 ## Probabilities in the Galaxy A Distribution Model for habitable Planets Copyright © Klaus Piontzik German Version

## 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 A·Fph·Fgae·FLiz = R · Fp · FLiz · L A·Fh·Fgae = 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 / (A·Fh) Fe = R · L / (A·Fh·Fga) Fe = R · L / (A·Fh·Fg·Fa)

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:

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

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. back home next A new version of the book is under construction. It will be published until April 2020 The new version will have 256 sites and it will be cheaper.
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