Dynamical Stability of Earth‐like Planetary Orbits in Binary Systems

This paper explores the stability of an Earth‐like planet orbiting a solar‐mass star in the presence of an outer‐lying intermediate‐mass companion. The overall goal is to estimate the fraction of binary systems that allow Earth‐like planets to remain stable over long timescales. We numerically determine the planet's ejection time τ ej over a range of companion masses (M C = 0.001–0.5 M ⊙ ), orbital eccentricities , and semimajor axes a . This suite of ∼40,000 numerical experiments suggests that the most important variables are the companion's mass M C and periastron distance R min = a(1 - ) to the primary star. At fixed M C , the ejection time is a steeply increasing function of R min over the range of parameter space considered here (although the ejection time has a distribution of values for a given R min ). Most of the integration times are limited to 10 Myr, but a small set of integrations extend to 500 Myr. For each companion mass, we find fitting formulae that approximate the mean ejection time as a function of R min . These functions can then be extrapolated to longer timescales. By combining the numerically determined ejection times with the observed distributions of orbital parameters for binary systems, we estimate that (at least) 50% of binaries allow an Earth‐like planet to remain stable over the 4.6 Gyr age of our solar system.