Ever since I worked on the Kepler data I’ve been aware that many planets around Kepler stars are in a highly elliptical orbit. A more recent ArXiV paper showed that more than half of exoplanets are in highly elliptical orbits.

I decided to use binary star orbits as a model for planetary orbits. The stars of binary stars are seldom of the same size, more frequently one is much smaller than the other. It turns out that there are currently 1866 spectroscopic binaries for whom the orbital eccentricity has been measured to known accuracy.

First the solar system. An eccentricity of 0 is circular. An eccentricity of 1 is parabolic – an infinitely long ellipse. The eccentricities to be found in the solar system include:
Venus 0.0068
Neptune 0.0086
Earth 0.0167
Jupiter 0.0484
Mercury 0.2056
Pluto 0.248.

Using all 1866 spectroscopic binaries I found that only 3% had an eccentricity less than Venus, 7% less than Earth, 12% less than Jupiter and 45% less than Pluto. Strongly elliptic orbits are the norm, near-circular orbits like those in our Solar System are rare.

It was already known that the upper limit on the ellipticity depends on orbital radius, and increases with increasing radius, though the reason for this is still obscure. Like the Kepler planets, most binary stars orbit much closer to their parent star than Earth to the Sun. Taking only those 49 spectroscopic binaries with an orbital period between 330 and 400 days (35 days either way from Earth’s) I was surprised to find that the relationship between cumulative probability and eccentricity is exactly linear out to an eccentricity of 0.7.

So, treating this as the so-called habitable zone, only 2.3% of binaries have an eccentricity less than that of Earth and only 34% have an eccentricity less than Pluto. The expected eccentricity of a binary in the habitable zone is e = 0.36, which is enough to transport any planet from inside to outside the habitable zone.

So, perhaps only one in twenty planets that are supposedly in the so-called habitable zone actually resides within the habitable zone.

Can’t comment on the figures, but here on Earth we have life forms that go through seasonal active and dormant cycles each year, and taking that to extremes might be feasible on some of those planets that pop in and out of the habitable zone.