Drake Equation (original)

Last modified by

KurtHeckman

on

May 19, 2023, 9:32:20 PM

Created by

MichaelBartmess

on

Aug 1, 2014, 2:15:45 AM

$N = 1 * 50 * 5 * 100 * 100 * 20 * 100000000$

$(R_"*")"Rate Star Formation"$

$(f_p)"Fraction Stars With Planets"$

$(n_e)"Number Planets per Star Supporting Life"$

$(f_l)"Fraction Planets That Develop Life"$

$(f_i)"Fraction With Intelligent Life"$

$(f_c)"Fraction Detectable Signals"$

$(L)"Duration Civilization"$

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The Math / Science

The Drake Equation estimates the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy. The equation was conceived in 1961 by Frank Drake not for purposes of quantifying the number of civilizations, but intended as a way to stimulate scientific dialogue at the world's first search for extraterrestrial intelligence (SETI) meeting, in Green Bank, West Virginia¹. The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life. The Drake equation has proved controversial since several of its factors are currently unknown, and estimates of their values span a very wide range. This has led critics to label the equation a guesstimate, or even meaningless.

The Drake Equation is

N = R_* • f_p • n_e • f_l • f_i • f_c • L

where

N is the number of civilizations in our galaxy with which radio-communication might be possible
R_* is the average rate of star formation in our galaxy
f_p is the fraction of those starts that have planets
n_e is the average number of planets that can potentially support life per star that has planets
f_l is the fraction of planets that could support life that actually develop life at some point
f_i is the fraction of planets with life that actually develops intelligent life
f_c is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L is the length of time for which such an intelligent civilization releases detectable signals

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:

$R_"*"$	1/year (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative)
$f_p$	0.2-0.5 (one fifth to one half of all stars formed will have planets)
$n_e$	1-5 (stars with planets will have between 1 and 5 planets capable of developing life)
$f_l$	1 (100% of these planets will develop life)
$f_i$	1 (100% of which will develop intelligent life)
$f_c$	0.1-0.2 (10-20% of which will be able to communicate)
L	1000-100,000,000 years (which will last somewhere between 1000 and 100,000,000 years)

The Seager Equation is viewed as a major improvement on the Drake Equation.

History

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal Nature with the provocative title "Searching for Interstellar Communications.²³ Cocconi and Morrison argued that radio telescopes had become sensitive enough to pick up transmissions that might be broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a wavelength of 21 centimeters (1,420.4 megahertz). This is the wavelength of radio emission by neutral hydrogen, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in the radio spectrum.

Seven months later, radio astronomer Frank Drake became the first person to start a systematic search for intelligent signals from the cosmos. Using the 25 meter dish of the National Radio Astronomy Observatory in Green Bank, West Virginia, Drake listened in on two nearby Sun-like stars: Epsilon Eridani and Tau Ceti. In this project, which he called Project Ozma, he slowly scanned frequencies close to the 21 cm wavelength for six hours per day from April to July 1960.⁴ The project was well designed, cheap, simple by today's standards, and unsuccessful.

Soon thereafter, Drake hosted a "search for extraterrestrial intelligence" meeting on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.

The ten attendees were conference organiser Peter Pearman, Frank Drake, Philip Morrison, businessman and radio amateur Dana Atchley, chemist Melvin Calvin, astronomer Su-Shu Huang, neuroscientist John C. Lilly, inventor Barney Oliver, astronomer Carl Sagan and radio-astronomer Otto Struve.⁵These participants dubbed themselves "The Order of the Dolphin" (because of Lilly's work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.⁶⁷

Usage

The defaults for this equation use the maximum values stated by Drake and his colleagues in 1961.

$R_"*"$	1/year (1 star formed per year, on the average over the life of the galaxy)
$f_p$	0.5 (one half of all stars formed will have planets)
$n_e$	5 (stars with planets will have 5 planets capable of developing life)
$f_l$	1 (100% of these planets will develop life)
$f_i$	1 (100% of which will develop intelligent life)
$f_c$	0.2 (20% of which will be able to communicate)
L	100,000,000 years

Related Calculators:

Drake Equation (Original): Estimates number of civilizations able to communicate through space.
Seager Equation Calculator: This formula focuses on the search for planets with biosignature gases, gases produced by life that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes
Friedman Equation Calculator

Astronomical Units

Because of the enormity of space and the size of the objects studied, the field of astronomy employs units not commonly used in everyday life. Nonetheless, these units do translate into common units at a grand scale, and vCalc provides automatic conversions between units for calculator inputs and answers via the pull-down menus. The following is a brief description on the distance, mass and time units employed in the field of astronomy

Astronomy Distance Units

Astronomical Unit (au): Within our solar system, a common measure of distance is au, which stands for astronomical units. A single astronomical unit is the mean distance from the Sun's center to the center of the Earth.

