|about a now famous formula
Decades ago the well-known astronomer Frank Drake, still one of the leading SETI protagonists, introduced a formula, later named after him, which contains all of our knowledge, or more precisely, all of the lack of our knowledge. This last reason makes me not to present the formula itself, but to discuss its most important, best and least known factors. The formula itself is rather straightforward built by the already mentioned conditions for organic life on any planets.
from the best known...
Relatively accurate numbers are available for the number of stars in our galaxy and for the rate, with which new stars come into existance, and also more special for the mentioned spectral types of F, G and K for main sequence stars. The life spans of these are also well established. But already with the next factor we have real trouble: despite the discovery of many Jovian planets (a few dozens so far) outside of our solar system, we know empirically nothing about terrestrial planets in the universe besides the four in our planetary system. Only the probability, that there are also such in considerable numbers has grown due to these discoveries, which began only in 1996. That there is not yet a chance, to establish a realistic statistic about such planets (even not with the Jovian ones), I have also mentioned before. But these are the good news...
...to the least known
As you may have already read before, the most difficult question is the behaviour of another hypothetical civilizations and also their "lifetime". The last two factors affect largely the chance for any contacts. Here our example is nearly worthless, not only because it's unique, but also for the yet unkown time, for which we will be able to contact other civilizations. Any biologist will agree, that it would be naïve to think, this will be forever. But there are other obstacles for estimates too.
How are at all the chances for life to develop up to a certain point? And how long it can exist on a certain planet, companion of a certain star? To the last question the answer for our planet with our sun is in the range from 4 to 5 billion years. But we don't know, how long this would be under another circumstances, for example on another planet and even what could have happened, if one of the major crises on Earth had wiped out the life long ago. Could it reappear? Probably this was possible in the early stages of Earths evolution, but this is questionable, if some total devastating event would have wiped it out in later stages... At least this seems to be consensus of the most experts in the topic nowadays.
And remember: the most recent crisis in Earths biological history is caused by an animal, which calls itself "homo sapiens" (seems to be arrogant, I think sometimes). In the worst case these intelligent beings may extinct all life on their planet, if we consider our problems.
Another question: how fast life develops at the average to intelligent beings? Again we don't know for sure, but in our case it needed nearly 4 billion years. Therefore a few billion years may be a reasonable guess, but of course it's far from sure.
putting all together...
Another factors include mass, diameter and distance distributions of terrestrial planets, primordial and afterwards atmospheric compositions and so on and so on. Due to the many uncertain factors the results are very different. This hasn't changed since Francis Drake computed first values from the equation.
Most often the average distance between civilizations, which could at principle communicate with each other, is used as the primary result. This can vary largely as the added uncertainties of the factors. By factors of 1,000 or even more, to make it quite clear.
This is no satisfying knowledge, if it is any knowledge at all. But the worst thing about it is, that we would need such contacts to establish our statistics better. This is a classic circulus vitiosus!
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