The Cosmic Perspective (9th Edition)
The Cosmic Perspective (9th Edition)
9th Edition
ISBN: 9780134874364
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter 16, Problem 56EAP

Internal Temperature of the Sun. The Sun is essentially a gas cloud in which the forces of pressure and gravity balance each other. We can therefore use the equation in Mathematical Insight 16.1 to estimate the interior temperature of the Sun from its mass and particle density.

  1. What is the average number density of particles within the Sun, given that the average mass per particle is about  10 24  gram ? (Hint: The volume of a sphere of radius is equal to  4 π r 3 / 3 .)
  2. What is the approximate temperature necessary for gas pressure to balance gravity within the Sun, given the average particle density from part a?
  3. How does your estimate compare with the internal core temperature of the Sun?

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The radius of the Sun is 7x10⁸ m and its mass is 2x10³⁰kg.What is the density of the Sun (density = mass/volume)? The density of water is 1000 kg/m³. What is the ratio of the Sun's density to that of water?
If a sunspot has a temperature of 4,270 K and the average solar photosphere has a temperature of 5,780 K, how many times more energy is emitted in 1 second from a square meter of the photosphere compared to a square meter of the sunspot? (Hint: Use the Stefan-Boltzmann law,  E = σT4 (J/s/m2)  where E is the energy, σ is a proportionality constant equal to 5.67 ✕ 10−8 J/s/m2/K4, and T is the temperature in kelvins.)
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