Supernova! The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. The explosion was seen on the earth on July 4, 1054 C.E. The streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 X 1014 Hz; the red light received from streamers in the Crab Nebula pointed toward the earth has frequency 4.586 X 1014 Hz.
(a) Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (You may use the formulas derived in Problem 16.78. The speed of light is 3.00 X 108 m/s.)
(b) Assuming that the expansion speed bas been constant since the supernova explosion estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years.
(c) The angular diameter of the Crab Nebula as seen from earth is about 5 arc minutes (1 arc minute = 1/60, degree). Estimate the distance (in light years) to the Crab Nebula, and estimate the year in which the supernova explosion actually took place.