# Out there physics/astrology question

#### regina_felis

I have a rather odd question. I was watching the sunset today and started a series of thought....and it all led up to this::::

is it possible for two stars of the same size, or even of different sizes, to have one planet orbiting both, and be far enough away from each other that the planet orbits in a figure eight? in other words, would the pull of gravity of one star start the orbit and the pull of gravity of the next pull it off course and make it orbit around itself, then back and forth, so that it causes the planet to orbit in a figure eight? a rather out there question....just something i'm curious about and could think of no better place to find the answer than in a forum of physics geniuses...

Thanks!

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#### maximus

in a binary star system, planets still exist. but their orbit is very irregular and not it a perfect figure eight orbit. the less massive star would also orbit the more massive, so it'd be more confusing.

#### regina_felis

*interested* a smaller star would indeed orbit the larger...i hadn't thought of that....and how would two of the same size react to one another? would the gravity of both cause them to eventually collide, therefore destroying the system? that would only seem logical, would it not? and of the planet, i didn't figure the orbit would be perfect...i was simply wondering, is it theoretically possible for such a thing to happen...for a planet to orbit two different stars in a figure eight pattern...not a perfect eight, just that style.

Thanks again!

#### HallsofIvy

Homework Helper
"Orbiting" depends upon a balance between gravitational force and rotational inertia.

It is as possible for two equal mass stars to orbit one another as for two of different mass. If the inital angular velocity is two high, they will eventually drift apart, if too low they will crash together. If it is in the correct range, they will continue to orbit one another.

By the way, you might get more responses on a board like this if you said "astronomy" rather than "astrology"!

#### LURCH

There is no physical law or set of physical laws (of which I am aware) that would prevent a planet in a binary system from having the "figure-eight" orbit you describe.

The orbit is not impossible, it is simply highly improbable. The planet would essentially need to have two orbits. While orbiting one star, the planet would have to follow an ellipse with the star as one focus, and the other focus occupying a point between the two stars. This ellipse would have to be eccentric enough so that the planet, before reaching aphelion, crosses the La Grange Point between the two stars, and falls into an elliptical orbit around the second star. This second orbit would, of course, need to have the same properties as described for the first.

Staff Emeritus
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In Ian Stewart's book Does God Play Dice? The Mathematics of Chaos he discusses "Hill's reduced model" which consists of two massive bodies and a third whose mass is negligible in comparison to the other two, acting under gravity. He then says that Poincare showed the orbits of the massive pair are normal, but the orbit of the small body is chaotic (Poincare was studying chaos issues decades before the rediscovery of the subject).

Based on this it seems that even if the planet ever achieved a figure-eight orbit it wouldn't retain it but would go tumbling off into other orbits.

#### NEOclassic

Re:Not figure 8 but special double ellipsoidal!

Originally posted by regina_felis
I have a rather odd question. I was watching the sunset today and started a series of thought....and it all led up to this::::

is it possible for two stars of the same size, or even of different sizes, to have one planet orbiting both, and be far enough away from each other that the planet orbits in a figure eight?
Thanks!
Hi Tiffany,
Please consider the case of the recurring comet visitations to the solar system. Take the case of Haley's Comet for example. Many might consider the comet's path around the Sun to be parabolic or hyperbolic but only a special elliptical path is demanded in order to swing the Comet back toward the Sun. If the particular other star is of the same mass as the Sun then the orbit should be a true ellipse; if it differs then the orbital path could easily be egg-shaped. In this case there need not be any interaction between the gravitational fields of the two remote stellar bodies that remain as the ellipse foci. That the cycle period maintains constant suggests that the Sun's motion direction must be nearly the same as that of the particular companion star; i.e. otherwise any divergence of stellar paths would change the inter-stellar distance. Note: modest twisting of the comet orbit might be tolerated but in the case of a 180 degree twist (figure 8) the alternate reappearances wouold necessarily approach the Sun from another (mirror) direction. Cheers, Jim

#### chroot

Staff Emeritus
Gold Member
Re: Re:Not figure 8 but special double ellipsoidal!

Originally posted by NEOclassic
If the particular other star is of the same mass as the Sun then the orbit should be a true ellipse; if it differs then the orbital path could easily be egg-shaped.
You apparently have no idea what you're talking about. All orbits in Newtonian gravitation are conic sections: circles, ellipses, parabolae, hyperbolae. In the case two bodies orbiting each other, both bodies orbit in ellipses with the center of mass at one focus.

...egg-shaped. [zz)]

- Warren

#### NEOclassic

Re: At least Warren didn'r call me names!!

Originally posted by chroot
You apparently have no idea what you're talking about. All orbits in Newtonian gravitation are conic sections: circles, ellipses, parabolae, hyperbolae. In the case two bodies orbiting each other, both bodies orbit in ellipses with the center of mass at one focus.

...egg-shaped. [zz)]

- Warren
more quotes follow:

Originally posted by regina_felis
I have a rather odd question. I was watching the sunset today and started a series of thought....and it all led up to this::::

is it possible for two stars of the same size, or even of different sizes, to have one planet orbiting both, and be far enough away from each other that the planet orbits in a figure eight?
Thanks! quote:

Originally posted by NEOclassic
If the particular other star is of the same mass as the Sun then the orbit should be a true ellipse; if it differs then the orbital path could easily be egg-shaped.

