A technique is described for calculating the brightness of the atmosphere of the Earth that shines into the Earth's umbra during a total lunar eclipse making the Moon red. This "Rim of Fire" is due to refracted unscattered light from all the sunrises and sunsets rimming the Earth. In this article, a photograph of the totally eclipsed Moon was compared with the Full Moon and the difference in brightness calculated taking into account the exposure time and ISO setting. The results show that the Full Moon is over 14,000 times brighter than the totally eclipsed Moon. The relative brightness of the eclipsed Moon can be used to estimate that the luminance of the Rim of Fire is over 12 trillion watts. The experiment described in this paper would be suitable as a high school or university exercise.