# Binary Planets

1. Dec 10, 2004

### Muon12

<Hmm. I just realized that this post would be better suited for the "Celestial Mechanics" forum. Would you mind moving this post, since it appears that I am unable to do so myself without posting twice?>
To begin with, does anyone know of the confirmed existence of or believe in the possibility of binary planetary systems in which two say, earth sized or larger bodies of equal mass or of nearly equal mass are orbiting around each other while orbiting around a star in a stable orbit? The image I think of when picturing such a system is that of a rope with two balls attached on either end moving forward (or in circular motion) while the balls rotate around a central point, essentially "falling" over one another, independant of the system's outside movement. My fascination lies within the axis of rotation between these two bodies, particularly because of the unique gravitational state which would exist within such a region of space (between the two planets). Would gravity (within the aforementioned planetary system) cancel out locally if one where to enter the region (axis) central to the binary planets rotational motion? How might this change depending on the distance between these two planets? I suppose that if they were too close together, they would simply collide due to the overwhelming gravitational attration drawing one to the other. But with enough rotational velocity around a fixed point, could earth-sized or larger bodies still remain apart at relatively close distances like say, two-thirds that of the distance between the earth and the moon? I am not much of a physisist, so I haven't been able to do the math for myself...
Oh, I should also add that the orbital motion of the binary planets in this instance would be arbitrarily close to uniform circular motion and non-elliptical. This is just to simplify the problem a little bit.

Last edited: Dec 11, 2004
2. Dec 11, 2004

### tony873004

Here's my guesses.

In our solar system, there are no double planets where the two masses are virtually equal. Pluto / Charon, and Earth / Moon are the only candidates, but in both cases the primary is much large than the secondary.

In other star ststems, planets smaller than Neptune have not been detected at all. Double planets of any size have not been discovered either. That's not to say that they don't exist. Equipment needs to get a lot better to confidently conclude that.

Gravity probably would cancel out at that point, but it would still not be a stable point, similar to the L1, L2, & L3 points. The smallest of pertubations from a solar tide or other sources would be magnified over time, expelling an object from that point. Chaos would then take over.

The two objects could be as close together as the larger one's Roche limit. Tidal forces would probably seperate them even more over time.

By "abbitrairly close" do you mean like Earth / Moon? Naturally the objects would want to circularize their orbits,and external pertubations would prevent them from ever reaching perfect.

3. Dec 11, 2004

### Muon12

By arbitrarily close I mean with an eccentricity close to zero (say e< or = to .003), leaving a single focal point of motion. Unlike the earth and moon, say that these two planets of near (give or take a few thousand metric tons) or equal mass orbit on opposite sides around a central point simultaneously, creating a possible "gravitational whirlpool" of sorts, although observations of this region might not seem quite as dramatic as that of an ocean whirlpool... I know this is out of the blue to add in, but I have to consider what life would be like for complex life forms like you and I if we were to live on one of these worlds, especially if they were covered with as much water as earth. Our tidal patterns would surely be interesting, if not terrifying.

4. Dec 11, 2004

### turbo

It is likely that such "twin" planets would be tidally locked so that one side of each faces the other all the time. Day and night would be a function of their orbits around the common center of mass, so the only hydrological tidal effect would be from the planets' sun. If the plane of their orbits was aligned properly, there would be lots of chances to see solar eclipses in a broad zone surrounding their equators on the mutually-facing hemispheres.

5. Dec 11, 2004

### Chronos

The orbits would be elliptical [Kepler's law thing] so there would not be a stable zone where gravity would cancel out.

6. Dec 12, 2004

### Muon12

Interesting. Could you elaborate why the orbits would have to be elliptical? Also, is there a minimum distance that the two bodies would have to be from one another for them to revolve without eventually colliding? Or is that primarily dependant upon the original circumstances of their meeting, when they first became trapped within one another's gravitational fields? I won't let this one go quickly, as you can tell.

