Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 16, Problem 36Q
To determine
The speed of spicules in
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Question A2
a)
Calculate the mass loss rate of the Sun M due to the solar wind flow. Assume average
properties of the solar wind of number density 6 protons cm³, and a flow speed of 450 km
s-1. Express your answer in units of both kg per year, and solar masses per year.
b) Suppose the solar wind flow is perfectly radial. Calculate the expected rate of change of
solar rotation frequency dw at the present time, based on conservation of angular momen-
tum. Give your answer in units of rad s-1 y-1 (i.e., radians per second per year) and also
in terms of fractional change per year, i.e., 1 du.
w dt'
Use a current solar rotation period of P = 25.38 days to calculate the current angular
frequency of rotation w. The moment of inertia of a uniform sphere is MR². You can
assume that the radius of the Sun is approximately constant, and the change in its moment
of inertia due to the solar wind is only due to the mass loss.
Page 3
c) By observing the rotation period of stars similar to the…
a.Calculate the mass loss rate of the Sun M˙ due to the solar wind flow. Assume averageproperties of the solar wind of number density 6 protons cm−3, and a flow speed of 450 kms−1. Express your answer in units of both kg per year, and solar masses per year.
b.Suppose the solar wind flow is perfectly radial. Calculate the expected rate of change ofsolar rotation frequency dω/dt at the present time, based on conservation of angular momentum. Give your answer in units of rad s−1 y−1(i.e., radians per second per year) and alsoin terms of fractional change per year, i.e., 1/ωdω/dt .Use a current solar rotation period of P = 25.38 days to calculate the current angularfrequency of rotation ω. The moment of inertia of a uniform sphere is 2/5 MR2. You canassume that the radius of the Sun is approximately constant, and the change in its momentof inertia due to the solar wind is only due to the mass loss.
c.By observing the rotation period of stars similar to the Sun, it is inferred that their…
c) 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.
Chapter 16 Solutions
Universe
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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.arrow_forwardIf astronauts attempt interplanetary space travel, then heavy shielding will be required to protect them from solar radiation. If massive amounts of either fuel or water are carried, then the spacecraft must be very large. Therefore, if heavy shielding is required to protect the astronauts from solar radiation only if massive amounts of fuel are carried, then if astronauts attempt interplanetary space travel, then the spacecraft must be very large. (A = Astronauts attempt interplanetary space travel. H = Heavy shielding will be required to protect astronauts from solar radiation. F = Massive amounts of fuel are carried. W = Massive amounts of water are carried. L = The spacecraft must be very large.) AFHLW ∼•⊃∨≡(){}[]///arrow_forwardd) Calculate what temperature a thermal kinetic energy of 2 keV corresponds to, and compare this with the temperature in the core of the Sun.arrow_forward
- Like most spacecraft returning from orbit, the Apollo command module entered the atmosphere at 7.8 km/s. In front of the capsule was a shock front, the leading edge of the shock front we call a bow shock. Let’s consider the conditions as it passes an altitude of 40,000 feet, at 461 miles per hour. 1a) What are the density, pressure, and temperature behind the shock front? 1b) In the frame of the shock, what is the velocity at which the gas approaches the shock? What is the velocity with which the gas leaves the shock? 1c) In the frame fixed on the Earth, what is the velocity of the post- shock gas?arrow_forwardIf the emitted infrared radiation from Pluto, has a wavelength of maximum intensity at 75,000 nm, what is the temperature of Pluto assuming it follows Wien’s law?arrow_forwardthe number of air density in a childs balloon is roughly the same as sea level air, 10^19 particles/ cm ^3. if the balloon is now 18 cm in diameter, to what diameter in km would it need to expand to make the gas have the same density as ISM, about 1 particle/cm^3arrow_forward
- One of the methods for estimating the temperature at the center of the sun is based on the ideal gas equation. If the center is assumed to be a mixture of gases whose average molar mass is 2.04 g/mol, and the density and pressure are 1.14 g/cm3 and 2.01 x 109 atm, respectively, calculate the temperature.arrow_forwardfrom d to f please thank youarrow_forwardConsidering your answer to the above question, how does this timescale for the Sun's evaporation by the solar wind compare to the age of the Universe? O The solar wind evaporation time is much longer than the age of the Universe O The solar wind evaporation time is much shorter than the age of the Universe. O The solar wind evaporation time is close to the age of the Universe (ie, within a few billion yearsarrow_forward
- Calculate the ratio of the energy generation rate for the pp chain to the energy generation rate for the CNO cycle given the present conditions of the Sun: T=1.5696 x 107 K, p=1.527 x 105 Kg/m3, X=0.3397 and XCNO=0.0141.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_forwardExplain why some solar shock waves are thought to die out at heliocentric distances of 3-5 R. How can we observe this?arrow_forward
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