Q. A cluster of galaxies has a radius of about 5.2 million light-years (4.9×10^22) and an intracluster medium with a temperature of (6.5×10^7) K. Estimate the mass of the cluster. Give the answer in both kilograms and solar masses. Suppose combined luminosity of all the stars in the cluster is 8.1×10^12 L sun.
Q. A train moving toward a detector at 33m/s blows a 301 Hz horn. What frequency is detected by a train moving toward the first train at a speed of 17 m/s?