Probabilities in the Galaxy
A Distribution Model for habitable Planets
Copyright Klaus Piontzik Claude Brtels

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9.5 - Drake-Equation and General Basic Model

As Chapter 9.4 shows, the Drake equation can be considered as equivalent to the General Basic Model 8.4.2 after fitting. For this to be exactly the case, both equations must be equivalent to each other.

8.8.4 General Basic Model: NzexGal = A Fph Fgae FLiz
9.2.2 Transformed Drake-Equation: N = R Fp FLiz L

It must then apply:

NzexGal = N
AFphFgaeFLiz = R Fp FLiz L
AFhFgae = R L
   
9.5.1 Equation A Fh Fgae= R L

Equation 9.5.1 can be used in several ways to check and correct the parameters. Here Fe offers the probability for earth-like planets:

Fgae = R L / (AFh)
Fe = R L / (AFhFga)
Fe = R L / (AFhFgFa)

Fe = 400,000 11.5 / (100-300)109 10:603 1,212:3,286 51:130
Fe = 0.019,169 – 0.006,389
Fe = 1:52 – 1:156

This results in the earth similarity Fgae:

Fgae = 1,212:3,286 51:130 (1:52 – 1:156)
Fgae = 1:359 – 1:1078

With equation 9.5.1 the total number of stars in the galaxy can be determined:

AFhFgae = R L
A = R L/ (AFhFgae)

A Fh Fgae = R L
A = R L / (Fh Fgae)

A = 400,000 11.5 / 10:603 1:359 = 99.579 109

A = 400,000 11.5 / 10:603 1:1078 = 299.015 109

This is in line with the given limits.

There are two ways to solve the equation. Solving the equation according to L or R.


Possibility 1

L = A Fh Fgae / R

L = (100-300)109 10:603 1:359 : 11.5 = 401,689 – 1,205,068

L = (100-300)109 10:603 1:1078 : 11.5 = 133,772 – 401,316

On average, the life span of a civilization is:

L = 267,730 – 803,192 years

This results in the average life span of a civilization:

Lm = 535,461 years

This allows a correction for Axiom 7.2.1 to the lifetime of a civilization:

9.5.2 Axiom The average life span of a technological civilization is estimated at L = 535,000 267,000 years.

The maximum limits of a civilization's life span:

L = 133,000 – 1,205,000 years

This is well in line with the 1.15 million year cycle of civilisation in Chapter 7.4. The new maximum value allows a correction for Axiom 7.2.2 to the age of a civilization:

9.5.3 Axiom An old civilization is a culture that is at least 1.2 million years old.


Possibility 2

R = A Fh Fgae / L

R = (100-300)109 10:603 1:359 : 535.461 = 8.627 – 25.881

R = (100-300)109 10:603 1:1.078 : 535.461 = 2.873 – 8.619

On average, the star formation rate is:

R = 5.75 – 17.25

This results in the average star formation rate:

R = 11.5

This is exactly the same as the given mean value.


This observation allows to make a correction for the Drake equation. Insert the new values into equation 9.1.2:

N = (1.45-19) 201:14,000 1:9 1:111.203 535,461
N = 11 - 146 extraterrestrial technological civilizations

9.5.4 Theorem There are probably 11 to 146 technological civilizations in our galaxy.

This result will be referred to as the corrected Drake equation.

 

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