## The Drake Equation: An Update

The Drake equation was developed in the early 1960's as a way of determining how many advanced technological civilizations (civilizations that have reached the level of agriculture and other rudimentary technologies) exist today:

N= N(*) * f(p) * n(p) * f(l) * f(i) * f(c) * L

where:

N = the number of civilizations in our galaxy

N(*) = the number of stars in our galaxy

f(p) = fraction of those stars that have planets

n(p) = average number of planets in a star's habitable zone

f(l) = fraction of those planets where life appears

f(i) = fraction of those planets where life is intelligent

f(c) = fraction of those planets that produce a technological civilization

L = longevity of the civilization

When this equation was first put forward, only one of its variables was known (N(*)). What is interesting is that now we know three of them: N(*), f(p), and n(p).

N(*), the number of stars in our galaxy, is 100 billion.

f(p), the fraction of stars that have planets, is 100%.

n(p), the average number of planets with an environment suitable for life (what is now termed as the average number in a star's habitable zone), is about .2.

In a paper recently published in the journal *Astrobiology*, the authors Adam Frank and Woodruff Sullivan, simplify the Drake equation by combining the three "probability of life" variables into a single variable f(bt), the probability of a technological civilization evolving on a planet, and then ignoring L, the longevity of a civilization. When that is done, the Drake equation determines how many advanced technological civilizations have *ever* existed. Their simplified form looks like this:

A = N(ast) * f(bt)

A is the number of technological species that have ever existed.

N(ast) is the number of planets suitable for the development of intelligent life, combining the factors involving astrophysics: N(*), f(p), and n(p).

f(bt) is the fraction that have developed an intelligent civilization, combining the factors f(l), f(i), and f(c).

The current estimate of N(ast) for the Milky Way galaxy is 60 billion, i.e. there are 60 billion planets capable of producing life in our galaxy.

f(bt), the second element in the above equation, is the big unknown. But the pessimistic estimate is one in ten billion, i.e. one in ten billion planets in the habitable zone end up producing an advanced technological civilization.

If that were true, it would mean that over the lifetime of our galaxy there have been six civilizations. If f(bp) is given what is considered a more realistic number--one in a million--then there have been 60,000 civilizations over the course of our galaxy's lifetime.

Here is where the fun part comes in. We can re-introduce L, the average lifetime of a civilization, and see what it would need to be for more than one civilization to exist.

That is calculated using the following formula:

N = n(c) * (L / L(g)

where:

N = the number of civilizations in our galaxy now

n(c) = the number of civilizations over the galaxy's lifetime

L = the average lifetime of a civilization

L(g) = the lifetime of the Milky Way

The Milky Way is 13.2 billion years old, but has been capable of producing life for about 10 billion years, so that is the number I'll use below.

In the case of one civilization every million years, we get this:

N = 60,000 * (L / 10 billion)

If L is 10,000 years (the age of our civilization), then N = .06. That is, 6% of the time there is one civilization, 94% of the time there are none.

If L is a more optimistic 100,000 years, then N = .6. That is, 60% of the time there is one civilization, 40% of the time there are none.

(This assumes, of course, that the rate of civilization production is evenly spread over time.)To get N = 2 (one other civilization exists for us to communicate with), L would need to be about 333,000 years.

Given all that, it looks like the history of our galaxy may well be one of an occasional advanced technological civilization, followed by immense periods of nothingness, or, to put it another way, the probability that other civilizations have existed is a near certainty, as is the probability that we are alone.