Microlensing has paid off. This technique is a most powerful method for finding planets of every size about a target star. An international team has reported recent results of several years of searching. This BBC News report summarizes very well the report and many of the implications. One is the bold statement that every star that is not part of a multiple star system is certain to harbor at least one planet. This may be coupled with the discovery by other methods (transits and gravitational perturbations) that at least some multiple star systems also harbor planets. About half the stars are part of multiple systems, so this implies that the minimum number of planets in our Galaxy is greater than half the number of stars in the Galaxy.
The Galaxy is composed of at least 200 billion stars. If, then, there are 100 billion or more planets in the Galaxy, how many of these are similar to Earth? In size, at least, the report cited above claims this number is about 10 billion. This is a very conservative estimate, and I think it it likely that there are many more than this. I base my reasoning on the principle of mediocrity: Our solar system is most likely to be close to average. Can that be quantified?
Let's make a few rough estimates, based on what we know:
- Our Solar System has 8 planets.
- It contains at least three bodies, including Earth, that are expected to have large amounts of liquid water over great spans of time: Earth, Mars (for its first 2 billion years), and Europa (under a thick ice layer).
- There is one Earth, with life and even (somewhat) intelligent life.
Firstly, we find that if the mean value of a Poisson distribution is 5, the normalized distribution's height at 8 is 0.37, while if the mean is 6, the height at 8 is 0.64, so we'll use 6 as a lower bound. Secondly, if the mean is 12, the height at 8 is 0.57, and if the mean is 13, the height is 0.42, so we'll use 12 as an upper bound. That means that the most likely number of planets, for stars somewhat similar to the Sun, is between 6 and 12, and a further analysis indicates that most such stars will have a number of planets between the "sideboard" values of 3 and 17.
By a star "somewhat similar to the Sun" I mean a star of spectral type F, G or K that is not a member of a multiple star system. That is about 10% of all stars. The "sideboards" above indicate that there are at least 3 planets each, which multiplies out to 60 billion planets in the Galaxy about such stars, with a more likely number of 150-180 billion planets, and the potential for trillion or so.
Among these, how many might have liquid water for at least a couple of billion years? Repeating the process using 3, we get a range of mean values between 2 and 6, with "sideboards" of 1 and 8. Thus there are at least 20 billion planets holding liquid water, and more likely about 60 billion.
Finally, how many sister Earths? When your sample is 1, it is better to use an aggregation technique, and say, suppose that among ten stars, we were to find five sisters to Earth, what could we conclude? A similar analysis shows that a random group of ten stars might have a mean value in the range 4-8, with "sideboards" of 1-11. This works out to a per-star range of 0.4-0.8 with "sideboards" of 0.1-1.1. These seem reasonable. Thus, I conclude sister Earths number at least 8 billion, with 10+ billion even more likely.
Then why, above, did I state that I think there are many more than 10 billion? There are two sources of more Earths. One is the warmer half of the M stars, M0-M5, which outnumber all the F, G and K stars two-to-one. The other is large satellites of super-Jupiters that may be a little outside the habitable zone of the parent star, but who add heat to the satellite by tidal flexing. This is much more speculative, but is not likely to be zero, so it is more probable that there are millions or a few billions of these also (In the Sci-Fi film Avatar the "planet" Pandora is a giant satellite of a super-Jupiter, though you only see this in an early sequence).
I am encouraged that my very rough "mediocrity" estimates are in the same range as that of the scientists who have given this much more thought than I have. The next breakthrough to await is the ability to get a spectrum from an exoplanet. An atmosphere with water and oxygen will fairly shout "LIFE!" to the Universe.