Expert: Courtney Seligman - 3/28/2011

Question
QUESTION: Hello,

I had asked this question of another expert, but he mentioned his knowledge of orbital mechanics wasn't quite enough to fully answer my question. If you also think this is the wrong place to be asking this question, I'm open to suggestions of places or other experts to ask.

PUNCH LINE
Is it possible to have a planet "suspended" in between two binary stars, rotating on its axis but not orbiting the stars?

REASONING
The center of gravity in a binary system remains stationary relative to the binary system (though it may move relative to the rest of space) - it is stable. In addition, there should be "zero" gravity at this point - the gravitational pull on the planet by the two stars should be perfectly cancelled out. If both of these assumptions are true, a planet should be able to exist at this point in space, essentially motionless relative to the binary system except for its rotation.

You can see my initial question (which was a bit longer than this one) as well as the answers here: http://en.allexperts.com/q/Astronomy-1360/2011/3/Planetary-possibilities-binary-

ANSWER: You're basically asking if you could have a planet orbit between two binary stars at the same rate that the stars orbit each other, so that its position relative to each star remains the same.

The answer to your question is yes, but not exactly as you would like to suppose. What you're talking about is identical to one of the so-called Lagrange Points, specifically the one between a planet and its star, such as the location of the SOHO spacecraft, which has a "halo" orbit around the Lagrange Point (L1) between the Earth and Sun. (For more details about these points, see Lagrange Points, at http://cseligman.com/text/sky/lagrange.htm, and The Trojan Asteroids, linked from the page on Lagrange Points.

However, as noted in the discussion on that page, objects at L1, L2, and L3 have unstable orbits, and require extra forces (such as rocket jets) to keep them near the points for more than a very short period of time. So although a planet could orbit in the way you're wondering about for a little while, it would soon drift away from that point, and would almost certainly be eventually ejected from the system.

---------- FOLLOW-UP ----------

QUESTION: Thank you for the quick response.

That's not quite what I'm asking, no. I actually don't want the planet to orbit anything in the system, nor will its distance between each star remain constant, as the stars would have elliptical orbits. Rather, its position relative to the *system* remains the same. Also, as I understood it, the stars don't technically orbit each other, but a common point, the center of gravity or mass. Please correct my thinking if I'm wrong on that. Because that one assumption is the foundation of my model.

I'm attaching pictures of what I think is going on to perhaps clear my explaining up a little. Forgive the quality or lack thereof - I'm sure things are horribly out of proportion. But it gets the basic idea.

In the first figure, we have a center of mass A around which objects orbit, A in this model being a star, and the orbit of the primary object in this model, the planet B, and a secondary object C in the L1 orbit. A basic setup.

Figure two shows what I think you mean by using a Lagrange point within a binary system. Again, we have the center of gravity A around which each star B1 and B2 orbit. This is where my thinking might be most off, but if the star B1 replaces the planet in the first model and the center of gravity A which is nothing but empty space in this model is the same as a sun, then perhaps the lagrange point works the same as in the basic model. So I put it in the same place. But I don't know how the orbit of B2 will affect the L1 orbit. And now the planet is C, and is orbiting on L1.

Regardless of how my thinking is off in figure two, figure three shows my actual intent. Once again, a binary system, but with no L1 shown. Rather, planet C is at point A, where the center of gravity is. It is not orbiting anything (except as part of the system as a whole orbiting the center of the galaxy, as shown in figure 4); it essentially takes the place of the sun in the basic model of figure 1. Now, for things to work in that model, whatever is at point A must be of great enough mass to cause other objects to orbit around it.

But in a binary system, the stars orbit a point in space containing negligible mass, so my main question is whether adding a planet there is possible. It seems like it should be, but I'm wondering if that's because I have a simplistic understanding, and the gravitational anomalies that would occur would be much more complex than I could possibly comprehend.

So what do you think? Crazy, I know. But I'm quite curious whether this would work.

ANSWER: I see. You're wondering whether the planet could remain stationary at the so-called center of mass (or barycenter) of the system. Unfortunately, the answer to that is "no", unless you make the two stars exactly the same mass.

The center of mass is located between the two stars at a point which is proportional to their mass -- so if star A is twice as heavy as star B, star A would be twice as close to the center of mass (at all times) than star B, regardless of where either was in their mutual orbit(s) around the center of mass. Whereas if the two stars were exactly the same mass, the center of mass would lie exactly halfway between them. In that case, their gravitational force on a planet at the center of mass would exactly balance -- but in the same way as in the case of Lagrange Point L1, in which the balance is very precarious, and even the slightest motion of the planet from the exact center of mass would quickly cause it to move away from that point, and eventually (almost certainly) be ejected from the system.

So in the particular case noted in the previous paragraph, there is a sort of precarious "yes, that could happen", but also "no, that could not be a stable situation for any significant period of time".

If the two stars were NOT the same mass, the situation would be even worse. In the example where star A is twice as massive, and therefore twice as close to the center of mass, its gravitational pull on a planet at the center of mass would be eight times stronger than that of star B (2x because of its mass, and 4x because it is closer), so a planet couldn't remain at the center of mass of any non-equal-mass system for even a short period of time.

