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Author Topic: What controls the stability of a binary/double planet system?  (Read 3431 times)

Offline Somes J

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Hello. I have a question concerning the stability of a hypothetical binary planet system.

The hypothetical system is an Earthlike planet orbiting a relatively bright K class star at a distance of maybe .5-.7 AU. The planet is roughly Earth-sized and it has a very large moon, around 1/3 the mass of Earth (the idea here is that the moon would also be capable of supporting an Earthlike environment - basically this is the old Earthlike double planet concept). The moon would orbit the planet at a distance of around 40-50,000 km, with a period of around 30-35 hours, and both the planet and moon would be tidally locked to each other (like Pluto and Charon in our solar system). The planet's axis would be inclined at roughly 20-25 degrees (like Earth's) and the moon would orbit in the plane of the planet's equator. The planet would have no other natural satellites.

Now, the issue that's troubling me is tides. There would be huge tides (thousands of times ours), obviously, but since the planets are mutually tidelocked they'd be fixed so I imagine they'd only show up as a distortion in both worlds' overall shape, as generally unnoticed as the equatorial bulge on Earth. But there might also be variable tides, created by the eccentricity of the moon's orbit and any precession-type motions of the axis of the planet relative to the moon's orbital plane etc. Given how close together these worlds are even relatively small secondary variable tides could be catastrophic at the surface (oceans being raised many meters and penetrating deep inland etc.).

Say the moon starts out with a very very low eccentricity, like Neptune's moon Triton. Both planets may have been terraformed at some point in the deep geologic past, so maybe the aliens adjusted the orbit or something if that's necessary to justify it. But that was long, long ago, so my concern is would such an extremely circular orbit naturally stay extremely circular? From what I've heard strong tides tend to circularize orbits, and I've read that tidal dissipation scales by radius^6 whereas the strength of the tides only scales by radius^3, so based on that I'd think the near-perfectly circular orbit would be quite stable (the two worlds would gradually draw closer together as the solar tide took angular momentum out of the arrangement but it shouldn't become much more eccentric) but my knowledge of the relevant physics is extremely limited. I'm only an aspiring science fiction writer, not a professional astronomer.

Similarly I'd imagine that the huge tidal forces involved would keep the rotational axis of both the planet and the moon very close to 90 degrees to the plane of the moon's orbit, but again I lack the knowledge to be sure.

Would the inclined plane of the moon's orbit relative to the plane of the planet's orbit around the sun be a complication?

Basically I'm asking whether these worlds could realistically stay nice and Earthlike without artificial intervention or whether, once the terraformers were gone, we'd be back to looking at some sort of Io-like hellhole with massive ocean tides in a geologic instant. And if the latter, what could I do to make such an arrangement more plausibly stable?

Also, suppose we had a similar scenario but the moon was smaller, more like our moon or Mercury. Would that also be stable?

Sorry if this was a little long. Thanks, it'd be a huge help if I could get an answer.




Mod edit - formatted subject as a question - please do this to help keep the forum tidy and easier to navigate. Thanks.
« Last Edit: 19/01/2011 11:49:24 by BenV »


 

Offline Soul Surfer

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Interesting description.  Remember to that the solar tides would be considerably greater than the 1/3 of the lunar tides that we have on earth so there would always be substantial tides on the planet even if the binary planets orbits were reasonably stabilised.

Also the choice of an obit for the moon inclined at the axis rather than in the plane of the solar system is interesting.  This implies a fission origin as a result of excessive angular momentum in the planet's early life rather than a collision origin as is assumed for the earth's moon.  This would be affected by the sun and would be moved but I cannot say how it would evolve with time.
 

Offline CliffordK

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Interesting concept.

I was going to say that the sizes would have to be equal...  but I snagged this diagram off of Wikipedia.

http://en.wikipedia.org/wiki/Orbit



So, what you've done is slowed down the day to increase the equivalent distance of the geostationary orbit.

One Earth, I've wondered a bit about the Pangaea theory.  It just doesn't make a lot of sense.  The water should cover the planet evenly from the center of gravity, or the center of the earth-moon gravitational system.  With a tidally locked planet/moon, the extra gravitational pull might be sufficient enough to cause the building of continents, probably on the side facing the moon.  Remember, you would no longer have moving tides (except that caused by the sun), but rather a static tide.

Many people blame the moon for our active plate tectonics, while potentially devastating, they are also responsible for bringing heavy minerals up from the core of the earth, and potentially renewing the atmosphere.
 

Offline Somes J

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The water should cover the planet evenly from the center of gravity, or the center of the earth-moon gravitational system.  With a tidally locked planet/moon, the extra gravitational pull might be sufficient enough to cause the building of continents, probably on the side facing the moon.

I figure you'd probably have a situation similar to the (IIRC ~20 km high) equatorial bulge on Earth. The oceans and solid body of the planet would be permanently deformed, but it wouldn't ordinarily be perceptible to the planet's inhabitants. I could be wrong about that, maybe there'd be a deep ocean on the moon-facing side or something, but I'd think the plastic rock of the mantle would have had plenty of time to flow and fill out the tidal bulge.

Quote
Many people blame the moon for our active plate tectonics, while potentially devastating, they are also responsible for bringing heavy minerals up from the core of the earth, and potentially renewing the atmosphere.

Well with the sun being closer the solar tide would be stronger than our lunar tide, so I think that angle should be pretty much covered in any case.

My big worry is whether the system is stable enough that it doesn't drift into a configuration that generates scary variable super-tides.
 

Offline CliffordK

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I think the "super tides" would only be a problem if you loose the tidal lock.  With the tidal lock, you have no relative movement to cause the tides (except, as you mentioned with reference to the sun).  The fixed tide will deform the shape of the planet and define the continents. 

However.

When you read about the moon, there is a concept called Libration.

http://en.wikipedia.org/wiki/Orbit_of_the_Moon#Libration

As I understand it, it is a slight drift in the tidal lock due to influences of the sun.
 

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