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View Full Version : 2 Planets, 3 Moons, same orbit - possible?

Laibcoms
2008-Dec-04, 02:11 PM
Hi,

I've been reading old topics about shared orbits and how it could be possible or not possible. To my understanding, there are factors to be considered like gravity, mass, speed, etc.

I am not good at physics and mathematical computations of this magnitude (although I love physics and astronomy, but I never really delved any deeper). Now, I have a couple of questions which will be followed up by another adding another object to the computation.

My scenario:
a) 2 Planets share the same orbit much like Saturn's Epimetheus and Janus
b) The size of the planets can be explained as:
i. 10 Planet Earths can fit in Planet Alpha
ii. 8 Planet Earths can fit in Planet Beta
c) Both planets have their own satellites - the size of Moon - 1 moon each
d) There is a 3rd Moon, the size of Earth, which, every time the two planets meets up, the 3rd Moon is transfered to the new "slower" Planet (in reference to Saturn's E & J.

My questions then are:
First Set:
1) Is it possible that these 2 Planets explained above (letter a & b) share the same orbit, as in stable?
2) If it won't be stable, how long before something undesirable occurs (for example a collision, or the other planet is thrown out of orbit)?
3) What are the effects when the two planets meet each other - to their atmosphere, the sea level, the creatures, and possible the beings, say Human beings?
4) How long will such a process of orbital exchange occur for this size of planets? For E & J, if I remember what I've read, it takes them 100 days.
5) How long will it be between each process? For E & J, it takes them 4 years for the process to repeat again.
6) If the answer to #5 is more than 4 years, what adjustments should be made to fit it in within a 4-year span, or probably 2-years?

These succeeding Question Sets will collapse if the Set preceding it fails. So feel free to just ignore.
Second Set:
7) Adding letter c above, what are the effects and changes that will occur to the setup? (again, assuming the First Set is possible)
8) Adding letter d above, is it possible to have such a 'dance' - ie. the third moon of the size of Earth moves to the "next" "slower planet" every time the two planets meet up to exchange orbits?

Third Set:
9) What could be the changes to the scenario, like planet size or days, etc. which will be affected and must be adjusted at this point of possibility? (ie with a dancing 3rd moon being possible)
10) Anything else I failed to consider or I should consider at this point, since the full scenario is possible?

This is pretty long and yes, it has to do with a world I want to create (where other writers can use). But, I don't want a world wherein the planetary objects are beyond the realm of possibility.

I do not mind if it is near the boundary of the realm of possibility (much more interesting). I am curious as to how far this realm can go, and maybe from there, I will stretch it.

But, if it isn't possible at all, then there's no point, I have to think of a new setup of the universe I have in mind.

(Yes, it was inspired by Saturn's E & J. The third-moon [the dancing moon] is actually habitable as well.)

Thanks all and sorry for such a wild imagination.

Best Regards

dodecahedron
2008-Dec-05, 12:32 AM
One planet is at L4/L5 of the other, larger planet. Each planet has their own natural satellites.

Laibcoms
2008-Dec-05, 07:58 AM
One planet is at L4/L5 of the other, larger planet. Each planet has their own natural satellites.

Hi,

Thanks.

I'm reading on Lagrangian points, and I'm having a hard time understanding L4/L5 (L1 and L2 seems easier, although I am still not sure if I understood it correctly).

I'm viewing or imagining the situation from the perspective of someone watching the planets orbit, out in the space. I tend to understand it more clearly that way than viewing the orbits from the perspective of say, a planet like Earth (where we'll see Bean-shaped orbits).

So, if I understood Lagrangian correctly, L4/L5 means the objects in those points stay there relative to the bigger mass, in my example, the larger planet, is that correct?

It means then, an E & J scenario is not possible for planets?

---

I checked out Rocheworld, at least a summary, something like that but not too close that they share one atmosphere.

Thank you very much.

cran
2008-Dec-08, 09:08 AM
Hi,

I've been reading old topics about shared orbits and how it could be possible or not possible. To my understanding, there are factors to be considered like gravity, mass, speed, etc.

I am not good at physics and mathematical computations of this magnitude (although I love physics and astronomy, but I never really delved any deeper). Now, I have a couple of questions which will be followed up by another adding another object to the computation.

