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I'm worldbuilding a binary planetary system - the orbit of the system around the star can be slightly elliptical, but I'd prefer only slightly. The star mass is ~0.72 solar mass, and the two planets are 0.84 earth mass and 0.79 earth mass, respectively. The binary planetary system has a period of about 3.4 earth days and a distance of 1.12*10^8 m. Before I make any calendars, I thought it would prudent to ask about this. Basically, are there any qualities of orbital mechanics that would cause the planets (which are in the habitable zone) to orbit their barycenter such that the total number of days fit evenly into a year?

I suspect the answer is no, and that the year will not be a convenient whole number of days, especially since that doesn't happen with the earth-moon system and the only difference is that it's not a singular planet... but it seemed plausible enough to ask before I decide the calendar or orbital placement.

And yes, I know I can technically just handwave this and say it fits perfectly, but the suspension of disbelief required for that to be the case annoys me and I would not make the year last a whole number of days if there was not a legitimate reason for it to fall into that pattern.

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  • $\begingroup$ You're worried about your own suspension of disbelief? Unless you're feeding your worldbuilding efforts to astronomers, I very much doubt anyone would complain about a detail so small. We humans gladly refer to "365 days in a year!" while barely giving lip service to leap years and not caring in the slightest about leap hours, minutes and seconds. Nobody (including most astronomers) gets annoyed when calendars aren't exactly 365.2422 days long. (And I get a chance to link to my latest worldbuilding advice Meta page!. Woo-hoo!) $\endgroup$
    – JBH
    Commented Oct 26 at 22:06
  • $\begingroup$ The term "planetary system" usually means a system of planets orbiting a star. So "a binary planetary system" sounds like a binary star system with planets. If you are not asking about a star system with a binary star and planets you should change the title to reflect what you are asking about. $\endgroup$
    – M. A. Golding
    Commented Oct 27 at 4:39
  • $\begingroup$ @JBH I agree, humans don't care very much about that. But I'd also point out that the difference becomes a lot more important if your day is longer, at least in my opinion, and there are wider intervals of time which makes approximations less likely to be accurate. $\endgroup$
    – Max Bird
    Commented Oct 27 at 6:26
  • $\begingroup$ @M.A.Golding This is useful for me to know... if my wording was confusing, do you have a suggestion that would be clearer? $\endgroup$
    – Max Bird
    Commented Oct 27 at 6:27

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No, there is no particular reason for the orbital period of the components of a binary planet to be a divisor of the orbital period of the binary system as a whole around the star.

(Our Moon is so large that the Earth-Moon system is almost a double planet. The barycenter of the system is offset from the center of the Earth by about three quarters of Earth's radius.)

And, moreover, you really shouldn't handwave it away. The chances of two arbitrary unrelated numbers being in a straightforward relationship are between zero and none. What you can handwave is to make them almost fit a straightforward relationship, just like for example for Earth the year is an integer number of days plus almost exactly one quarter of a day so that a correction is needed only three times every four hundred years; or like how 235 synodic months make almost exactly 19 years.

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