WEBVTT 00:00:00.000 --> 00:00:02.840 This is College Physics Answers with Shaun Dychko. 00:00:02.994 --> 00:00:06.342 The intensity of light is the luminosity 00:00:06.340 --> 00:00:09.280 of the light source divided by the distance to it squared. 00:00:09.691 --> 00:00:12.125 So the intensity of the Sun is the Sun's luminosity 00:00:12.125 --> 00:00:14.120 divided by the distance to the Sun squared 00:00:14.354 --> 00:00:18.502 and the intensity of the Andromeda galaxy 00:00:18.500 --> 00:00:22.697 is the luminosity of the Andromeda galaxy divided by the distance to it squared. 00:00:23.165 --> 00:00:26.754 And so the luminosity of the Andromeda galaxy we are told is 00:00:26.750 --> 00:00:29.748 10 to the 12 times the luminosity of the Sun 00:00:30.217 --> 00:00:33.942 and the distance to the Andromeda galaxy is 2 times 10 to the 6 light years 00:00:33.940 --> 00:00:37.257 which we can convert into a number times 00:00:37.250 --> 00:00:39.714 the distance to the Sun. 00:00:39.950 --> 00:00:42.720 So we multiply by this many kilometers per light year 00:00:42.720 --> 00:00:45.268 and so the light years cancel and this gives us the number of kilometers 00:00:45.260 --> 00:00:46.651 to the Andromeda galaxy 00:00:46.834 --> 00:00:49.897 and then we convert that into solar radii 00:00:49.890 --> 00:00:57.657 by saying there's one solar radius for every 149.6 times 10 to the 6 kilometers 00:00:58.148 --> 00:00:59.988 and that gets squared 00:01:00.171 --> 00:01:04.114 and doing this calculation 10 to the 12 divided by all these numbers 00:01:04.110 --> 00:01:06.571 works out to 6.25 times 10 to the minus 11 00:01:06.570 --> 00:01:09.257 and we are left with L s over r s squared 00:01:09.250 --> 00:01:11.702 and this is the luminosity of 00:01:12.537 --> 00:01:15.942 or I should say the intensity or brightness of the Sun 00:01:16.468 --> 00:01:18.240 as we wrote up here. 00:01:18.690 --> 00:01:22.228 So we can substitute that with I s 00:01:23.634 --> 00:01:26.354 and that means the relative brightness of the Andromeda galaxy 00:01:26.350 --> 00:01:28.217 is this factor times I s; 00:01:28.210 --> 00:01:30.914 it is 6 times 10 to the minus 11.