The Kepler Space Telescope has located many multi-planet systems since its inception, which combined with discoveries made by other planet-hunting missions has enabled scientists to begin to construct models of planetary systems orbiting other stars. This is particularly complicated where not all planets are visible to the space telescope, which is only capable of directly detecting fairly large planets. One such system is Kepler-68, where two large planets orbiting close to the star have been directly observed by the telescope as they pass in front of it, and the presence of a third, larger and more distant, planet has been inferred by the actions of its gravity upon the star and two observable planets.
In a paper published on the online arXiv database at Cornell University Library on 9 November 2015 and submitted for publication in the Astrophysical Journal Letters Stephen Kane of the Department of Physics & Astronomy at SanFrancisco State University describes a model of the Kepler-68 system, which calculates the masses and orbits of the planets, as well as plotting the system's Habitable Zone (the zone in which an Earth-mass planet could potentially host liquid water), and the possibility of a small rocky planer orbiting within that zone.
Kepler-68 A (when naming bodies in other stellar systems stars are indicated with an upper case letter while planers are indicated with lower case letters) is a Sun-like star with a mass equivalent to 1.079 times that of the Sun and an effective surface temperature of 5793 K (compared to 5778 K for the Sun). It has a slightly larger radius, 1.243 times that of the Sun, and is somewhat brighter, with a luminosity 1.564 times the Sun's.
The two inner planets of Kepler-68 A, Kepler-68 b and Kepler-68 c, have orbital periods of 5.399 and 9.605 days respectively, indicating that they orbit at 0.061 AU and 0.091 AU (i.e. 6.1 and 9.1% of the distance at which the Earth orbits the Sun), and are calculated to have masses equivalent to 8.3 and 4.8 times that of the Earth.
The third, inferred, planet, Kepler-68 c, is calculated to have a mass equivalent to 0.947 times that of Jupiter, and to orbit Kepler-68 A every 580 days, giving it an average orbital distance of 1.4 AU (1.4 times the distance at which the planer Earth orbits the Sun). However the gravitational influences exerted suggest that its orbit is not circular, rather has an eccentric orbit that takes it from 1.15 AU from the star at its closest to 1.65 AU at its furthest.
Kane calculated two possible ranges for the habitable zone of the Kepler-68 system, a conservative estimate, in which an Earth-like planet would be expected to host liquid water, and an optimistic estimate, within which a small rocky planet could possibly host liquid water. The conservative estimate ranges from 1.19 AU to 2.09 AU from the star, while the optimistic estimate ranges from 0.94 AU to 2.21 AU.
A top-down view of the Kepler-68 system showing the extent of the Habitable Zone and orbits of the planets. The physical scale depicted is 3.36 AU on a side. The conservative Habitable Zone is shown as light-gray and optimistic extension to the Habitable Zone is shown as dark-gray. The inner-most (unlabeled) orbit is that of planet b. Kane (2015).
This means that the distinctly un-Earth-like Kepler-68 c orbits entirely within the conservative habitable-zone of the system, which greatly reduces the possibility of an Earth-like planet aslo being found; the gravitational influence of very large planets makes it hard for smaller planets to occupy nearby orbits without being nudged onto completely different paths, and most likely being wither thrown out of the system altogether or falling into the star. However Kane calculates that a stable zone does exist within the habitable-zone that could host an Earth-like planet, between 1.8 AU and 1.9 AU from the star (outside the orbit of Kepler-68 c). This is in addition to the possibility of an Earth-like moon orbiting the large planet itself (a popular scenario in science fiction movies, but not one all planetary scientists are convinced is possible).
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