Explorations: Introduction to Astronomy (Arny), 6th Edition

Chapter 12: The Sun, Our Star

Problems

1
Given that the angular diameter of the Sun is 1/2 degree and that its distance is 1.5 ´ 108 kilometers, go through the math to determine the Sun's diameter.
2
Suppose you were an astronomy student on Jupiter. Use the orbital data for Jupiter (distance from Sun 5.2 AU; period 11.8 years) to measure the Sun's mass using the modified form of Kepler's third law.
3
In this problem, you will calculate approximately 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 ´ pT. 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, p, is its mass per volume, which for a sphere is M / (4πR3/3); 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, πR2. Thus, the pressure force is πR2P. 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.
4
Calculate the escape velocity from the Sun.
5
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 cm. How does the density you find compare with the density of Jupiter?
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