Background: This is an essay I wrote for a Uni class called "Philosophy of The Cosmos"  if you're an ANU student or plan to be at any point, you should take this course as it's interesting and fairly straightforward. If you don't know what the Drake's Equation is kill yourself, but first watch this. Also there's an actual scientific paper referenced (it's the fourth reference in the bibliography), which is also worth reading if you think this sort of mega speculative stuff is cool. So without further ado, feast your eyes upon my sheer genius (*cough, cough*):
Before presenting the equations and estimates it is worth noting that for the purposes of this essay, Drake’s Equation is useless. Drake’s equation is for life forms, in the galaxy, trying to communicate with earth. Here the concern is with biosystems. Biosystems are simply systems which contain life. Their domain can be on planets, moons, comets and asteroids. The equations presented below will reflect this fact. The other thing worth noting is that a different equation will be used to obtain the lower number in the range. This is because the lower number represents the more conservative approach: this means not only using smaller estimates but also the removal of factors that are implausible or highly speculative. Thus two equations will be used.
A) Biosystems in The Galaxy:
Conservative Factor s

Value

Non Conservative Factors

Value

Sf 
100 Billion
 Sf 
400 Billion

Pn

0.5

Pn

1

Pn ave

4

Pn av

8

Mpn

7.9

Mpn

21

Ps

0.02

Ps

0.8

Plf

5.68 x 10^{3}

Plf

0.05

An

10^12
 
Alf

5x10^{8}
 
Final Values

1.8 x 10^{8}

1.3x10^{17}

Note: the final value is obtained by multiplying all the factors together.
Number of Stars in galaxy: Sf – This ranged from 400 Billion[1] to 100 Billion[2], these numbers are observable and detectable, and should need little justification.
Fraction of stars with planets: Pn – This factor determines that of the stars, how many have planets in our galaxy. A lot of evidence suggests this number is 1[3] (I.e 100% of stars have planets), however on the conservative side we say half (if there is no clear way to determine a conservative value, it will be the nonconservative value times 0.5)
Average number of planets per star: Pn ave – For our nonconservative value we model this off our own solar system, with 8 planets per star, our conservative value is simply this halved (4).
Number of Moons per planet: Mpn – Some of the best candidates for life outside Earth and within the solar system are moons (Titan and Europa), so for this reason Moons have been included in our estimate. Once again for the nonconservative estimate this was modeled off the number of moons per planet (total number of moons/number of planets) which is 168/8 = 21. The figures for calculating this were taken from:http://nssdc.gsfc.nasa.gov/planetary/factsheet/ .For the conservative estimate, the range of moons (630 = 63) was taken and divided by number of planets in the solar system. This gave a value of 7.9
Planets suitable for biosystems: Ps – In our own solar system, of the 176 planets and moons, there immediately springs to mind 4 bodies (moons and planets) which life could inhabit. These are: Mars, Earth, Europa and Titan. Dividing 4 by 176 gives us our conservative estimate. Our nonconservative estimate is much harder to calculate. Given the nature of extremophiles to be able to survive even the most, extreme, conditions, it is hard to estimate what number of planets and moons are unsuitable for life. I am going to say, that in fact 80% of all moons and planets in the solar system are suitable for life, though not necessarily life as we know it.
Planets on which life/biosystems actually arise: Plf  our conservative estimate can be modeled on the solar system, where 1 in 176 bodies have produced life. This gives us a scaling value 5.68x10^{3} for planetary bodies on which biosystems emerge. For our nonconservative value, speculation is accounted for. We have one planet where we are certain there is life, but several moons and planets on which it is entirely plausible that biosystems exists. We take into account Mars, Europa, Titan, and the gas giants: Jupiter, Saturn, Uranus and Neptune, to reach our nonconservative value of 0.05 (8/176 rounded up).
Small bodies in unstable orbits: Sb – This figure, 10^12 was taken from: http://wattlearchive.anu.edu.au/file.php/12997/lecture_notes/POTC201238JGAstrobiology4compact.pdf , I take small bodies in unstable orbits to mean meteors, comets and asteroids. Because of the fairly speculative nature of biosystems arising on such objects, this factor is excluded from the more conservative estimate.
