Problem Solving


1		The star Rigel radiates most strongly at about 200 nanometers. How hot is it?



2		The bright southern star a Centauri radiates most strongly at about 500 nanometers. What is its temperature? How does this compare to the Sun's?



3		Arcturus is about half as hot as the Sun but is about 100 times more luminous. What is its radius compared to the Sun's?



4		A stellar companion of Sirius has a temperature of about 27,000 K and a luminosity of about 10²² L_sun. What is its radius compared to the Sun's? What is its radius compared to the Earth's?



5		Sirius has a parallax of 0.377 arc seconds. How far away is it?



6		The parallax of Proxima Centauri is about 0.763 arc seconds. How far away is it?



7		The parallax of the red giant Betelgeuse is just barely measurable and has a value of about 0.005 arc seconds. What is its distance? Suppose the measurement is in error by ± 0.003 arc seconds. What limits can you set on its distance?



8		Two stars in a binary system have an orbital period, P, of 5 years and an orbital separation, a, of 10 AU_sun. What is their combined mass?



9		Two stars in a binary system have an orbital period, P, of 2 years and an orbital separation, a, of 4 AU. What is their combined mass?



10		Two stars in a binary system are determined from their position on the H-R diagram and the mass-luminosity relation to have a combined mass of 8M_sun. Their orbital period, P, is 1 year. What is their orbital separation, a?



11		A line in a star’s spectrum lies at 400.0 nanometers. In the laboratory, that same line lies at 400.2 nanometers. How fast is the star moving along the line of sight; that is, what is its radial velocity? Is it moving toward or away from us?

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