Geometric ProbabilityWhich is why the Kepler results really are in line with what we know of the universe. Kepler has been up there for a short while, and has a possible list of nearly 2000 planets just looking at about 150,000 stars for only a couple of years! So if only 1% statistically transit, that would mean that just randomly 1500 systems would have the correct orientation (given the results to date, that makes sense). And given that about 7500 stars were eliminated from consideration due to being variable of one sort or another... I think it would be pretty safe to say that pretty much every star out there has at least some sort of planetary body around it.
Transits can only be detected if the planetary orbit is near the line-of-sight (LOS) between the observer and the star. This requires that the planet's orbital pole be within an angle of d*/a (part 1 of the figure below) measured from the center of the star and perpendicular to the LOS, where d* is the stellar diameter (= 0.0093 AU for the Sun) and a is the planet's orbital radius.
This is possible for all 2pi angles about the LOS, i.e., for a total of 4pi d*/2a steradians of pole positions on the celestial sphere (part 2 of figure).
Thus the geometric probability for seeing a transit for any random planetary orbit is simply d*/2a (part 3 of figure) (Borucki and Summers, 1984, Koch and Borucki, 1996).
For the Earth and Venus this is 0.47% and 0.65% respectively (see above Table). Because grazing transits are not easily detected, those with a duration less than half of a central transit are ignored. Since a chord equal to half the diameter is at a distance of 0.866 of the radius from the center of a circle, the usable transits account for 86.6% of the total. If other planetary systems are similar to our solar system in that they also contain two Earth-size planets in inner orbits, and since the orbits are not co-planar to within 2d*/D, the probabilities can be added. Thus, approximately 0.011 x 0.866 = 1% of the solar-like stars with planets should show Earth-size transits.
And what we know of evolution and life here on earth (particularly in regards to its resilience and ability to pop up just about anywhere), it's a safe bet that life out there will be relatively common. Granted, we only have a smaple size of one at the moment. However, should we find evidence on Mars or Europa for instance, that will really open the field up. With the possibility of life being pretty common, that begs the question of intelligent life out there. We (notionally) have a smaple size of one on this too. Sadly, the factors involved in our ascent to (supposed) intelligence are unknown and very difficult to translate to any other of a myriad of possibilities. But given the large numbers involved, I'm pretty sure they are out there. I just highly doubt we'll ever get to talk to any of them.
And just to leave you with another preliminary paper about the probability of earthlike planets out there, Dr. Phil Plait covers this as well:
A paper has been accepted for publication in a science journal (PDF) where the author has analyzed data from NASA’s Kepler planet-finding observatory, trying to figure out how many Earth-sized planets there might be in the galaxy orbiting their stars in their habitable zones; that is, at the right distance so that the star warms the planet enough to have liquid water. In the paper, he estimates that on average 34% (+/-14%) of Sun-like stars have terrestrial planets in that Goldilocks zone.CLICK HERE TO READ THE REST OF THE POST.
I can explain how he got this number. But I can also explain why I think this needs to be taken with a grain of salt. Let me be clear: it’s possible he’s right, and I suspect he may very well be. His math looks good to me. But a couple of assumptions he had to make need to be pointed out, and I want that to be clear before the media start running around saying there are billions of Earths in the galaxy based on this.
Here’s the deal. Kepler is an orbiting observatory that’s staring at about 100,000 stars, looking for dips in their light when an orbiting planet passes in front of them from our perspective. The length of time the dip takes gives us the orbital period of the planet, and the size of the planet (if the star’s size is known, generally true) can be determined by how much light is blocked. I talk about how this works in a little more detail in an earlier post.