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fortyseven
2003-Sep-27, 04:34 AM
I&#39;ve read of scenearios where 6,12,and 24(but not 48 or more) objects(e.g. moons) of identical mass can orbit a planet in stable orbits for long periods of time. In a scenario where Earth has 6 Moon-sized moons, each moon is the L4 or L5 of another moon. I gather that they are in stable orbits because their gravitational pulls on each other balance each other out, but what would their gravitational pulls on Earth be?

Planetwatcher
2003-Sep-28, 01:00 AM
I&#39;ve read of scenearios where 6,12,and 24(but not 48 or more) objects(e.g. moons) of identical mass can orbit a planet in stable orbits for long periods of time. I&#39;m sorry, but this is obserd, because Jupiter is confirmed to have at least 60 moons of various sizes, and orbits. Some even orbit in retrograde, which is to say the opposite direction of the usual.

kashi
2003-Sep-28, 01:17 AM
Welcome to the forum fortyseven. A very interesting question indeed. I like this theory, but I haven&#39;t ever heard it before. Perhaps Fraser can find someone knowledgeable in the astronomy profession to answer this.

Planetwatcher I think you missed the point. The ratio between the size and mass or Juptier and that of its moons is much greater than between that of Earth and its moon. There is much more space around Jupiter for moons&#33; Plus fortyseven specifically said "moons of identical mass"&#33; Also...who&#39;s to say that Jupiter&#39;s moons haven&#39;t collided with each other or with Jupiter in the past?

Kashi

fortyseven
2003-Sep-28, 05:07 AM
Thanks kashi. I don&#39;t remember where I read it. It was a report or paper regarding computer simulations of an elaborate Earth-Moons system. The L4 and L5 points of 2-body systems are points where the gravitational forces are cancelled out, 60 degrees forward and 60 degrees backward in the orbit of the smaller body. In the Jupiter-Sun System, there are collections of asteroids at the L4 and L5 points.

If the Moon had Moon-sized moons at the L4 and L5 points, there would be 3 Moons. Of course, the moons at the L4 and L5 points would have their own L4 and L5 points, 2 of which would be empty. So then there would be 5, and of course we just add another moon, making 6.

A diagram would help I know ;) There is one IIRC near the front of the novel Tiber.

12 and 24 moons are also stable according to the computer sims in the report I read, but 48 isnt.

If I knew what values to put for the x and y vectors for the Moon, I could do the sim myself online at a gravity sim site.

Anyway, I hope this was helpful.

Guest_fortyseven
2003-Dec-31, 02:46 AM
http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html

there&#39;s a diagram here.

damienpaul
2004-Jan-04, 02:50 AM
very interesting theory, but what of jupiter&#39;s 60+ moons - perhaps we are looking at mass instability?

Guest
2004-Jan-04, 06:12 PM
I&#39;m talking about the same size or somewhat smaller, in the same orbit around a planet.

fortyseven
2004-Jan-04, 06:14 PM
The last post was mine.

Jupiter has much smaller moons and many orbits.

fortyseven
2004-Jan-04, 06:22 PM
Jupiter is WAY bigger than its moons and they are in many orbits.

I&#39;m talking about Moon sized in the same orbit around Earth size planet.

Littlemews
2004-Jan-04, 09:11 PM
Originally posted by fortyseven@Sep 27 2003, 04:34 AM
I&#39;ve read of scenearios where 6,12,and 24(but not 48 or more) objects(e.g. moons) of identical mass can orbit a planet in stable orbits for long periods of time. In a scenario where Earth has 6 Moon-sized moons, each moon is the L4 or L5 of another moon. I gather that they are in stable orbits because their gravitational pulls on each other balance each other out, but what would their gravitational pulls on Earth be?
It depends on the Mass (How strong Gravity) of that planet and I believe Earth has enough Mass to pull 2-3 moons orbit itself even with the same size of Earth...or else like pluto and Charon.

damienpaul
2004-Jan-05, 11:52 AM
i think i comprehend this theory, i am keen to learn more of it&#33;

jkmccrann
2005-Dec-22, 08:18 AM
I've read of scenearios where 6,12,and 24(but not 48 or more) objects(e.g. moons) of identical mass can orbit a planet in stable orbits for long periods of time. In a scenario where Earth has 6 Moon-sized moons, each moon is the L4 or L5 of another moon. I gather that they are in stable orbits because their gravitational pulls on each other balance each other out, but what would their gravitational pulls on Earth be?

Where have you read this? It sounds like a bit of a stretch to me, surely such a configuration would be quite vulnerable to other influences and in the end unsustainable.

tony873004
2005-Dec-22, 10:27 PM
I couldn't get 6 to work.

I started with 6 Moon-mass moons in circular orbits around an Earth-mass planet with the same distance as the Earth/Moon distance. I seperated them by 60 degrees.

After only 2 orbits, the symetrical pattern started losing its shape.

After 3 orbits, the entire system was in chaos, with moons being ejected.

And this is with circular orbits and no pertubation from the Sun or other planets.

alainprice
2005-Dec-22, 11:18 PM
Moon A is to be positioned at the L4 Lagrange point of the Earth-Sun system. Likewise, Moon B goes at the L5 point.
Once that is done, new lagrange points show up with respect to Earth and its new moons.

The only thing I don't get is the mass. Lagrange points are stable for mass ratios EXCEEDING 25. If we put a moon into a moon's Lagrange point, it needs to be at least 25 times less massive.

grant hutchison
2005-Dec-22, 11:21 PM
You've evidently visited this page (http://burtleburtle.net/bob/physics/kempler.html) simulating "Klemperer rosettes", or one that has copied from it.
Klemperer actually described a more complex (and interesting) gravitational equilibrium in his original paper (http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1962AJ.....67..162K|Some), and described the situation of multiple equal masses as "trivial".
Klemperer's rosettes (either as described by Klemperer or in the "trivial" version) are all unstable to perturbations, but are all indefinitely stable in the (entirely theoretical!) state of perfect mathematical alignment and absence of outside perturbation. Bob Jenkins (who runs the Klemperer webpage I link to above) finds some are stable and some are not in his simulations (6, 12, 24 stable, 48 unstable, as you report) - I suspect this is because of the digital limitations of numerical simulation and the length of time it takes to run a simulation.

(To be fair, I have to report that Bob vigorously disagreed with this idea when I put it to him!)

Grant Hutchison

PS: If the name seems familiar, it's because Larry Niven used it in Ringworld. Unfortunately, he spelled Klemperer's name wrongly, and used the "trivial" scenario instead of the one Klemperer actually described.

alainprice
2005-Dec-23, 04:33 AM
*Long clapping*

Grant, you never cease to deliver. And this is a topic I will follow. Would you happen to know of any good gravity simulators? For example, one based on general relativity, or even special relativity, which allows an arbitrary amount of masses with different velocities.

grant hutchison
2005-Dec-23, 07:49 PM
For example, one based on general relativity, or even special relativity, which allows an arbitrary amount of masses with different velocities.I don't know of any gravity simulators that incorporate relativity, sorry; unless tony873004 has recently carried out a major upgrade on his.

Grant Hutchison

tony873004
2005-Dec-27, 07:34 PM
One day :)...

But in my sim as it is now, the effects of GR would get lost in the noise of things more significant.