the space case (drake) equation

15
The Space Cases The Drake Equation

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Page 1: The Space Case (Drake) Equation

The Space Cases

The Drake Equation

Page 2: The Space Case (Drake) Equation

The # of planets with interstellarly communicative life forms in the Milky Way galaxy

The original formula was: N = R*fpneflfifcL

What is the Drake Equation Attempting to Calculate?

Page 3: The Space Case (Drake) Equation

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 parameters

2. 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)

How Does the Space Case Equation Differ from the original Drake Equation?

Page 4: The Space Case (Drake) Equation

= # 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

The Space Case Equation Part I

Page 5: The Space Case (Drake) Equation

Or, once the latter part of the equation has been determined:

The Space Case Equation Part II: Dispersion

Page 6: The Space Case (Drake) Equation

In the highly improbable event the planets with interstellarly communicative life forms were uniformly dispersed across the galaxy, how many light years would it take for a light signal sent by one to reach the other?*

*This equation does not attempt to factor in the usage of wormholes

What is the Dispersion Equation Answering?

Page 7: The Space Case (Drake) Equation

Why ?This is the formula for determining the volume of a cylinder. Such as…

The Space Case Equation Part II: Explained

Page 8: The Space Case (Drake) Equation

So why ? Why is the galaxy’s volume being divided by x to begin with?

The galaxy’s volume divided by x (the resulting factor produced from Part I of the equation) represents the quadrant 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 the universe we live in being a “flat” universe it has no curvature); Therefore it is in essence 1 Dimensional, as opposed to the 3 Dimensional calculation of volume

The Space Case Equation Part II: Explained

Page 9: The Space Case (Drake) Equation

Simply put, if the volume of the quadrant a possible Drake planet resides in is represented by “V” and the distance light needs to travel to reach a certain point is “y” then…

And with the miracle of mathematics the equation can be rewritten as:

The Space Case Equation Part II: Explained

Page 10: The Space Case (Drake) Equation

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.

The Space Case Equation Part II: Explained

Page 11: The Space Case (Drake) Equation

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

Possible Figures: Part I

Page 12: The Space Case (Drake) Equation

Radius of the Milky Way Galaxy: 50,000 light years

Height of the Milky Way Galaxy: 1000 light years

Possible Figures: Part II

Page 13: The Space Case (Drake) Equation

Part I: (400,000,000,000 x .15 x .375 x .5 x .01)/(12,200,000,000 / 10,000) = 92.213

Part II: = 85,174,944,517.67

The Results with Set Possible Figures

Page 14: The Space Case (Drake) Equation

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.

Interpreting the “Data”

Page 15: The Space Case (Drake) Equation

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>

Works Cited