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# The Space Case (Drake) Equation

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### The Space Case (Drake) Equation

1. 1. The Space Cases
2. 2. The # of planets with interstellarly communicative lifeforms in the Milky Way galaxyThe original formula was: N = R*fpnef lfifcL
3. 3. Well, one, it is answering a slightly different question. Or rather, slightly different questions. The Drake Equation attempts to answer the question “How many planets with interstellarly communicative life forms are there in the Milky Way galaxy today?” The Space Case Equation attempts to answer three questions:1. How many planets with interstellarly communicative life forms (“Drake planets”) have ever existed in a galaxy, based upon the galaxy’s parameters2. Based upon the galaxy’s age and the mean # of years a Drake planet is active, how many are likely to exist at any given point in the galaxy’s history? (Including the present)3. What is the mean distance between two active Drake planets? (Measured in light years)
4. 4.  = # of stars present in galaxy = % of stars with planets = % of planets in the habitable zone = % of habitable planets with life = % of habitable planets with life that have developed interstellar communications a = age of the galaxy L = mean # of years communicative civilizations remain active * “Drake planet” refers to a planet that possesses a race and/or races of interstellarly communicative life forms
5. 5. Or, once the latter part of the equation has beendetermined:
6. 6. In the highly improbable event the planets withinterstellarly communicative life forms were uniformlydispersed across the galaxy, how many light yearswould it take for a light signal sent by one to reach theother?**This equation does not attempt to factor in the usageof wormholes
7. 7.  Why ? This is the formula for determining the volume of a cylinder. Such as…
8. 8. So why ? Why is the galaxy’s volumebeing divided by x to begin with?The galaxy’s volume divided by x (the resulting factorproduced from Part I of the equation) represents thequadrant a hypothetical Drake planet resides in.Why take the cubic root of volume divided by x?Light moves in a straight line in all directions (due to theuniverse we live in being a “flat” universe it has nocurvature); Therefore it is in essence 1 Dimensional, asopposed to the 3 Dimensional calculation of volume
9. 9. Simply put, if the volume of the quadrant a possibleDrake planet resides in is represented by “V” and thedistance light needs to travel to reach a certain point is“y” then…And with the miracle of mathematics the equation canbe rewritten as:
10. 10. Even more simply put, look at this rubix cube: The cube has a height of three units, a width of three units, and a length of three units How do you find the volume? 3 x 3 x 3 = 27 cubic units Suppose you only knew the volume, and you needed to find the height/width/length. You would need to find the cubic root of 27 units, which is 3.
11. 11.  400 Billion = # of stars present in galaxy 15% = % of stars with planets 37.5% = % of planets in the habitable zone 50% = % of habitable planets with life 1% = % of habitable planets with life that have developed interstellar communications 12.2 Billion = age of the galaxy 10,000 = mean # of years communicative civilizations remain active
12. 12. Radius of the Milky Way Galaxy: 50,000 lightyearsHeight of the Milky Way Galaxy: 1000 light years
13. 13. Part I: (400,000,000,000 x .15 x .375 x .5 x .01)/(12,200,000,000 / 10,000) = 92.213Part II: =85,174,944,517.67
14. 14.  There are an estimated 92 Drake planets. That is, there are 92 planets in the Milky Way galaxy with extant interstellarly communicative life forms. If these planets were uniform in distance throughout the Milky Way galaxy, there would be one interstellarly communicative civilization per 85.2 billion cubic light years. This space is approximately 1% of the volume of the galaxy in its entirety (1.08%). But, light travels in a straight line. Meaning y (light years needed to travel to the nearest interstellarly communicative civilization) would be = 85,174,944,517 which is 4,399.8 light years.
15. 15.  Bennett, Jeffrey, and Seth Shostak. Life in the Universe. 3rd. San Francisco, CA: Pearson Education, Inc., 2007. Print. Christian, Eric, and Samar Safi-Harb. "Size of the Milky Way." Imagine the Universe. NASA, 01 Dec 2005. Web. 18 Oct 2011. <http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980317b.html>. Frommer, Hartmut, and Christine Kronberg. "The Milky Way Galaxy." Messier. N.p., 25 Aug 2005. Web. 18 Oct 2011. <http://messier.seds.org/more/mw.html>. Koppes, Steve. "Scientist refines cosmic clock to determine age of Milky Way ." University Of Chicago News Office. N.p., 01 Jul 2005. Web. 18 Oct 2011. <http://www-news.uchicago.edu/releases/05/050629.milkyway.shtml>. Ohio State University. "In all the universe, just 15 percent of solar systems are like ours." ScienceDaily, 6 Jan. 2010. Web. 18 Oct. 2011. <http://www.sciencedaily.com/releases/2010/01/100105161540.htm>