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I want to have a two-world binary planet system where both have intelligent life, orbiting a single star. The two planets are assumed to be tidally locked to each other and orbit each other every 36 hours. Science allows for this just fine, my main concern is realistic distancing between the planets.

I want them distanced enough that gravity is maximumly halved on the inner-facing sides of the planets.

Since they are tidally locked, it would be weird for each to have its own magnetic poles, I think, so would it be possible for a system like this to share a magnetosphere or would they have to be too far apart?

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    $\begingroup$ You're asking two questions here, I think... one is how close the planets will be to each other to meet your gravitational requirements, the other is the magnetic field question. My gut instinct is that if both planets are gravitationally locked, they're either going to be too close for the relationship to be stable, or too far away for either planet to rotate quickly enough to generate a magnetic field, let alone share one. $\endgroup$ – Morris The Cat Oct 28 '19 at 17:02
  • $\begingroup$ Why on Earth would gravity be "maximumly halved on the inner-facing sides of the planets"? That is to say, why would gravitational acceleration be different on the inner-facing sides compared to the outer-facing sides? $\endgroup$ – AlexP Oct 28 '19 at 18:36
  • $\begingroup$ A 36 hour orbit means the planet’s are touching each other and ripping each other apart. Our moon orbits in 28 days. $\endgroup$ – Vogon Poet Oct 29 '19 at 3:35
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We can treat a planet as a magnetic dipole. In this case, the strength of the field scales as an inverse cube law (rather than the more familiar inverse square law), with some angular dependence. At the magnetic equator, we can write this as $$B(r)=B_S\left(\frac{r}{R_p}\right)^{-3}$$ where $R_p$ is the radius of the planet and $B_S$ is the magnetic field at the planet's surface. Therefore, if the other planet orbits, say, $10R_p$ away, the magnetic field coming from the other planet will be 0.1% of the surface field on the source planet. Even if we cut that in half, the field strength rises to only 1%, which is arguably not enough to provide the second planet with any of the benefits of the first.

For comparison, the Moon orbits Earth at 60 Earth radii, and is only about 1% the mass of Earth. Bringing the other planet close enough to experience a strong magnetic field would cause massive tidal effects, which would probably offset the benefits of a magnetic field!

The upside of a close orbit, of course, is that it reduces the time needed for the planets to become tidally locked to one another. That timescale goes as $\tau\propto r^6$, where $r$ is the distance between the centers of the planets. If $r$ is large, tidal locking may take a long time, but if $r$ is small, tidal locking can happen on reasonable timescales.

Some numbers

You seem to want the gravitational force from one planet to a person on the other planet's surface to be half the surface gravity of the other planet. That means that the distance from the center of one planet to the surface of the other is $\sqrt{2}R_p$. This means you'd have a surface magnetic field on the second planet of $B_S(\sqrt{2})^{-3}\approx0.35B_S$ - not bad.

On the other hand, you'd have some extremely strong tidal forces. The distance between the planet's cores is about $2.5R_p$. Tidal forces scale as $F_T\propto m/r^{3}$, where $m$ is the mass of the perturbing planet, and so you've got tidal forces about 1.3 million times as strong as the Earth experiences from the Moon.

This is . . . not a setup conducive to life.

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  • $\begingroup$ Would the tidal forces be problematic once the planets were locked to each other? $\endgroup$ – Starfish Prime Oct 28 '19 at 19:14
  • $\begingroup$ I would think so, yes. The calculations for tidal forces don't take rotation into account, so tidal locking presumably wouldn't change that. $\endgroup$ – HDE 226868 Oct 28 '19 at 19:39
  • $\begingroup$ Hmm. I was actually going to say something completely different, but it suddenly occurs to me that tidally locked binary planets like this probably aren't good candidates for having a dynamo-driven magnetic field in the first place, which might rather upset the OP's plans. Or indeed the plans of anyone wanting a habitable binary planetary system. $\endgroup$ – Starfish Prime Oct 28 '19 at 19:56

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