Small Bodies in unstable orbits biosystem likelihood factor: Sblf – This is taken to be 5 x 10^{8}, the reason is that of all observed bodies, none have shown strongly either a disposition towards life or any actual life itself. The factor is not set to 10^{12} as it is still possible biosystems can and do emerge on such bodies.
Final values:
We find that our conservative value places the number of biosystems in the galaxy at 1.8x10^{8} and our nonconservative value is 1.3 x 10^{17}. The difference is one of nine orders of magnitude. So how reliable are these results? It is safer to go with the more conservative value, but keeping in mind that we are looking at biosystems and life as we know it, it certainly seems plausible that there is at least one biosystem per star, especially if all stars are likely to have planets and the Copernican principal is applied to the emergence of biosystems.
B) Biosystems in the universe:
For this calculation, we apply a galactic Copernican principal, and assume that our galaxy holds no special place in the universe. Assuming this we can calculate the number of biosystems in the galaxy by using the following equation:
Bu = Bg x Ng
In other words, the number of Biosystems in the galaxy is multipled by the number of galaxies in the universe. Any attempt to add a scaling factor of some sort is ignored, since following the Copernican principle any such factor would be near one, and result in no significant change to the overall value (especially not in terms of order of magnitude).
The number of galaxies in the universe (Ng) seems to be somewhere between 100 billion and 125 billion[4].
Applying our conservative value for Bg against the lower limit of Ng we have:
Bu = Bg x Ng = (1.8x10^{8})x(100x10^{9}) = 1.8x10^{20}
Applying our nonconservative value with the upper limit of our values for Ng, we have:
Bu = Bg x Ng = (1.3x10^{17})x(125x10^{9}) = 1.6x10^{28}
Once again, the difference in order of magnitude is considerable, but considering the size of the universe, the less conservative value seems to be least unlikely. I wouldn’t say either of these values is definitive, but I think they suggest a reasonable range to expect for the emergence of biosystems in the universe.
C) Biosystems in the Universe:
How many biosystems in the Universe are there? This depends on what theory of the Universe we use/accept. If we say our Universe is the only one, it is an almost impossible question to answer since every value would be based entirely on speculation. If we apply a multiverse view, in which the universe is one of an infinite number of universes, the number of biosystems, is of course, infinite. In fact, this question can be answered by saying the number of biosystems in the Universe probably sits between two values: 1 and infinity. I am one hundred percent certain of the lower bound, but it is extremely hard to be certain of the upper bound on this range.
Conclusions:
If I was to be entirely honest, the only value that is certain for the number of biosystems in the Universe, the Universe and our galaxy, is 1. But, there are many good reasons to think the life has, will, and does emerge elsewhere in the universe. It need not be intelligent life, or sophisticated, and this greatly increases the likelihood of its existence. The numbers calculated, conservative and nonconservative, are large from an earthling perspective, but if we apply the Copernican principle to the life and the galaxy, it makes sense that there should be at least one biosystem for every star. If we then apply this to the number of stars in the universe, we realize that the universe should be teeming with life. Before anything definitive can be said, we need to actually find life elsewhere, until then, the best we have is an estimate that may be correct, or several orders of magnitude wrong.
Bibliography:
Internet Sources:
http://www.youtube.com/watch?v=MlikCebQSlY  Last Accessed on the 12^{th} of June 2012
http://www.astrodigital.org/astronomy/drake_equation.html Last accessed on the 11^{th} of June 2012
http://nssdc.gsfc.nasa.gov/planetary/factsheet/  Last Accessed on the 12^{th} of June 2012
http://www.mso.anu.edu.au/~charley/papers/LineweaverGrether03.pdf Last Accessed on the 12^{th} of June 2012
http://wattlearchive.anu.edu.au/file.php/12997/lecture_notes/POTC201238JGAstrobiology4compact.pdf  Last Accessed on the 12^{th} of June 2012
http://hypertextbook.com/facts/1999/TopazMurray.shtml  Last Accessed on the 12^{th} of June 2012
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