Roche World

The Roche World is my* somewhat unimaginative name for a planet composed of two separate rocky masses orbiting each other but sharing a single atmosphere. Impossible, you say? Perhaps so, but read on for why I think not.

Binary stars come in three types:

  1. If both stars are within their Roche Lobes, they form a detached binary.
  2. If one star overflows its Roche Lobe and material starts to fall into the other star, they form a semi-detached binary.
  3. If both stars fill their Roche Lobes and material can flow freely between them, they form a contact binary.

Usually, people only worry about these things in relation to stars, but the fact is the equations that describe binary stars apply to any system of two massive bodies orbiting each other, be they enormous balls of fusion plasma, large lumps of solid rock, or cosmic-scale globs of tapioca pudding and Jello.

But far more interesting than the Jello, from a sci-fi point of view, are the large lumps of solid rock, i.e. binary planets. We don't know of any real-life binary planets, (unless you count Pluto) although Earth/Moon comes close. But we do know of a large number of binary asteroids, which suggests that, with a lack of evidence to the contrary, large binary planets should be possible.

So, one can have two large lumps of rock orbiting around each other, but can one get them close enough to share an atmosphere? In other words, can we make them big enough and close enough that the atmosphere's of both sub-planets overflow their Roche Lobes? One's first impression might be that one or both would go inside their Roche Limit and be pulled apart by the tide, but in fact if the two masses are of roughly equal mass and density the Roche Limit of both bodies is quite sufficiently small. After playing around with a spreadsheet on and off for a couple of days, I came up with the following:

Mass 1 (kg)                           4.68E+24
Radius 1 (m)                          6328000
Density 1 (g/cm^3)                    4.407013131
Surface Gravity (equatorial):         7.793911354
	
Mass 2 (kg)                           4.61E+24
Radius 2 (m)                          6285000
Density 2 (g/cm^3)                    4.432987126
Surface Gravity (equatorial):         7.786573708
	
Solid Roche Limit (m):                9108695.42
Liquid Roche Limit (m):	           15302739.18
	
Separation of Centers of Mass (m):    16750000
Mass Ratio:                           1.014685466
Roche Lobe Radius 1 (m)**:            6368069.03
Roche Lobe Radius 2 (m)**:            6325790.624
	
Lobe 1 Overflow (km):                 -40.06903044
Lobe 2 Overflow (km):                 -40.79062448

Day Length (hours):                   4.78776995

So, for the given masses, density, and separation between the bodies, the surface of each body would lie approximately 40 kilometers below the equipotential surface defining its Roche Lobe assuming that they are all spheres. Of course, they are not spheres, they are actually pointy egg shapes, but the approximation will do for my purposes right now, as the equations that define the exact shapes and surface-to-Lobe separations at all points are extremely difficult to work out and beyond the scope of this write-up. If we install an atmosphere of 60 kilometers depth, similar to Earth's, that leaves 20 or so extra kilometers of air outside the Roche Lobes of either planet, free to shift back and forth between the two, and further tweakings of the numbers can increase or decrease that amount by however much is desired.

There is, however, one itsy bitsy problem with the Roche World- it's unstable. Over geologic timescales, friction with the shared atmosphere will slowly reduce the angular velocity of the system, drawing the two bodies closer together until they either stick together into a weird peanut-shaped planet that would then continue to settle until it reached a reasonable approximation of a sphere after another few billion years, or one of them goes within its Roche Limit and starts to break up, raining firey destruction down on its counterpart until we are left with a single medium-sized planet and thick ring system. One hopes for coolness's sake that any intelligent life that might evolve on this world would find a way to save it. Then again, given the unlikelyhood of a contact binary planet forming naturally, perhaps the sufficiently advanced civilization (not us) that constructed it would do their best to preserve it.

Living on a Roche World

If there's life on one half of a Roche World, you can bet it'll have ended up on the other half as well. It's interesting to wonder what sort of sociological implications that would have. Would the inhabitants of one half look up in the sky to see green (or whatever the color of vegetation is here) continents and winding rivers and consider it to be some sort of Heaven, Hell, or Land of the Giants? The level of wierdness between the two halves would be orders of magnitude higher than the level of wierdness between Europe and Australia- stories of one-legged headless men with eyes in their chests might be all the more common.

The Roche World presents some interesting challenges to a technological civillization. One might consider flying an airship between the two worlds- in fact, that's what got me started figuring this all out- but the air around the L1 point would be a quite chaotic vortex where high altitude winds from either half smack together from opposite directions. Only someone extremely stupid, extremely brave, or with an extremely strong ship would dare make the attempt. Then again, similar things were said about circumnavigating the world in a balloon.

With the two halves of the double planet so close together, the L1-L3 Lagrange points would all be within the atmosphere, rather than way out in the middle of nowhere in space. The L4 and L5 points, being no further away from either body than the bodies are from themselves are out in space- but still close enough to collect a significant amount of gas escaping from the upper atmosphere. Additonally, due to the low mass ratio between the two bodies, L4 and L5 are unstable around a Roche World. Space stations and satelites put there would have to be designed to be a bit more corrosion resistant than is necessary in hard vacuum.

The closest stable orbit around a binary system is approximately 3 times farther from the barycenter than the two bodies are from each other. This might seem to make space launches a bit more difficult than they are from Earth, but consider that the Roche World has to rotate extremely quickly to keep from collapsing- so quickly, in fact, that the sun would be more like a strobelight. If one launches in the same direction as the planet rotates, just as we do on Earth, one gets a significant boost. Additionally, if you fly up to an altitude of 41 kilometers, you're already beyond the L2/L3 Lagrange point- you could quite literally fly a jetplane into orbit. Possibly even a Zeppelin, although I'd be worried about the gas bag popping.


*StrawberryFrog has informed me that the idea under nearly the same name (minus the space) appears in a Robert Forward series. See http://sites.inka.de/mips/reviews/Rocheworld.html Well, I'll be darned. Just goes to show that all of my great ideas have already occured to others.
**The listed Roche Lobe Radii are for a sphere with the same volume as the actual Roche Lobe. In real life, the Roche Lobes are egg-shaped, and tidal forces will stretch the planets into shapes that roughly follow the equipotential surfaces. If both planets exactly filled their Roche Lobes, the listed radii would be less than the actual distance between centers of mass of the planets, but they would stretch and deform into spindle-shapes which meet at the L1 Lagrange point.

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