Problem #1: When a massive star explodes as a supernova, it shines with a luminosity ten billion times greater than that of the Sun for a short period of time. If such a supernova explosion were to appear in our sky as bright as the Sun, how far away from us must it be located?
Problem #2: Radio wavelength observations of a gas cloud near the Galactic Center show spectral line emission at a frequency of 1421.65 MHz (1 MHz = 106 Hz). Astronomers have determined that this emission line is generated by the spin-flip transition of atomic hydrogen, which has a rest frequency of 1420.406 MHz. Based on these observations, calculate the speed of the gas cloud toward or away from the Earth.
Problem #3: a) If the interstellar medium has an average density of 4.5 x 10-18 kg/m3, what volume of interstellar medium contains enough mass to make a 1 Mo star?
b) If this volume were spherical in shape, what radius would it have? (Hint: the volume of a sphere is 4/3 x pi x radius3.)