7. Dec 13, 2004

### enigma

Staff Emeritus
Random perturbations. There are no circular orbits, or if there are, they don't stay that way for long. It may be possible (although not probable) for two planets to form in the configuration being described, but I don't think they'd stay that way long enough for them to cool down when the star is forming.

I seem to recall that one of our members put several simulations of multi-body systems on their own website. Several were stable, although only for "perfect" universes. Once any sort of perturbations were introduced, the system decayed very rapidly (less than 10 orbits).

8. Dec 13, 2004

### Nereid

Staff Emeritus
If you wait long enough, even in the absence of any external influences, the two 'planets' will collide. Why? Because the system loses energy through gravitational radiation, just like PSR1913+16, observations of which lead to Nobel prizes for Taylor and Hulse. Of course, if the planets have low masses, and their mutual orbit is very large, this time may be waayyy beyond a trillion years.

More likely, mutual tides (no 'planet' is perfectly rigid) will be the dominant factor, though all sorts of others may also be important (e.g. mass loss at the top of the atmospheres, encounters with other massive objects, passages through dense molecular clouds, differential radiation effects, collisions, mass accretion from interstellar grains, ....).

9. Dec 13, 2004

### pervect

Staff Emeritus
You'll need to keep the two planets further apart than the roche limit. This is only 2.5 planetary diameters when they have the same density, so they can get _very_ close before this happens, much closer than the earth & moon.

Here's a link to a worldbuilding website which discusses the Roche Limit

http://curriculum.calstatela.edu/courses/builders/lessons/less/les1/moons/roche.html

You might find the worldbuilding site interesting in and of itself, it offers technical information on the physics of "building" worlds to SF writers and would-be SF writers, so it talks a lot about the physics of "building" worlds.

Planets being very close together will undoubtedly tidal lock to each other.

The point at which the gravitatioanl attractions balance in a rotating coordiante system exits even when the planets have different masses. It's called the Lagrange point L1. It's a very interesting place which is very important to three body orbital dynamics. The dynamics allows for low energy orbital transfers via orbits that travel near these points - the math is a bit tricky, but it's gotten some publicity as the "Interplanetary Superhighway". The Genesis mission (which unortunately crashed when its chute failed to deploy), and a tour of Jupiters moons are two missions which have been planned using orbital dynamics based around the L1 points.

There's a SF book about a pair of orbiting worlds similar to what you describe called "Rocheworld" written by Robert Forward that you might be interested in. It's fiction, but it's "hard" fiction, written by a physicist. The writing from a literary point of view is not that great, alas.

Last edited by a moderator: Apr 21, 2017
10. Dec 13, 2004

### Jenab

I examined the problem of "twin Earths" once. I assumed a binary planet having each component habitable and of Earth's mass, with their mutual center of mass going around a star in a circular orbit with radius giving a subsolar temperature of 393.6K (same as Earth with respect to the sun).

For single habitable planets, not a moon of another planet, the star mass range is 0.8 to 1.5 solar masses. Twin Earths may occur only with stars in the very top end of this range: 1.3 to 1.5 solar masses. However, if a strong greenhouse effect can be presumed continuous, the allowable star mass can be lowered to about 1.1.

The upper bound on star mass is the result of an arbitrary decree that the star must remain on the main sequence a total of 3 billion years as a condition for any of its planets to become habitable. The luminosity is about proportionate to the mass raised to the fourth power. Big stars burn up faster than little stars do. So habitable planets in general occur only to main sequence stars of 1.5 solar masses or less.

The lower bound on the star's mass results from a condition that the twin Earths be neither rotationally bound to each other in mutual tidal lock nor tidally separated from each other by the star's gravity. Below a certain star mass, those two requirements are in conflict, meaning that the twin Earths, as defined, are not possible for stars whose masses are too low.

The planets' orbital distance from the star must remain at that having the required subsolar temperature, meaning that the distance between the twin-Earth barycenter and the star varies with the (about) square of the star's mass. Lessen the star's mass, and you even more greatly lessen the radius at which the twin-Earth orbits.

