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#1
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How big is L5?
In article ,
Alex Terrell wrote: The Earth Moon L5 (or L4) position is often mentioned as a gravitationally stable region ideal for space colonies. I assume that means that items in the vicinity of L5 (or L4) are attracted to, or orbit about, the central point. They orbit around it, more or less. The underlying story is actually quite complex, but that's the bottom line. But can anyone tell me how big the region is? How many kilomters towards Earth would you need to be before you drifted away. There isn't a sharp boundary. Quite large orbits around the point are stable in principle (although stability in practice is a much more complicated question, given things like solar perturbations). Also, any indications of the gravitational gradients within L5? How far would objects need to be apart so as not to drift into the central area and bump into each other? As noted above, what happens is that they oscillate around the point, rather than drifting toward it. There is no tendency for them to drift toward the central point and then stop. -- MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer first ground-station pass 1651, all nominal! | |
#2
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How big is L5?
Henry Spencer wrote:
They orbit around it, more or less. The underlying story is actually quite complex, but that's the bottom line. ... As noted above, what happens is that they oscillate around the point, rather than drifting toward it. There is no tendency for them to drift toward the central point and then stop. Ideally (no other objects than the primary and secondary, test particle has zero mass), with what period do the objects orbit around the Trojan point? Does that period depend on their distance from the point? -- Erik Max Francis && && http://www.alcyone.com/max/ __ San Jose, CA, USA && 37 20 N 121 53 W && &tSftDotIotE / \ That's what I'm about / Holding out / Holding out for my baby \__/ Sandra St. Victor |
#3
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How big is L5?
"Henry Spencer" wrote:
In article , Alex Terrell wrote: Also, any indications of the gravitational gradients within L5? How far would objects need to be apart so as not to drift into the central area and bump into each other? As noted above, what happens is that they oscillate around the point, rather than drifting toward it. There is no tendency for them to drift toward the central point and then stop. Which is a pretty obvious conclusion if you think about it. We're talking gravitational potentials here, so think hills and valleys. Except in space there's no friction, so if you fall into a valley (and for some reason don't fall out) you're going to roll around in it, up and down each side, rather than fall toward the exact bottom and stick there. There are forces directing you toward the bottom but no forces that'll make you stick there once you arrive. |
#4
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How big is L5?
"Christopher M. Jones" wrote in message ...
"Henry Spencer" wrote: In article , Alex Terrell wrote: Also, any indications of the gravitational gradients within L5? How far would objects need to be apart so as not to drift into the central area and bump into each other? As noted above, what happens is that they oscillate around the point, rather than drifting toward it. There is no tendency for them to drift toward the central point and then stop. Which is a pretty obvious conclusion if you think about it. We're talking gravitational potentials here, so think hills and valleys. Except in space there's no friction, so if you fall into a valley (and for some reason don't fall out) you're going to roll around in it, up and down each side, rather than fall toward the exact bottom and stick there. There are forces directing you toward the bottom but no forces that'll make you stick there once you arrive. I believe L1, L2 and L3 are saddles or hilltops, whilst L4 and L5 are troughs. The question really is how steep are the sides of the "troughs", and how far does one have to go "uphill" before one starts going "downhill". If I put a space station 10 km from L5, I assume it will orbit about L5. What about 100km? What about 1,000km? I guess 10,000km towards Earth, and the space station will leave L5 and orbit about the Earth independently. |
#5
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How big is L5?
