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In a related question I'm trying to find some conclusive reference(s) helping explain if some halo orbits around the sun-earth or earth-moon $L_1$ or $L_2$ locations can actually be somewhat stable (say, for half-a-dozen orbits). There I mentioned the quote by Dennis Wingo describing ISEE-3's original Halo orbit. He describes Sun-Earth $L_1$ as "a point about 1.5 million kilometers from earth where a spacecraft can safely orbit without using any fuel."

The site http://spacecraftforall.com/a-new-orbit is an interactive thing - if you leave it alone it will usually start the video in about 10 or 15 seconds.

Here I would just like to know specifically - did ISEE-3 spend a few years in a halo orbit around sun-earth $L_1$ without using any fuel, or at least without the regular station keeping thrust maneuvers needed in unstable orbits? (e.g. like DSCOVR needs to do)

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It is true that in some libration points, and this includes ESL-1 (Earth-Sun-Libration point 1), you can orbit the location with zero fuel. Think of it as Einstein's visualization of a dimple in space time (which is what gravity is) and that the spacecraft orbits the deepest point of the dimple.

However, the problem is that in a tight ESL-1 orbit, the spacecraft is in a direct line of sight to the sun. This creates a communications problem because the sun's radio frequency noise is orders of magnitude higher power than the transmitters on the spacecraft. Therefore what spacecraft actually do is orbit the libration point near the "top" of the gravitational dimple.

For ISEE-3 this was about 500,000 km from the center of the ESL-1 point. This is how far away from the ESL-1 point the spacecraft had to be in order to be outside of the sun's radio frequency interference. This required dV to remain in that orbit. If my memory serves the order of magnitude of this dV was around 30 meters/sec/year.

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    $\begingroup$ Dennis, welcome to Space Exploration Stack Exchange! This looks like the start of a good answer, but since you're new around here you may want to include some references to back up your claims. Also, since uhoh asked about fuel, you may want to see if you can come up with fuel expenditure for the dV/year. $\endgroup$ – called2voyage May 19 '16 at 14:59
  • $\begingroup$ Thanks for your help! I got started on this with the linked sibling question which cites a JAXA patent stating that the stable halo orbits around $L_1$ are too large for some applications, here you are suggesting they are too small. Is there a "Goldilocks Zone" for halo orbits? I could really use a reference or two - even if it's behind a paywall I can start there and find something that can be linked-to here. $\endgroup$ – uhoh May 20 '16 at 0:48
  • $\begingroup$ This doesn't sound right to me. The collinear L points aren't stable. That includes L3, L1 and L2. When potential is illustrated as dimples, the L4 and L5 are atop hills and L1 and L2 are on saddle points. $\endgroup$ – HopDavid May 20 '16 at 3:54
  • $\begingroup$ @HopDavid these are orbits around $L_1$ (or $L_2$). Remember the saddles and dimples we talk about in 2D and 3D have to be calculated for a single - and usually zero - velocity. The "potential" in the rotating frame is a pseudo-potential and includes velocity terms. It's why every explanation that uses those plots always ahem's and guffaws when it gets to $L_4$ and $L_5$, which for sun-earth and earth-moon are stable and yet the plots show a maximum which then is explained away by saying this isn't actually the correct plot to look at anyway. Need a way to see potential in 6 dimensions! $\endgroup$ – uhoh May 20 '16 at 13:36
  • $\begingroup$ @HopDavid for example in the article Lagrangian Point the caption under the first contour plot has to backpedal: "Counterintuitively, the L4 and L5 points are the high points of the potential. At the points themselves these forces are balanced." $\endgroup$ – uhoh May 20 '16 at 13:41

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