Now, if you wanted to change the scenario to putting a spacecraft in between the two stars, so that the crew of the spacecraft could observe the stars "up close and personal", the fact that a spacecraft could use motive power to change or maintain its position might allow it to remain close to the center of mass for a while, if the two stars were of nearly equal mass. If they weren't, even that wouldn't work for long (too much power would be required), but a quasi-stable orbit might be attained at either star's L1 point, presuming that isn't so close to the star that it would vaporize the spacecraft.

There is, however, a place that you could put a planet (or a spacecraft) in a more or less stable orbit for long periods of time -- namely, either the L4 or L5 ("Trojan Asteroid") points, 60 degrees ahead of or behind whichever star is considered to be orbiting the other one. That wouldn't keep the planet (or spacecraft) in a stationary position, as it would have the same orbital size and period as the star it was ahead of or behind; but it would be a stable situation, whereas any position between the two stars would either be completely unstable, or at best quasi-stable.

I hope this answered your question adequately; but if you have any other questions you'd like to ask, or a different approach that you'd like to try, let me know and I'll do what I can to give you a satisfactory answer.

---------- FOLLOW-UP ----------

QUESTION: I actually do have a couple questions regarding what you've said.

In the same star mass scenario, when you say the planet could only remain stable for a short time, short on what scale? Are we talking ten years short - short even for a human life span? Or 2,000 years short - short for the life span of the universe? I guess this partly depends on any "slightest motion of the planet from the exact center of mass". How slight is slight, and what could cause that? If a planet ever were to get into a position where it WAS stable, how much would it take to make it unstable? A slight solar breeze, a large enough earthquake, a house sized meteor striking, a football field sized meteor striking? Because potentially, if the planet is stable, and there isn't any such extraneous forces exerted, the planet might remain stable for a while, right?

Second question: If the planet were in the L4 or L5 position, what would that mean for the planet? Even if there's an axial tilt, I'm assuming there'd be no seasons since the angle of the tilt compared to the star wouldn't change? There'd only be days and nights caused by a rotation? Or would the variations in its position inherent in the L4/5 positions (it sort of orbits that point, yes?) be enough to cause hot and cold periods? I don't even have a concept of how much closer or further an L4/5's distance from the star in AU would be compared to earth's distance to the sun. I'm assuming this depends on the orbital period of the star. But would it have to be a ridiculously small orbital period (small for a binary system) for the distance from L4/5 to the star to be about 1 AU?

Sorry, I know that's a lot more than just two questions. Take your time answering!

Answer
Depending upon the relative and total masses of the stars (remember, the situation is less stable if the stars have different masses), and how far apart they are, the planet would drift a little away from the center of mass within a few days, and accelerate away from the position (like a ball rolling downhill) over a period of a few months. Within a year or two, its one-time presence near the balance point would be a distant memory.

The L4/5 points form an equilateral triangle with respect to the stars, so to put the planet an AU from each star, the stars would have to be an AU apart. That's not terribly unusual, so I don't see why it couldn't work. There are small variations in the position of objects near L4/5 points, like balls rolling around in a bowl -- they spend most of their time near the bottom of the bowl, but can roll up one side a little ways before rolling back down, then up the other side. However, the change in position relative to the stars would be fairly small when compared to the average distance, so any change in the weather caused by that change would be small when compared to climatic zone (how close you are to the Pole or Equator) and day/night changes.

You are correct in assuming that since the planet would maintain the same position relative to the stars, it wouldn't have seasons in the normal sense -- just an exaggeration of climatic zones caused by the tilt. That is, the hemisphere tilted away from the stars would have colder weather, and the one tilted toward it would have warmer weather, so there would be a more or less permanent "summer" hemisphere, and a more or less permanent "winter" hemisphere. However, odds are that the stars would cause precessional changes in the axis, so that which hemisphere had summer or winter would gradually change, over a period of several thousand years.

Finally, I should note that day/night changes would be very different from here, because the two stars' always being 60 degrees apart in the planet's sky means that half the planet would see both stars at once, and 30 degrees on either side of that half would see one star or the other, so only a third of the planet would see neither star. Counting twilight, that means truly dark skies would last only about a quarter of the day/night period. On the Earth, we can see most of the stars on any given night, because we see half the sky at any given time of night, plus other parts which go down after dusk, or come up before dawn. On your proposed planet, far fewer stars would have a chance to rotate into view during the dark part of the night, so only a little over half the sky would be visible at any given time of the year.

Also, depending upon how bright the stars are, large portions of the "summer" hemisphere might be too torrid for life to survive, and similarly large portions of the "winter" hemisphere might be too frigid. (Obviously, it would be much warmer when both stars are up, than when only one or neither was up.) There is even a good chance that the planet's rotation would be controlled by tidal forces exerted by the stars, so that it rotated perpendicular to its orbit and had no tilt, like Mercury. And if such tidal forces were sufficiently significant, the planet might end up with one side always facing both stars, and the (central third) of the other side always facing away from them both. However, with an AU separation, it would take a long time for tidal forces to accomplish such a task, so there's no reason the planet couldn't have a substantial tilt and a more reasonable day length for hundreds of millions or even billions of years.

I had to rush through this a bit, as I have to leave for work soon, and am typing between bites of my dinner; so please forgive any spelling or grammatical errors.