My scenario:
a) 2 Planets share the same orbit much like Saturn's Epimetheus and Janus
b) The size of the planets can be explained as:
i. 10 Planet Earths can fit in Planet Alpha
ii. 8 Planet Earths can fit in Planet Beta
c) Both planets have their own satellites - the size of Moon - 1 moon each
d) There is a 3rd Moon, the size of Earth, which, every time the two planets meets up, the 3rd Moon is transfered to the new "slower" Planet (in reference to Saturn's E & J.

My questions then are:
First Set:
1) Is it possible that these 2 Planets explained above (letter a & b) share the same orbit, as in stable?
thinking about the Earth/Moon system, and the Pluto/Charon system ...
yes, it's possible for two bodies to co-orbit a star around a common centre -
in the Earth/Moon case, the common centre is within the Earth ...
in the scenario you envisage, the common centre would likely lie between the co-orbiting planets,
but biased towards the larger/more massive planet -
you'll have to (find someone to) do the math to work out the co-orbital period and separation required to make the system plausible,
and allow for stable satellites of each primary ...
your "Strange Attractor" third satellite might also be possible, if more complex in a stable arrangement ...

2) If it won't be stable, how long before something undesirable occurs (for example a collision, or the other planet is thrown out of orbit)?
if it's not stable, then it could get messy relatively quickly -
as in, before Chapter 2 ...

3) What are the effects when the two planets meet each other - to their atmosphere, the sea level, the creatures, and possible the beings, say Human beings? that depends on what you mean by "meet" ...
in a stable co-orbit, each body will always exert some tidal influence on the other -
those tides will vary according to relative positions of the planets and the primary star ...
the range and complexities of the various tides (and remember, you'll probably need to include the satellites in these calculations)
on each of the bodies will depend on their relative masses,
compositions (ie, what stuff each is made of),
range of distances, and alignments ...
your "Strange Attractor" satellite, if at all Earth-like, will probably be tectonically unstable during transition ...
and also when at opposite ends of the "figure 8" - ie, when it and the two planets are aligned ...
more so, if that alignment includes the primary star ...
so, not a nice place to live ...

4) How long will such a process of orbital exchange occur for this size of planets? For E & J, if I remember what I've read, it takes them 100 days.
5) How long will it be between each process? For E & J, it takes them 4 years for the process to repeat again.
6) If the answer to #5 is more than 4 years, what adjustments should be made to fit it in within a 4-year span, or probably 2-years? the number-crunching needed here
will depend quite a lot on the range of possibilities obtained from number-crunching needed for the first steps ...

ETA: a co-orbiting family like that could well have more outer satellites orbiting the common centre ...

astromark
2008-Dec-08, 10:05 AM
The mechanics of orbital stability are gravity based. Velocity and mass being important to calculating distances and orbital periods. None of the scenes you paint seem impossible. All be it unlikely. I have noticed that the unlikely is often the case... So its a big fat yes to your fiction being possible. Asking then what of stability when we do not have details... can not do...but why not just go for whatever... you have that freedom in fiction... I would think that almost every conceivable configuration might be possible. Mightn't it ?

JohnD
2008-Dec-08, 10:31 AM
Clearly LaGrange points work for small objects that are insignificant in relation to the mas of the planet. Or even two small satellties of a truly masive planet. But will the Lgs 'work' for two planets that are about the same size?

The small objects in the Lg points will not affect the 'primary' but the two planets will affect each other and I fear that such a system will be mothing like as stable.
John

timb
2008-Dec-08, 12:08 PM
The short answer is no. Co-orbital1 equal mass planets are not stable. This has been discussed before and even the minimum ratio for stability was posted, so I suggest you use the search engine.

1. Not orbiting one another.

tony873004
2008-Dec-08, 06:06 PM
...But will the Lgs 'work' for two planets that are about the same size?...

Yes. As long as the combined mass of the planets does not exceed about 4% of the mass of the star it will be stable, even if the planets are equal mass.

timb
2008-Dec-08, 08:56 PM
You're right. According to Extrasolar Trojans: The Viability and Detectability of Planets in the 1:1 Resonance (http://aps.arxiv.org/abs/astro-ph/0204091) the L4 and L5 Lagrangian orbits are stable for equal-mass planets so long as their masses are no more than 3.812% of the mass of the the three-body system. The L1 point it always unstable.

cran
2008-Dec-09, 02:03 AM
The short answer is no. Co-orbital1 equal mass planets are not stable. This has been discussed before and even the minimum ratio for stability was posted, so I suggest you use the search engine.