Astronomical Unit (au)	Distance from Sun (au)
149,597,870.691 kilometers 92,955,807.267 miles 499.015 light seconds 8.3169 light minutes 0.1386 light hours 0.00001581 light years 389.17 Lunar Orbit Radii	(0.39 au) Mercury (0.72 au) Venus (1.0 au) Earth (1.52 au) Mars (5.20 au) Jupiter (9.57 au) Saturn (19.16 au) Uranus (30.18 au) Neptune (39.48 au) Pluto

Astronomical Unit (au)

Distance from Sun (au)

149,597,870.691 kilometers
92,955,807.267 miles

499.015 light seconds
8.3169 light minutes
0.1386 light hours
0.00001581 light years

389.17 Lunar Orbit Radii

(0.39 au) Mercury
(0.72 au) Venus
(1.0 au) Earth
(1.52 au) Mars
(5.20 au) Jupiter
(9.57 au) Saturn
(19.16 au) Uranus
(30.18 au) Neptune
(39.48 au) Pluto

Light Travel in Time: Light is a primary observable when studying celestial bodies. For this reason, the distance to these objects are measured in the amount of time it would take light to travel from there to the Earth. We can say that an object is one light-year away, and that means that the object is at a distance where it took an entire year for light from the object to travel to Earth. Since the speed of light is 299,792,458.0 meters per second, one can compute the distance equal to a light year as follows:

1 light year = 299,792,458.0 (meters / second) x 31,536,000 (seconds / year) = 9,460,528,405,000,000 meters

The same exercise can be used for light traveling shorter periods of times, light seconds, light minutes, light hours and light days. Since even these units are not enough when computing distances across the universe, there is also a light relative distance of kilo-light years (1000 light years), or the distance light travels in a thousand years!

Light Second	Light Minute	Light Hour	Light Day	Light Year	Kilo-Light Year
299,786 km 186,278 miles 0.002 au	17,987,163 km 11,176,705 miles 0.12023 au	1,079,229,797 km 670,602,305 miles 7.214 au	25,901,515,140 km 16,094,455,343 miles 173.14 au	9,460,528,405,000 km 5,878,499,814,210 miles 63,240 au 0.306 parsecs	9,460,528,405,000,000 km 5,878,499,814,210,000 miles 63,240,000 au 306 parsecs

Light Second

Light Minute

Light Hour

Light Day

Light Year

Kilo-Light Year

299,786 km

186,278 miles

0.002 au

17,987,163 km

11,176,705 miles

0.12023 au

1,079,229,797 km

670,602,305 miles

7.214 au

25,901,515,140 km

16,094,455,343 miles

173.14 au

9,460,528,405,000 km

5,878,499,814,210 miles

63,240 au

0.306 parsecs

9,460,528,405,000,000 km

5,878,499,814,210,000 miles

63,240,000 au

306 parsecs

Angle Shift Seen from Earth: Because the Earth goes around the Sun, our observation of distant objects such as stars results in an angular shift when observed at opposite sides of the elliptical orbit. This shift is used as the basis of a unit knows as a parsec. A parsec was traditionally defined as the distance where one astronomical unit subtends an angle of one arcsecond. A parsec was redefined in 2015 to 648000/π astronomical units. Proxima Centauri, is the nearest star to the Sun and is approximately 1.3 parsecs (4.2 light-years) from the Sun. A mega-parsec is a million parsecs.

Parsec	Mega-parsec
30,856,770,000,000 kilometers 19,173,507,963,493 miles 206,264.7 au 3.26 light years	30,856,770,000,000,000,000 kilometers 19,173,507,963,493,200,000 miles 206,264,767,389 au 3,261,632 light years

Astronomy Mass Units

Astronomical units also apply to the mass of enormous objects such as moons, planets and stars. For this reason, astronomy also employs mass units that compare other objects to ones familiar to us. For example, stars are often measured in mass units of solar masses. This is a comparison of their mass to the mass of our sun (one solar_mass). For planets, astronomers use Earth masses and Jupiter masses for understanding the relative size of rocky planets and gas giants.

Earth Masses	Jupiter Masses	Solar Masses
5.97219 x10²⁴ kg 0.00314657 Jupiter Masses 0.000003 Solar Masses	1.898 x 10²⁷ kg 0.00095446 Solar Masses 317.806 Earth Masses	1.98855 x 10³⁰ kilograms 1047.708 Jupiter Masses 332,968 Earth Masses

Astronomy Time Units

Astronomers use the same time units as everyone else, from the very small nanoseconds, to seconds, minutes, hours, days and years. This is true with two exceptions known as sidereal days and sidereal years. These refer to time relative to the celestial objects (the fixed stars). The Earth rotates every 24 hours relative to the Sun. But we are moving in a circle around the Sun. In comparison, the Earth rotates every 23 hours, 56 minutes and 4.0905 seconds (23.9344696 hours) compared to the stars in the celestial sphere. This is known as a sidereal day.

In the same vein, a sidereal year is the time it takes the Earth to complete one orbit around the Sun relative to the celestial sphere. Where a year is 365 days, a sidereal year is 365.256363004 days, or 1,224.5 seconds more than a calendar year.