the data.
Chapter 16 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
Ch. 16 - Prob. 1QCh. 16 - Prob. 2QCh. 16 - Prob. 3QCh. 16 - Prob. 4QCh. 16 - Prob. 5QCh. 16 - Prob. 6QCh. 16 - Prob. 7QCh. 16 - Prob. 8QCh. 16 - Prob. 9QCh. 16 - Prob. 10Q
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- Show 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_forwardUse the provided equation of hydrostatic equilibrium to find a very rough estimate of the central pressure in the Sun.arrow_forwardIf the nuclear fusion reaction of converting 4 H → He occurs at an efficiency of 0.7%, and that mass is converted into energy according to the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2) in years if the luminosity of the Sun is 3.83 × 1033 ergs s−1. Assume the Sun’s core (10% of the total mass) is converted from H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g.arrow_forward
- (a) Assuming the surface temperature of the sun to be 5700°K, use Stefan's law, (1-2), to determine the rest mass lost per second to radiation by the sun. Take the sun's diameter to be 1.4 x 109 m. (b) What fraction of the sun's rest mass is lost each year from electromagnetic radiation? Take the sun's rest mass to be 2.0 x 1030 kg.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_forwardAssume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius.Assume further that the composition of the core is 31% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of 6.33E11 kg/s, how long, in years, will it be before the hydrogen is entirely consumed? Mass of the Sun is 2.0x1030 kg.arrow_forward
- = 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_forwardc) Derive the Schwarzschild criterion for the onset of convection in an ideal gas, namely d ln T d ln P 7-1 Y Explain all steps in your derivation, and justify any assumptions that you make. d) In a region of convective instability near the surface of a solar-type star of total mass M, the temperature and pressure are related approximately by the expression P KT5/2. Show that the temperature gradient for an ideal gas in hydrostatic = equilibrium in this convection zone is given by dT dr 2Gm(r)μ 5Rr² Further, assuming that the mass in the convection zone is small compared to M, show that at a depth h measured from the top of the convection zone, the temperature is approximately given by T = Ts + 2GMμ -h₂ 5RR² when his small compared to R, and Ts is the temperature at the top of the convection zone.arrow_forwardIf the nuclear fusion reaction of converting 4 H → He occurs at an efficiency of 0.7%, and that mass is converted into energy according to the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2) in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839°ø1033 erg. Assume the Sun’s core (10% of the total mass) is converted from H into He. The Sun’s mass is M⊙ = 1.9891 °ø 1033 g.arrow_forward
- The Sun is estimated to have about 5.00 billion years left in it’s “normal” (main sequence) lifetime. Assume the average “burn” rate that you computed in question #1, what % of the Sun’s current mass will have been converted at the end of it’s estimated 5.00 billion years of additional life? Actually, the Sun will lose more mass due to the solar wind, CMEs, the neutrio flux etc. the answer to number one was 3.683x10^14arrow_forward1) a) At what rate is the Sun's mass decreasing due to nuclear reactions Am/At? Use E=mc? and Lsun=3.839x1026 W and give your answer in Msun/year. b) And due to solar wind? Calculate the flow using v=500 km/s measured on Earth, n=7x106 particles/m³ and µ=1. c) Assuming that those 2 processes rates remain constant during the Sun's main-sequence life, would either mass loss process significantly affect the total mass of the Sun? Use that the Sun's lifetime in the main-sequence is ~ 1010 years.arrow_forwardThe sun has a radius of 6.959 × 108 m and a surface temperature of 5.81 x 10° K. When the sun radiates at a rate of 3.91 x 1026 W and is a perfect emitter. What is the rate of energy emitted per square meter? Stefan-Boltzmann constant is 5.67 x 10-8 J/s-m2 K4 a) 5.6 x 107 W/m2 b) 12.8 x 107 W/m2 c) 6.4 x 107 W/m2 25.6 x 107 W/m2 5.6 x 1017 W/m2arrow_forward
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