The tidal influence of the star increases inversely in proportion to the cube of the distance and directly in proportion to the star's mass. Using again the mass-luminosity relationship, the tidal force is proportional to the star's mass raised to the power of -5 (minus five, or thereabout).

In other words, as stars of progressively lower mass are considered, the components of the twin-Earth are limited to smaller and smaller separations. This is a greatest permitted separation.

Assuming that tidal friction spindown for an Earthlike planet occurs over three billion years when the components' are near enough that their tidal drag, one upon the other, is equal to that of the sun on Venus, there's a smallest permitted separation that will keep the pair freely rotating.

The greatest permitted separation becomes less than the least permitted separation if the star's mass is less than (about) 1.3 solar masses. So freely rotating twin Earths are possible only to stars of 1.3-1.5 solar masses.

Of course, if you don't mind month-or-so long nights, then you can dispense with the smallest permitted separation, and in that case you can put the planets as closely together as you wish, until tidal heating or the Roche limit puts an end to the habitability requirement. I assumed that free rotation was necessary to habitability.

Jerry Abbott

11. Dec 13, 2004

### pervect

Staff Emeritus
Interesting - I would have gone for putting the planets very close together, tidally locked, and making the orbital period 1-2 days, which would put them very close together .

It turns out that the Roche period depends on the density of the satellite and not on the characteristics of the primary - for a lunar satellite denisty, it turns out to be 10 hours (see "Roche period" in the John Stockton's URL below), and it would be even shorter if the moon had a higher density to match that of the Earth.

http://www.merlyn.demon.co.uk/gravity3.htm

So a 1-2 day orbit should be outside the Roche limit.

At this level of closeness, the planets will undoubtedly tidal lock before they cool down, both because the tidal locking goes as the sixth power of the distance (so it will happen Really Fast), and because so much heat would be generated by the tidal interactions that cooling probably wouldn't be possible until tidal lock was achieved.

What I haven't looked at closely is what happens when you add the Sun into this picture or other perturbing bodies. I think things would be generally OK though - you'd have the same level of solar tides on each planet that would act to slow down the "day", but you would have a much larger amount of angular momentum in the two-planet bound system than you had in the case of the Earth rotating around its axis. What this means is that the day would not vary with time nearly as much as the Earth's day has.

12. Dec 13, 2004

### Nereid

Staff Emeritus
In such a binary system, what would the 'geomagnetic' interactions be?

Would the rate of loss, from the combined system, of volatiles - esp H - be greater than the Earth currently experiences? (this isn't immediately obvious to me; the Earth's magnetic field does a sterling job of reducing the rate at which the atmosphere would otherwise be lost, due to the solar wind (and esp flares).

If you have tidal lock, how would plate tectonics be affected?

And so on.

13. Dec 13, 2004

### tony873004

With a tidal lock, the planets wouldn't experience any tides if their orbits were round.

I'm not sure, but doesn't the Roche limit apply for forming objects only. Two Earths would also have their own gravitational strength holding them together. Even if the two Earths were only a few hundred miles, surface to surface, Earth 1 would exert about 0.96 g on the near side of Earth 2, and about 0.12 g on the far side of Earth 2, for a difference of 0.84 g across the planet. But Earth 2 would have 1g holding it together at the surface on the near side, and 1g holding it together at the surface on the far side, for a total of 2g across the planet (unlike an object trying to form), so it wouldn't fall apart.

Just my guess

Last edited: Dec 14, 2004
14. Dec 14, 2004

### LURCH

Yes, they would be elliptical in the real universe, but wouldn't they be elliptical around a common center of gravity (where gravitation from the two would cancel out)?

15. Dec 14, 2004

### pervect

Staff Emeritus
If the orbit was elliptical, there would be daily tides, due to the difference between closest approach and furthest approach of the binary orbits.

These tides would dissipate energy - because it dissipates energy, orbits tends to circularize. Because the planets are so close together, this circularizaton process would tend to happen fairly quickly. (But I don't have a timescale).

