Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 12: The Sun, Our Star

Problems

1
Using the values in the appendix, how many times larger in diameter is the Sun than the Earth? And in volume?
2
Use the observation that the angular diameter of the Sun is 0.5° degree and that its distance is 1.5 × 108 kilometers to determine the Sun's diameter.
3
Suppose you were an astronomy student on Neptune. Use the orbital data for Neptune (distance from Sun = 30.05 AU; period = 164.8 years) to measure the Sun's mass using the modified form of Kepler's third law.
4
Show that the Sun's surface gravity is about 30 times Earth's.
5
Calculate the escape velocity from the Sun. Compare this to the speed of rising material in the granulation given in section 12.1. If the escape velocity were less, what would happen at the center of the granulation cells?
6
In this problem, you will calculate an estimate of the temperature of the Sun's core. You can do it either step by step or by writing out all the algebra to obtain a final result. You will need the following ideas: The pressure, P, in a gas is given by P = constant × .T. If we measure length in meters, mass in kilograms, and T in kelvin, then the constant has the value of about 8300 m2 sec-2 K-1. The density of a body, ρ, is its mass per volume. The volume of a sphere is 4pR3/3. The pressure force from the interior is P × A, where A is the area over which the pressure acts. You can take that as the Sun's cross section, pR2, so the pressure force is pR2P. Finally, you need to invoke hydrostatic equilibrium: pressure forces must balance gravitational forces. Approximate the gravitational force holding the Sun together by assuming it is split into two equal halves and apply Newton's law of gravity to calculate the force between the halves. Assume they are separated by 1 solar radius.
7
Calculate the Sun's density in grams per cubic centimeter. The Sun's mass is approximately 2 × 1033 grams. Its radius is approximately 7 × 1010 centimeters. How does the density you find compare with the density of Jupiter?
8
Calculate the energy (in Joules) that would be released if a 60 kg person were converted entirely into energy.
9
The Sun's total energy output is 4 × 1026 watts, and 1 watt is 1 Joule/second. Use the energy yield from the proton–proton chain to determine how many proton– proton chain fusion cycles must be happening each second in the solar core.
10
Estimate the lifetime of the Sun. Assume that 10% of the Sun's total mass is processed through the proton– proton chain (there is only so much hydrogen available to the core), and that for each p–p chain reaction 6.6793 × 10–27 kg of mass is processed and 4.3 × 10–12 J of energy is liberated as per the values at the end of section 12.2. Assuming the Sun's power output given in table 1 is constant, how many years will it shine?
11
Examining Figure 12.27, what temperature would you expect for the sea surface at the end of the graph if the sunspot numbers had continued to rise after 1980?
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