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I'm continuing my inquiry about the fictional planet I have described here: https://worldbuilding.stackexchange.com/questions/231162/length-of-seasons-on-a-planet-with-eliptical-orbit.

I'm now settled on the planet orbiting Delta Pavonis. According to data from Wikipedia and calculations, the habitable zone is from 0.78 to 1.56 AU.

My question is, what would be this planet's orbital period, keeping orbital eccentricity as high as possible while the planet stays within the habitable zone at all times?

I have tried calculating this using WolframAlpha, but it provides only formulae with the semi-major axis and primary and secondary mass, not eccentricity nor perihelion & aphelion distances.

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From the Keplerian-Newtonian two-body approximation (which is more than good enough for most fictional worldbuilding), eccentricity doesn't matter for orbital period. When the mass of the satellite is small enough to be ignorable, all orbits with the same semi-major axis around the same central body have the same period, regardless of eccentricity, periapsis distance, or apoapsis distance.

Add the periapsis distance to the apoapsis distance, and divide the resulting value by 2. That will give you the semi-major axis to plug into the orbital period formula.

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