"Christopher M. Jones" writes:
"Henry Spencer" wrote: In article , Alex Terrell wrote: Also, any indications of the gravitational gradients within L5? How far would objects need to be apart so as not to drift into the central area and bump into each other? As noted above, what happens is that they oscillate around the point, rather than drifting toward it. There is no tendency for them to drift toward the central point and then stop. Which is a pretty obvious conclusion if you think about it. We're talking gravitational potentials here, so think hills and valleys. Except in space there's no friction, so if you fall into a valley (and for some reason don't fall out) you're going to roll around in it, up and down each side, rather than fall toward the exact bottom and stick there. There are forces directing you toward the bottom but no forces that'll make you stick there once you arrive. ....Except that that _isn't_ how L4 and L5 work !!! If you examine the "effective potential" in the co-rotating frame, you will find that L4 and L5 are both at the summits of "hills," not the troughs of "valleys." What "stabilizes" orbits about L4 or L5 is the "coriolis force:" As a body falls "downhill," it gains velocity, and since the coriolis "force" is both perpendicular to and proportional to elocity, the body is deflected until it finds itselef moving "uphill" and slowing down again. (The dynamics are quite similar to those of a charged particle in a Penning trap: The electrostatic forces produce stable oscillations perpendicular to the X-Y plane and unstable motion in the X-Y plane; the magnetic field along the Z-axis deflects the motion of particle in the X-Y plane so that particles falling "outward" get whipped around until they are moving "inward" again, so that they move in a cycloidal path around the Z-axis.) -- Gordon D. Pusch perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;' |
#6
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How big is L5?
In article ,
Erik Max Francis wrote: They orbit around it, more or less. The underlying story is actually quite complex, but that's the bottom line... Ideally (no other objects than the primary and secondary, test particle has zero mass), with what period do the objects orbit around the Trojan point? In the general case, it's actually quite a complex motion, because the particle oscillates around the point along all three axes, but the period can be *different* on each axis. Only in special cases does the particle follow something approximating a simple orbit around the point. Does that period depend on their distance from the point? In some cases -- perhaps all, I don't remember for sure -- no, it's independent of distance. -- MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer first ground-station pass 1651, all nominal! | |
#7
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How big is L5?
Hop David wrote:
I used to have that misconception. The L1, 2 & 3 are saddlepoints and L4 & 5 are hill tops. http://www.physics.montana.edu/facul.../lagrange.html The stability is due to Coriolis effect, not a valley between the walls of gravity and centrifugal force. You're not alone; it's an extremely common misunderstanding, simply because of the weirdness of the stability of the Trojan points (as you say, due to Coriolis pseudoforces, not the usual mechanism). Plenty of informative Web sites have it wrong, as well. It "seems" obvious it's a valley, first perceptions can be wrong. -- Erik Max Francis && && http://www.alcyone.com/max/ __ San Jose, CA, USA && 37 20 N 121 53 W && &tSftDotIotE / \ You are inspiration to my life / You are the reason why I smile \__/ India Arie |
#8
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How big is L5?
Hop David wrote in message ...
Alex Terrell wrote: "Christopher M. Jones" wrote in message ... "Henry Spencer" wrote: In article , Alex Terrell wrote: Also, any indications of the gravitational gradients within L5? How far would objects need to be apart so as not to drift into the central area and bump into each other? As noted above, what happens is that they oscillate around the point, rather than drifting toward it. There is no tendency for them to drift toward the central point and then stop. Which is a pretty obvious conclusion if you think about it. We're talking gravitational potentials here, so think hills and valleys. Except in space there's no friction, so if you fall into a valley (and for some reason don't fall out) you're going to roll around in it, up and down each side, rather than fall toward the exact bottom and stick there. There are forces directing you toward the bottom but no forces that'll make you stick there once you arrive. I believe L1, L2 and L3 are saddles or hilltops, whilst L4 and L5 are troughs. The question really is how steep are the sides of the "troughs", and how far does one have to go "uphill" before one starts going "downhill". I used to have that misconception. The L1, 2 & 3 are saddlepoints and L4 & 5 are hill tops. http://www.physics.montana.edu/facul.../lagrange.html The stability is due to Coriolis effect, not a valley between the walls of gravity and centrifugal force. Hop http://clowder.net/hop/index.html One learns something new every time. Would that mean that it's difficulty to place something exactly on the Lagrange Point? Or is the effect still that the combined potential and kinetic energies of something in a Lagrange point are minimised. How much delta V is needed to actually escape from L4/L5? |
#9
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How big is L5?
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