Solution to Exercise

The ratio of luminosities is the ratio of the 4th power of the temperature, by the Stefan-Boltzman Law. Thus,

  1. In the first example, star B is more luminous than star A by a factor of (4000/2000)4 = 24 = 16.

  2. In the second example, star B is more luminous than star A by a factor of (8000/5000)4 = 6.55.
Note that the solutions are simply the ratio of the 4th power of the temperatures because of the assumption that the surface areas are the same. If the surface areas were different, we would also have to correct for that.