You apparently have no idea what you're talking about. All orbits in Newtonian gravitation are conic sections: circles, ellipses, parabolae, hyperbolae. In the case two bodies orbiting each other, both bodies orbit in ellipses with the center of mass at one focus.

...egg-shaped.

- Warren

Warren, It is you and not I who has no idea of what I’ve been talking about!! The orbit I’m concerned with (as a response to Tiffany’s query) re: the orbital behavior of a planet’s path, which is dependent on two non-interacting stellar bodies. While a recurring comet is not the usual one focus situation of the Sun-planet ellipse, it is in reality a two-foci ellipse with the Sun at one focus and another stellar body at the alternate focus of the comet’s orbit. Your snide reference to “egg-shaped” rather than the more proper (although perhaps pretentious to youthful Tiffany) “ovate” does nonetheless obtain in the case that the alternate focus stellar body mass is not equal to that of the Sun. My modeling has nothing whatever to do with Newton-Kepler laws of Celestial Mechanics of two independent stellar bodies and your reply suggests that your reading of my post was not thorough. Cheers, Jim

#### HallsofIvy

Homework Helper
While a recurring comet is not the usual one focus situation of the Sun-planet ellipse, it is in reality a two-foci ellipse with the Sun at one focus and another stellar body at the alternate focus of the comet’s orbit.
Do you have any evidence for this? What other "stellar body" is at the other focus of, say, Halley's comet?

While a recurring comet is not the usual one focus situation of the Sun-planet ellipse, it is in reality a two-foci ellipse with the Sun at one focus and another stellar body at the alternate focus of the comet’s orbit.

Evidence?

And by the way, I'm sure you didn't mean it as such, but an ellipse always has 2 foci. If it had only one it would then be a circle.

Hows does this proposed system work? It dosnt sound likely to me......

No orbit could really be egged shaped. Indeed, any equations for orbital shapes take on the form of a conic section. As for a figure 8 orbit, I do not believe such a thing is possible. Let us examine the case.

The center of the 8 would be at the L point (also the center of mass of the two star system). Here the gravitational pull from both stars is equal but opposite. IF planet A were to start off in orbit around one, and cross this L point, and for some reason be attracted to break (yes, break) orbit of the other star and enter orbit of the other, then it would imply one of two things: The other star somehow exerted more force on the planet than the other star (not possible at the L point), or the planet somehow gained/lost energy. Since case 1 cannot happen, let us look at case 2. If the planet gained or lost energy (depending how you want to look at it), then it would move into just one orbit around 1 star and never return to the L point. Conclusion: A figure 8 orbit around two stars is not possible.

Edit: I realize I made the assumption the cross would have to be at the L point. Let me fix this. If we assume the crossover happens at some other point than the center of mass, it is still impossible. If the planet has enough energy to break away from its original orbit around one star, then on the return back path, it would slingshot out of the system. So it still wouldn't matter. If the object has enough velocity to break out of orbit of one star or the other, it would be ejected eventually.

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#### regina_felis

*shakes her head and giggles softly* ok, so far i've heard reasonable arguments for both cases, possible and impossible....so which is it? i admit i'm not very bright with physics...and to the person that pointed out my "astrology" mistake, you're correct, i should have put "astronomy" instead....however, it's not that big of a deal *smile*

as for the arguments possible/impossible...it seems that if not impossible, this system is highly improbable. As for the two stars not interacting at all, that would be impossible, as both have gravatational fields, which would draw them to each other, would it not? so with stars of equal mass, would they not be orbiting each other while the plamet orbits them as well? and with stars of different mass, i don't see how it's even possible for one planet to take orbit around both, as the one with the greater mass would have a greater gravatational pull. so instead, both the smaller star and the said planet would be orbitting the larger star.

i guess that's all i can think to say at the moment....thank you all for your help. i reallize it was a rather odd question, but it gave me something to think about.

Not quite. Two objects of comparable masses (indeed any two body system actually) will orbit the center of mass of both objects. Even so with the earth moon system (hence why the earth's axis wobbles).

Anywho, the system you inquire about is impossible. The mechanics and physics do not permit it.

#### NEOclassic

Originally posted by HallsofIvy
Do you have any evidence for this? What other "stellar body" is at the other focus of, say, Halley's comet?
Hi Halls,
According to Karl F Kuhn (ASTRONOMY pub 1989) on page 371: "Comet Halley is now (shortly after Halley's appearance in 1986) on its way toward the outer portion of its elliptical orbit . . will continue out past Neptune's orbit before returning to our region of the Solar System in 2061 A.D."
While the alternate focal mass is unknown its distance should be calculable and I would imagine that that body lies very close to the radial line that connects the Sun and the creation engine at the axis of rotation of the Milky Way galaxy. Cheers, Jim

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There need not be any mass at the other focal point in the elliptical orbit. To be honest, such a thing would completely disrupt the orbit. Consider one of Kepler's Laws, that is, bodies in orbit trace out equal areas in equal times. This means (and it is no surprise) that as the orbiting body approaches the mass at the focal point, it accelerates and moves faster and faster (after all, it is getting closer, so the object puts more force on it). Well, if the sun is not the only point in the orbit, then the object must again move faster and faster out at that end. But this would mean that its orbit is much larger than we know it to be. Not only that, but this other object must be orbiting the sun as well (or at the least, orbiting their common center of mass). This would add in an unobserved doppler effect to all redshift spectra we observe coming in from extra-solar sources.

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