__The following illustration is an outgrowth of a presentation "Orbital and Acoustic Resonance" at CONTACT 2006, concerning comensurabilites among the orbits of multiple planet systems. Star masses, spectral types, and planet periods below reflect data available in mid 2006; these are updated frequently and those with professional interest in more current values are referred to the Extrasolar Planets Encyclopedia, http://exoplanet.eu/ and its referenced literature.
__The illustration displays planets as dots to the right of their stars at a distance proportional to the exponent of two of their orbital periods in days. In the grid, each horizontal division represents a factor of two in period, and also a factor of about 2.5 in insolation. Note that this relationship between period and insolation ratios holds for all stars and is independent of mass, luminosity, or distance from the star.
__Among multiplanet systems, the typical period spacing of such systems, from Gliese 876 to Sol, is similar despite the wide range of mass and luminosity. Red dwarfs can pack as many planets into their habitability zones as stars many times brighter than Sol.
__The illustration includes a representation of the "habitability zone" of each star. Note the fuzzy ends of the habitability zone. This is meant to indicate that there is no hard limit, but that it may be increasingly difficult for nature, or planetary engineers, to create a habitable planet as insolation differs significantly from what we have on Earth.
__While this zone is represented to be from about 2.5 to 0.4 times Earth's insolation, please note that there is considerable discussion in the literature of just how wide such a zone should be and where it should be centered. A planet's surface conditions depend on the depth and composition of its atmosphere, its orbital eccentricity and equatorial tilt, and its internal heating factors as well as insolation. Factors affecting the retention and composition of an atmosphere include the world's mass, exposure to stellar winds, accretional history, tidal circumstances and age.
__Note how often extrasolar giant planets are found in or near their star's habitability zone. With the right kind of magnetic field, these planets may have habitable moons. In our solar system, Saturn's magnetic field produces a relatively low temperature magnetosphere which is friendly to satellite atmospheres, unlike that of Jupiter, Uranus and Neptune. If this one-out-of-four statistic applies outside the solar system, and Jupiter sized and larger planets average about four planet-sized moons, one might expect the number of habitable moons around sunlike stars to be comparable to the number of giant planets in habitable zones. While the habitable zone period range doesn't shrink as stars get smaller, tidal constraints (i.e., the Hill sphere radius) limit the number of stable orbits available around a warm Jupiter near a late star and one can expect the number of potentially habitable moons to drop as star mass decreases with a cutoff around spectral class M5 or so. Our sample of roughly 40-50 habitable zone giant planets, might reasonably host a total of 10 or so statellites with liquid surface water.
__Our own solar system demonstrates stable small planet orbits with period ratios of 3/2 (Pluto/Neptune) and (8/5) (Earth/Venus). While it is doubtful, looking at our asteroid belt, that a giant planet's gravity would allow a world to form in such an orbit, gradual migration of giant planets may capture a terrestrial world in such a resonance. This being the case, it seems difficult to exclude habitable zone terrestrial planets from any of the systems depicted here, though the chances of a stable planetary orbit between giant planets in a two/one resonance, such as Gliese 876 b and c, would seem to be very small.
Gerald Nordley, 20 Sep. 2006