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Re: Book: Rare Earth: Why Complex Life is Uncommon in the Universe
The Drake Equation
Ward and Brownlee provide an alternative version of the Drake Equation, modified to estimate the number of planets in this galaxy currently inhabited by complex multi-cellular (metazoan) life. Their modified equation is as follows: "N* x fp x fpm x ne x ng x fi x fc x fl x fm x fj x fme = N where: N* = stars in the Milky Way galaxy fp = fraction of stars with planets fpm = fraction of metal-rich planets ne = planets in a star's habitable zone ng = stars in a galactic habitable zone fi = fraction of habitable planets where life does arise fc = fraction of planets where complex metazoans arize fl = percentage of a lifetime of a planet that is marked by the presence of complex metazoans fm = fraction of planets with a large moon fj = fraction of solar systems with Jupiter-sized planets fme = fraction of planets with a critically low number of mass extinction events" First of all, this equation contains numerous errors and redundancies in its terms. For example, "stars in a galactic habitable zone" should be a fraction, and it should be something like "fraction of those planets orbiting stars in a galactic habitable zone". Each term needs to reference all of the terms before it in some way, like the terms given in the original Drake Equation. Even after these errors are corrected, there is still an additional logical error. The authors state that "as any term in such an equation approaches zero, so too does the final product." But this is only valid as far as each condition specified is absolutely necessary for complex life. In reality, each term should be modified by the chance that complex life can form without that feature. For example, "fm = fraction of planets with a large moon" should be replaced by something like: (fm + fm' x (1 - fm)) where fm' = the fraction of planets without a large moon that can develop complex metazoans. Since fm and fm' must always be between zero and one, this term can never be less than fm' even if fm approaches zero. The equation with each term modified in this way now takes into account the chance that the authors' proposed requirements for complex life are not absolute. Now it is more than a simple matter of proving that one of the terms approaches zero in order to claim that complex life is rare. |
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Re: Book: Rare Earth: Why Complex Life is Uncommon in the Universe
Bad Jupiters, no Jupiters?
Are planets like Jupiter rare or common? Are they necessary for complex life to evolve in a system, yet more likely to be detrimental than helpful? The authors argue that a large Jupiter-like planet in a stable, fairly distant, circular orbit is necessary for complex life to develop on one of the inner planets of a system. Such a planet would sweep the inner solar system leaving it relatively clean of many of the comets and asteroids which could sterilize the planet by collision. I am going to argue that Jupiter sized planets in orbits exactly where the are needed may be common. But it is also possible that without a Jupiter, it would simply take longer for the early bombardment of a new planet to slow down enough so that life can develop. Right now this is just speculation but perhaps it could be tested with computer simulation. In any case it does allow for the possibility that nearby Jupiter sized planets are not an absolute necessity for complex life. Ward and Brownlee cite the fact that, so far, all programs to detect extra-solar planets have found only Jupiter sized planets in either very close or very elliptical orbits around their star. These so called "bad Jupiters" should interfere with any planets in a star's habitable zone enough to prevent the possibility of complex life forming there. But the reason these are the only extra-solar planets we detect, is that they are the only kinds we could detect at the time Rare Earth was written. We see these bad Jupiters in about 5% of the nearby star systems, while in the remaining 95% we detect nothing. The authors admit it is quite possible that many of the remaining 95% have planetary systems similar to our own, since we cannot detect those at the distances of nearby stars. Finally, theories of planet formation suggest that Jupiter like planets will form exactly where they are needed to support life on the inner planets: just outside the star's habitable zone, and the ones that are in closer or more elliptical orbits are those that migrate there by chance gravitational interactions. "In disks as massive as the minimum-mass disk for the Solar system, gas giants can form only slightly outside the “ice boundary” at a few AU." "We also examine the dynamical evolution of protoplanets by considering the effect of orbital migration of giant planets due to their tidal interactions with the gas disks, after they have opened up gaps in the disks. The effect of migration is to sharpen the boundaries and to enhance the contrast of the planet desert. It also clarifies the separation between the three populations of rocky, gas-giant, and ice-giant planets." - Towards a Deterministic Model of Planetary Formation I: a Desert in the Mass and Semi Major Axis Distributions of Extra Solar Planets - S. Ida and D. N. C. Lin This suggests that "good Jupiters" might not be so rare after all. |
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