1. Not orbiting one another.

using the search engine turns up 123 posts/threads - most of which seem to be about known co-orbitals, various types of orbits, or the definition of "planet" ...

so, unless you're referring to one of the two posts I've included below,
I'm sure we'd all appreciate the link to the actual discussion you are referring to ...

tony873004
17-February-2006, 10:28 AM
They can be perturbed from outside influences, but they won't perturb each other out of their orbits. It was the conclusion of the Theia article, that it grew large enough that the Earth : Theia mass ratio made the system unstable.

But the conclusion of the author of the paper I linked to, and the conclusion of the numeric solution I performed is that the Earth : Theia mass ratio is irrelavant. The only relavant ratio is the (Earth mass + Theia mass) : Sun mass.http://www.bautforum.com/archive/index.php/t-38142.html

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eburacum45
12-November-2004, 07:05 PM
This page discusses the stability of moons and planets in multiple orbits; I am not sure the simulation is entirely reliable, but it does seem to show that some configurations are unstable, and some are stable at least in the medium term.
http://burtleburtle.net/bob/physics/kempler.html

I don't kow hnow stable the fictional Ecotopia Lab ring in Orion's Arm is;
I suspect not very stable at all, and it must need a lot of active station keeping. Here it is in Celestia;
http://www.orionsarm.com/worlds/Ecotopia-theLab.jpg
there are 312 in total, but I have only made 43 so far.http://www.bautforum.com/archive/index.php/t-14254.html

--------------

timb
2008-Dec-09, 02:12 AM
using the search engine turns up 123 posts/threads - most of which seem to be about known co-orbitals, various types of orbits, or the definition of "planet" ...

so, unless you're referring to one of the two posts I've included below,
I'm sure we'd all appreciate the link to the actual discussion you are referring to ...

I've already located the thread and pulled out the most relevant reference in my previous post in this thread. I'm not going to search for it again.

cran
2008-Dec-09, 02:27 AM
You're right. According to Extrasolar Trojans: The Viability and Detectability of Planets in the 1:1 Resonance (http://aps.arxiv.org/abs/astro-ph/0204091) the L4 and L5 Lagrangian orbits are stable for equal-mass planets so long as their masses are no more than 3.812% of the mass of the the three-body system. The L1 point it always unstable.

are you sure you're discussing the same thing? There's nothing in the OP about Lagrangian orbits ...

and the opening pars of the paper you refer to seem to disagree with your blanket "no" assertion ...

There are a variety of stable co-orbtial configurations, and we specifically examine three different versions of the 1:1 resonance. These include tadpole and horseshoe type orbits, as well as a more exotic configuration which occurs when one planet has a highly eccentric orbit while the other planet moves on a nearly circular orbit. We show that pairs of planets in 1:1 resonance yield characteristic radial velocity signatures which are not prone to the sin(i) degeneracy... Finally, we argue that hydrodynamical simulations and torqued three-body calculations indicate that 1:1 resonant pairs might readily form and migrate within protostellar disks...

In the case of equal mass planets, a numerical survey indicates that horseshoe configurations are stable over long periods for mass ratios μ < 0.0004, indicating that a pair of Saturn-mass planets can exist
in this resonance...

All three of these resonant configurations can be stable over timescales comparable to or longer than stellar lifetimes ...

timb
2008-Dec-09, 02:35 AM
are you sure you're discussing the same thing? There's nothing in the OP about Lagrangian orbits ...

and the opening pars of the paper you refer to seem to disagree with your blanket "no" assertion ...

That's right, I was wrong. That's why I said "You're right" when tony873004 contradicted me. Why should I address the OP? My post was a reply to JohnD's question.

cran
2008-Dec-09, 03:16 AM
That's right, I was wrong. That's why I said "You're right" when tony873004 contradicted me. Why should I address the OP? My post was a reply to JohnD's question.
ah, I see ...

I'll know to look out for unaddressed asides in future ...

JohnD
2008-Dec-09, 06:44 PM
Thanks, timb and tony!
Laibcoms, that paper raises the possibility of "horseshoe" and "tadpole" orbits, rather more exciting than boring old planets stuck in 1:1 resonance!

John