ps2

Problem Set 2 Astronomy 3

Professor Blitz

Due: Friday March 11, 2015

1) An object has an emission line at a wavelength of 600 nm (nanometers) in its spectrum when it is at rest. Astronomer Josh looks at this object with a telescope equipped with a spectrometer and observes the spectral line at a wavelength of 606 nm. Is the object moving toward or away from Josh? How fast is it moving? Josh observes this object to be moving in a perfect circle around him at 0.001 c, where c is the speed of light. What is the wavelength of the emission line from the object that Josh observes? 2) A star has a luminosity of 1000 times the luminosity of the Sun, but only 5 times its mass. How long can this star live compared to the lifetime of the Sun? 3) From the Period-Luminosity relation for Cepheid variable stars, you deduce that the luminosity of a particular star is 50 times the luminosity of an RR Lyrae star. You measure the apparent brightness of the RR Lyrae variable to be 1% of the brightness of the Cepheid variable. If the RR Lyrae variable is at a distance of 1,000 pc, how far away is the Cepheid variable? 4) The energy output of the Sun is 4 x 1033 ergs/s. How much mass does the Sun convert into energy per second to maintain this energy output? Express your answer in tons of hydrogen per second. Note that there are 103 grams per kilogram and 103 kilograms per metric ton. The world uses about 6.7 x 109 tons of coal per year. How does the rate of coal consumption on Earth compare to the rate of hydrogen consumption in the Sun? 5) In Mr. Tompkins the booking clerk was exonerated by the policeman of shooting the ticket collector even though the booking clerk was running toward the ticket collector with a smoking gun. Explain in your own words how the professor convinced the policeman that the booking clerk was innocent of the murder.