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If two planets (roughly Earth sized) in a binary planet system were tidal locked with one another what would be the necessary orbital angle and degree of axial tilt of each planet to satisfy the following circumstances?

  1. At least one planet has a large habitable zone (Earth-like climate) on the light side with mild seasons from which the other planet can be seen during the day.

  2. The day cycle of the same planet should be between 20 and 30 hours.

  3. The sun could be seen setting behind the other planet, and the corona of the sun could be seen each night.

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  • $\begingroup$ What is the diameter and brightness of the parent star? What do you mean a large habitable zone "on the light side" when the planet has a 20-30 hour day? $\endgroup$ – Slarty Oct 26 '17 at 1:32
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    $\begingroup$ I'm confused. You mention a habitable zone on a 'light side' and later mention a day. Do you want your planets tidally locked to the sun (Habitable zone is in eternal twilight, days and nights do not exist) or to eachother (Normal day/night cycle, with a planet hovering at a fixed point in the sky)? $\endgroup$ – UIDAlexD Oct 26 '17 at 15:29
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The 30 hour requirement is the stickler. For an earth sized planet this is very close to the Roche Limit. Get too close and the tidal forces are bigger than the gravitational forces and you end up with a disk of gravel.

Tidal force is an (inverse) 3rd power law. Distances and masses are sensitive.

Robert Forward wrote two books, Roche World and Return to Roche World about such a binary.

Note about geometer: Both planets will have a normal day -- there is no permanent dark side. However the hemispheres facing each other will in effect have a much shorter day. The other planet will be at a distance of somewhere around 40,000 km and so will present about a 25 degree disk. This will provide a daily 2 hour eclipse at the equator,getting somewhat shorter as you move poleward.

This assumes that the plane of their mutual orbit is the same as the plane of the orbit. If it's tilted, as is the earth/moon system then the eclipses will vary through the year. While this can be calculated, you may do better to make a scale model of the two planets, and play with a flashlight.

Multiparagraph response to Bob. @BobDylan A single planet can be tidally locked to its star, much like the moon is to the earth. For decades we thought that Mercury was one such planet. If it has an atmosphere, you get huge convection from the front face to the back face, and hurricane winds from the back face at the surface.

Two planets cannot both be locked to the primary while orbiting each other. They will lock to each other instead. Tidal force from a nearby planet is much stronger than the tide from the star.

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  • $\begingroup$ I guess this question really displayed my lack of knowledge on this subject. I was under the impression that when tidal locked planets orbited each other and the sun, one side of each planet would be continuously dark and the other continuously light. Is there, perhaps, a planetary circumstance where this would occur? Sorry for my ignorance. $\endgroup$ – BobDylan Oct 26 '17 at 5:29
  • $\begingroup$ Even if the plants were orbiting each other perpendicular to the plane of the ecliptic (the disc swept out by their centre of mass as they orbit around the sun) they would both still receive light and darkness on a seasonal basis. Because angular momentum is conserved the axis of rotation would always point in the same direction. But don't give up! have a think and ask another one. $\endgroup$ – Slarty Oct 26 '17 at 8:51
  • $\begingroup$ "However the hemispheres facing each other will in effect have a much shorter day" Shouldn't these regions have two sunrises (east => ducks behind other planet; comes from behind other planet => west) in the timespan of what amounts to a single sunrise on the outer regions (where they don't see the other planet, east => west)? $\endgroup$ – Flater Oct 26 '17 at 12:34
  • $\begingroup$ @Flater Yes. If the co-orbiting period were 24 hours the central point would have something like morning 6-10, eclipse, afternoon 2-6. As you move away form the equator, the eclipse period gets shorter. As you move east or west, the morning vs afternoon changes lengths. I would expect very different ecologies between the facing side and the back side $\endgroup$ – Sherwood Botsford Oct 30 '17 at 14:51

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