<p>One can certainly imagine double planet &quot;Rocheworlds&quot; (like the one in Robert Forward's eponymous novel) where two terrestrial worlds fill their Roche lobes until they touch.</p>
<p>On its own this is perfectly fine: there are indeed a fair number of <a href="https://en.wikipedia.org/wiki/90_Antiope" rel="nofollow noreferrer">asteroids</a> and <a href="https://en.wikipedia.org/wiki/79360_Sila%E2%80%93Nunam" rel="nofollow noreferrer">trans-Neptunian objects</a> forming tight pairs or a merged dumbbell shaped <a href="https://en.wikipedia.org/wiki/Contact_binary_(small_Solar_System_body)" rel="nofollow noreferrer">contact binary</a>. The planets would be tidally locked to each other, not dissipating energy through tides.</p>
<p>The problem is that when the rest of the solar system is taken into account tidal dissipation begins to matter. The tides will cause the planets to move a bit relative to each other, and strong tidal dissipation will dampen that motion - dragging them inwards. Hence, relatively quickly since the tidal dissipation would be strong in big and soft terrestrials, the double planet would merge.</p>
<p>The orbital speed calculation looks a bit messy. Basically, the mass of the touching planets (that we need for the speed) is their density times the volume of their Roche lobe, which lacks analytical expression. However, one can <a href="https://en.wikipedia.org/wiki/Roche_lobe#Geometry" rel="nofollow noreferrer">approximate them fairly well as spheres</a> of radius (see also <a href="http://adsabs.harvard.edu/full/1983ApJ...268..368E" rel="nofollow noreferrer">Eggleton</a>) <span class="math-container">$r=0.38 R$</span> where <span class="math-container">$R$</span> is their orbital distance. So we get <span class="math-container">$$M\approx 0.2298 \rho R^3.$$</span> Kepler's law gives us the period <span class="math-container">$$T^2 = \left(\frac{4\pi^2}{2GM}\right)R^3$$</span> (note the <span class="math-container">$2GM$</span> term rather than <span class="math-container">$GM$</span> - this is for a double pair), or <span class="math-container">$$T = \sqrt{\frac{2\pi^2}{ 0.2298 G \rho}}.$$</span> For Earth-density worlds I get <span class="math-container">$T=4.2512$</span> hours. Note that this is independent of the size of the system!</p>
<p>Can systems like this form? Probably. Can they remain long enough that life emerges on the planets and they become Earth-like? Hard to tell, but I suspect the answer is something like &quot;yes, if they start sufficiently far away from each other then they will spiral in slowly enough that there is a biosphere when things get really tight.&quot; I suspect such coincidences in time and formation are rare. But the universe is large.</p>

CC BY-SA 4.0
2020-09-23T12:32:53.943Z
I see, it's independent of the size of the system for a *constant density*, like a pair of [these Earth-density giants](https://space.stackexchange.com/q/14383/12102)
uhoh
CC BY-SA 4.0
2020-09-23T12:25:17.917Z
2020-09-23T12:25:17.917Z
Anders Sandberg
<p>If there were two Earth-like planets in a tight orbit around each other, how close could they be to each other without colliding?
How quickly would they have to orbit to be stable?
Would they be habitable?
Could something similar to a Roche lobe form from their atmospheres?</p>

<orbit>
What is the tightest orbit binary planets can orbit each other?
Kaden Spencer
# What is the tightest orbit binary planets can orbit each other?

(Asked by: username_0 on 2020-09-21)

If there were two Earth-like planets in a tight orbit around each other, how close could they be to each other without colliding?
How quickly would they have to orbit to be stable?
Would they be habitable?
Could something similar to a Roche lobe form from their atmospheres?

**Tags:** orbit

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## 1 answers

### Answer by username_1 on 2020-09-23. Score: 2

One can certainly imagine double planet "Rocheworlds" (like the one in Robert Forward's eponymous novel) where two terrestrial worlds fill their Roche lobes until they touch.

On its own this is perfectly fine: there are indeed a fair number of [asteroids](https://en.wikipedia.org/wiki/90_Antiope) and [trans-Neptunian objects](https://en.wikipedia.org/wiki/79360_Sila%E2%80%93Nunam) forming tight pairs or a merged dumbbell shaped [contact binary](https://en.wikipedia.org/wiki/Contact_binary_(small_Solar_System_body)). The planets would be tidally locked to each other, not dissipating energy through tides.

The problem is that when the rest of the solar system is taken into account tidal dissipation begins to matter. The tides will cause the planets to move a bit relative to each other, and strong tidal dissipation will dampen that motion - dragging them inwards. Hence, relatively quickly since the tidal dissipation would be strong in big and soft terrestrials, the double planet would merge.

The orbital speed calculation looks a bit messy. Basically, the mass of the touching planets (that we need for the speed) is their density times the volume of their Roche lobe, which lacks analytical expression. However, one can [approximate them fairly well as spheres](https://en.wikipedia.org/wiki/Roche_lobe#Geometry) of radius (see also [Eggleton](http://adsabs.harvard.edu/full/1983ApJ...268..368E)) $r=0.38 R$ where $R$ is their orbital distance. So we get $$M\approx 0.2298 \rho R^3.$$ Kepler's law gives us the period $$T^2 = \left(\frac{4\pi^2}{2GM}\right)R^3$$ (note the $2GM$ term rather than $GM$ - this is for a double pair), or $$T = \sqrt{\frac{2\pi^2}{ 0.2298 G \rho}}.$$ For Earth-density worlds I get $T=4.2512$ hours. Note that this is independent of the size of the system!

Can systems like this form? Probably. Can they remain long enough that life emerges on the planets and they become Earth-like? Hard to tell, but I suspect the answer is something like "yes, if they start sufficiently far away from each other then they will spiral in slowly enough that there is a biosphere when things get really tight." I suspect such coincidences in time and formation are rare. But the universe is large.

> **Comments:**
> **username_2**: I see, it's independent of the size of the system for a *constant density*, like a pair of [these Earth-density giants](https://space.stackexchange.com/q/14383/12102)  

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