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Good day! For the story I have prepared information about the binary planet system.

The action will take place on the smaller (minor) of the two planets, which is supposed to be habitable. The habitability of the larger planet is not obligatory, but it is not excluded.

I would be grateful if you shared your opinion on whether a habitable world is possible on such a small planet with the given data.

I have some difficulties with calculating the duration and periodicity of eclipses on a small planet. By analogy with the Pluto-Charon system, eclipses should be at least 2 times a year. I got eclipses twice a year every day during 4 days lasting from 13 to 22 minutes (and I am not sure that I calculated correctly). It would be great if someone could give me some advice.

Below is the data about the system.

General data

  1. Star: 0.7 solar masses.
  2. Semi-major axis of orbit - 105,781,944km, ~0.71AU.
  3. Orbital period - 259 Earth days, 13 Earth hours.

Data on the binary planet system

  1. Semi-major axis - 57,349km
  2. Mass of the major planet - 1 Earth
  3. Mass of the minor planet - 0.5 Earth
  4. Orbital period of the binary system - 31 hours
  5. Both planets are tidally locked

Minor planet

  1. Gravitational acceleration ~9.01ms-2 (92% of Earth's gravity)
  2. Radius of the planet ~4704km
  3. Density of the planet ~6853.15kgm-3 or 6.85315gcm-3
  4. Axial tilt of the planet ~25°
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  • $\begingroup$ Some of this data isn't particularly relevant to habitability (e.g., axial tilt), but at a glance, I can't see why this isn't inside the envelope. Bear in mind per the help center that our main focus is imaginary worlds, so our sweet spot is believability, not factual reality. If believability is what you're looking for, I believe you're good to go with a fun idea. $\endgroup$
    – JBH
    Commented Sep 9 at 0:47
  • $\begingroup$ On the other hand... if anyone knows of a good website that ideally helps worldbuilders calculate these details in a realistic manner, that would be a great addition to the List of Worldbuilding Resources. $\endgroup$
    – JBH
    Commented Sep 9 at 0:50
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    $\begingroup$ Of course, I don't claim scientific accuracy, just wanted to create a more or less believable world. This is my first attempt. If it seems that way to you, then I'm very glad! $\endgroup$
    – Tanya
    Commented Sep 9 at 0:58
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    $\begingroup$ @Tanya Thanks, have edited for you, it's a good idea to use the @[username here] notation when you reply to a comment so that the person who left it gets a specific notification. $\endgroup$
    – Ash
    Commented Sep 9 at 5:48
  • $\begingroup$ @Ash Thank you very, very much! $\endgroup$
    – Tanya
    Commented Sep 9 at 5:56

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According to this handy calculator the Goldilocks Zone of this system is from 0.7 to 1.0 AU, your worlds orbit right at the inner edge of this, they're going to be fairly warm with an Earthlike atmosphere, on the edge of runaway greenhouse in fact. Axial tilt of 25° means the seasons are going to be ~10% more pronounced than what we experience on Earth and the tropics are 50° across.

As currently written there is no indication that the rotation of the binary planets around their barycentre has any tilt from their ecliptic plane, if that is the case then ellipses will be a daily occurrence that one can set their watch to with a fixed shadow tracks across both worlds. Tilting the rotation compared to the elliptic will create more earthlike eclipse pairs, in this system they'll be 129 days, 18 hours, and change apart instead of six months. I'm not sure how to go about the celestial sphere plots that would be required to predict the intervals between these pairs.

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  • $\begingroup$ Thank you! Then I'll move them further away from the star. The orbit was calculated based on some Wikipedia data :) $\endgroup$
    – Tanya
    Commented Sep 9 at 6:04
  • $\begingroup$ @Tanya Wouldn't need to be far, 0.09AU would put them dead centre, so would a slightly smaller, cooler star. $\endgroup$
    – Ash
    Commented Sep 9 at 6:49
  • $\begingroup$ Thank you, @Ash! Yes, I just noticed thanks to your calculator that I didn't take into account the temperature of the star. For about 5000K it looks normal. $\endgroup$
    – Tanya
    Commented Sep 9 at 11:37
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    $\begingroup$ @Tanya You have listed the axial tilt, obliquity, of the minor planet i.e. it's individual tilt compare to the system elliptic, this has no effect on the rate of binary eclipses. What you need to alter to change the rate of eclipses of the binary pair is the tilt of the axis of rotation around their shared Barycentre, as long as that axis is perpendicular to the elliptic eclipses occur daily once you tilt that axis compared to the elliptic you reduce the rate of eclipses. Cont... $\endgroup$
    – Ash
    Commented Sep 16 at 9:57
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    $\begingroup$ @Tanya The Barycentre for the Pluto-Charon system is practically inside Pluto because it's ~10x more massive than Charon very close. Your scenario is going to have a Barycentre far outside the worlds, approx. 1/3 of the distance from the centre of the major planet ~13000km above it's surface because the mass difference is so much lower and they're so much farther apart. So the axial tilt of the worlds is not necessarily indicative of the axial tilt of their mutual rotation, you can have the minor planet in equatorial orbit of the major one but you need to say so. $\endgroup$
    – Ash
    Commented Sep 16 at 10:23

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