This article is intended to provide a review of some modifications to the Drake equation, a 1961 concept presented by Frank Drake to determine the number of extra-terrestrial civilizations able to communicate. A reduced version of the Drake equation will then be presented. This can be used to estimate an important question for astrobiology, the frequency with which planets are habitable. Finally, a concept is presented that can also integrate the habitability of moons into the reduced Drake equation.
In 1950, the Italian physicist Enrico Fermi expressed his astonishment with the sentence "Where is Everybody?" that humanity does not receive signals from extraterrestrial civilizations. A solution to this contradiction for isotropic signals, known as Fermi's paradox, is provided by a model by Claudio Grimaldi. In the present work, with the help of a physical model for signal power, the finite range of isotropic signals assumed in Grimaldi's model is specifically calculated. For this purpose, the FAST telescope in Guizhou and a hypothetical satellite network spanning the Earth are regarded as exemplary receiving instruments. In addition, corresponding signal powers are determined for three potentially habitable planets discovered by the Kepler mission and for stars close to the Sun. It turns out that even the FAST telescope cannot receive corresponding signals, but this is theoretically possible with a satellite network, similar to the GPS network. Accordingly, Grimaldi's assumption turns out to be correct, but the maximum range is considerably smaller than Grimaldi assumed.
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