The perturbing effects of the sun (and other bodies, the sun is probably the most significant, however) would prevent the circularization process from being complete.

I haven't attempted to work out the details of how close to circular the orbits would become, or how fast (the timescale) at which circularization would occur.

For a quick but slightly more detailed discussion of tidal orbit circularization see for instance:

http://yarchive.net/space/orbits/tidal_circularize.html

Last edited: Dec 14, 2004
16. Dec 14, 2004

### pervect

Staff Emeritus
It's not clear to me that anyone knows exactly why the earth has a magnetic field. If I'm wrong, perhaps you or someone could point me to a link that discusses this, it's not something I'm extremely familiar with. My impression, though, is that it's generally understood that currents through the conducting nickel-iron core cause the magnetic field, but its not clear what keeps the magnetic field from decaying, or why it reverses direction periodically.

So it's a bit hard to answer whether or not the binary planets would have a magnetic field without a better understanding of why the Earth has a magnetic field.

As far as plate tectonic effects go, I don't see offhand why they should be any different. Sure, the binary earth pair will be slightly off-round, but that shouldn't make any practical difference to the internal structure that I can see. I may be missing something here as well, but so far I haven't been able to think of any plausible reason why the plate tectonics would be different due just to the presence of (in effect) an extremely large moon. If the material composition of the planets were different, or the sizes were siginficantly different from Earth, that would probably affect the tectonics, though.

Quick question - are there any planets in the solar system that have plate tectonics other than Earth? Do we know?

17. Dec 14, 2004

### Nereid

Staff Emeritus
Assume both planets had a magnetic field the same as Earth's ... how would they interact with each other? with the solar wind?

As you say, what keeps the Earth's magnetic field going (and reversing every so often) isn't well understood, so we don't really know what effect a twin - nearby? - would have.
What drives plate tectonics? Interior heat ... residual heat from the Earth's formation ... and rotation. If the Earth's rotation rate were slower (tidal locking, remember?), at what point would plate tectonics stop? Once stopped, it may never re-start; once stopped, the carbon-cycle (?) would shut down.

I forgot one more important factor - precession. Would an Earth twin lead to a runaway greenhouse? a snowball Earth?
AFAIK, there are none; for starters, only planets lacking wall-to-wall craters would be candidates, so apart from Earth, only Venus, Mars, Io, Europa, Titan and Triton qualify (we know too little about Pluto and Charon). Venus seems to be missing plate tectonics, and if Mars had it, it stopped a very long time ago (Olympus Mons would be impossible if there were moving plates). Io's vulcanism is not due to plate tectonics; any such would be minor. Europa does seem to have something a little like plate tectonics; Triton is too poorly studied to say, and we'll have to wait at least until Huygens does its thing to know about Titan!

18. Dec 15, 2004

### Chronos

They have no choice but to be elliptical because the speed of gravity is not infinite - a frame dragging and gravitational wave thing. My crackpot theory of the day is: the speed of gravity can be derived solely from these effects. I further predict it will be exactly the same as the speed of light.

Last edited: Dec 15, 2004
19. Dec 15, 2004

### pervect

Staff Emeritus
An interesting question. A real wild-ass guess would have the planets poles anti-aligning because it's the lowest energy state. What that would mean to the magnetosphere I'm not sure.

The tidal lock would be between the pair of planets, though (not to the sun) - the planets will be rotating at about the same rate that the Earth does relative to the fixed stars.

Another interesting question. I think precession is going to be hellishly rapid, but I cant fully justify that without more thought. (Certainly low orbit satellites have fast orbital plane precession, though).

But it's not clear that this will necessarily be a problem unless the precession becomes chaotic. If the moon stabalizes the Earth, the binary planet might very well do the same - except enormously more so.

20. Dec 15, 2004

### pervect

Staff Emeritus
I don't think a simple thing like a binary pair of planets is going to say much about the speed of gravity. Binary neutron stars have enough gravity to generate relativistic effects - but I would expect that binary planets would not.