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 (Electrons can come in two "flavors", spin up and spin down. Transitions between such state is much less energy intensive than, say, a transition from the ground state to the first excited state in hydrogen). Based on these observations, calculate the speed of the gas cloud toward or away from the Earth.

Problem #3: a) If the interstellar medium from which stars are being made has an average density of 4.5 x 10^-18 kg/m³, what volume of interstellar medium contains enough mass to make a 1 M_o (one solar mass) 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.)