#### Introduction:

Drake equation developed the equation: where is the rate of star formation, is the fraction of stars that have planets, average number of planets per star that could support life, is the fraction of planets that have life, is the fraction having intelligent life, is the fraction that develops sufficient technology, and is the lifetime for the civilization. The parameter is the number of civilizations in the galaxy. This equation is a series of parameters when multiplied together account for all the factors leading to a civilization capable of interstellar communications. Despite a lot of tantalizing clues, we have only one example, us. As a result, we can set the number of civilizations in the galaxy capable of interstellar communications to be at least one.

We’ll take a quick review of the terms of the Drake equation, making note of some connections with civilizations on the Kardashev scale. In later articles, we’ll take a deeper dive into each of these terms and extend them as necessary.

#### Terms from astrophysics:

The first term, , is the stellar formation rate. It is a term that can be computed from astrophysics. A conservative value is about 1.5 to 3 stars being formed per year. We will explore how advanced civilizations, such as a Type 3 galactic civilization, could change this number to suit their needs.

The second term, , is the fraction of stars that have planets. This is currently estimated at approximately 1. All stars seem to have planets. Advanced civilizations, such as a Type 2 stellar civilization, could alter this number.

The number of planets that could support life per system, , is the third term. Estimates are from 0 to 4. It all depends upon the life zones. Some planets might be outside of the life zones but still have environments that meet the conditions. Obviously, advanced civilizations could alter this number.

#### Terms from biology:

The fraction of those worlds having life, , is speculation. Right now, because of what we have in the solar system, the value is about 0.25 if we consider Earth, Mars, Europa, and Enceladus habitable. Sufficiently advanced civilizations will push this number to 1 and increase the value of .

The long path from life to intelligent life is established by the parameter . Geologically and biologically speaking, we have no idea the value of this number. We could take it as a chance to survive a mass extinction, however such an extinction might increase the probability of intelligence arising before the next extinction.

#### Terms based upon other factors:

Another important consideration if the rise of technology. The parameter is the fraction of intelligent species developing the technology necessary for communications with the stars. Using our own Earth as the example, only us out of all the various hominids developed the advanced technologies necessary for stellar communications. That does not count all the various civilizations that rose within the emergent homo sapiens that died out before the technological hurdles could be overcome. Any value will be at best a guess.

Lastly, we look at the lifetime of a civilization capable of interstellar communications, . This is the hardest to assess. But we can realize that this number could likely be anything from seconds to billions of years. For us, the possibility of radio communications began around 1900, so conservatively, we can say 122 years.

#### Extending Drake’s equation to class 1, 2, and 3 civilizations:

We can modify Drake’s equation by adding six additional terms, , and for the fraction of civilizations at the said level and the average lifetime of the same. These parameters give the numbers , , and . of civilizations that make it to type 1, type 2, and type 3 civilizations: , , and . This is the science of the Drake equation applied to science fiction. The lifetime of a civilization depends on the civilization type. There are also factors which depend upon the numbers of civilizations of various types present in the galaxy or in the local area.