Problem Solving


1		Given that the angular diameter of the Sun is 1/2 degree and that its distance is 1.5 X 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 X 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 X 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 2X10³³ grams. Its radius is approximately 7 X10¹⁰ cm. How does the density you find compare with the density of Jupiter?

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