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My answer to Does the distance to L2 vary? is

The correct answer is "No, they are only mathematically defined when the orbit is circular".

but @DavidHammen's answer explains that they can be defined in the elliptical restricted three body problem and @PM2Ring's answer shows that JLP's Horizons provides eight specifically defined Lagrange points from which you can calculate distances to other things; L1, L2, L4 and L5 for the Earth/Moon system and for the Sun/Earth-Moon-Barycenter system.

Question: How (the heck) does JPL define the exact position of Lagrange points in the real solar system where (I thought that) they can't be defined?

There must be some kind of compromise here as Horizons reflects a realistic n-body simulation without any "restricted three body" conditions that I know of. They must use some equation or rule to calculate the position of these spots that I don't believe can be defined. What is it?

uhoh
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  • What sort of answer are you looking for here? A reference to JPL DE docs? Or reasonable-sounding guesses? ;) – PM 2Ring Feb 17 '22 at 22:43
  • Eg, for the EM L1, from the full n-body Solar System sim, you know the exact positions & velocities of the Earth & Moon, and the EMB. You then find the point between the Earth & the Moon (which has a known angular velocity relative to the EMB) such that the centrifugal force is balanced by the gravity from the Earth & Moon, ignoring everything else. I guess it's a lot like calculating osculating elements. – PM 2Ring Feb 17 '22 at 22:46
  • @PM2Ring it should be possible to quickly verify if the "ignoring everything else" method is what they use or not. – uhoh Feb 17 '22 at 23:05
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    I suppose you could ask Horizons to compute a trajectory from TLE data for a body at a Lagrange point, and see if it drifts. It's a pity that the Lagrange point body data files don't link to the relevant docs... – PM 2Ring Feb 17 '22 at 23:15
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    Keep in mind that Horizons (or SPICE) do not compute trajectories. Those tools instead rely on trajectories that are calculated elsewhere and are encapsulated to Horizons / SPICE in the form of SPK files. Also keep in mind that JPL does not release the orbit propagation software from which the Development Ephemerides and other ephemerides built. I don't think this question is answerable as written. I could hazard a guess, but it would just be a guess. – David Hammen Feb 18 '22 at 09:00
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    My guess is pretty much the same as that of @PM2Ring : Calculate the osculating elements of the Earth-Moon barycenter with respect to the Sun and apply the very ugly but well-known algorithms for the five ER3PB Lagrange points. But that's just a guess. – David Hammen Feb 18 '22 at 09:07
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    @DavidHammen Sure, it uses pre-computed trajectories for major bodies (including spacecraft), but Horizons does compute trajectories of small bodies. From https://ssd.jpl.nasa.gov/horizons/manual.html#defs "the trajectory is numerically integrated on demand from an initial set of previously statistically estimated orbital elements in the JPL database." Also see https://ssd.jpl.nasa.gov/horizons/manual.html#user & https://ssd.jpl.nasa.gov/horizons/manual.html#tles – PM 2Ring Feb 18 '22 at 10:49
  • @DavidHammen There are several ways this question can be answered as written. 1) Ask Horizons "How far is the Sun/EMB L1 point from EMB today?" then use an equation and see if we can get the same number. If it works six months in the past/future as well, then that's how they do it. 2) Find a source where it's explained, 3) write an email to @JonGiorgini and let him know about this question... – uhoh Feb 18 '22 at 10:53
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    The JPL Planetary and Lunar Ephemerides DE440 and DE441 doesn't mention "Lagrange". Here's a tantalizing snippet "These four Lagrange Point SPK files were generated this date by Min-Kun Chung of the Navigation and Mission Design Section at JPL, using a program named LTOOL and based on the just released de431 planetary ephemeris." – PM 2Ring Feb 18 '22 at 12:28
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    LTool was developed by Martin W. Lo and Roby S. Wilson http://www.ieec.cat/hosted/web-libpoint/abstracts/lo2.pdf Wikipedia says "Martin Lo is well known for discovering the Interplanetary Superhighway, also known as the Interplanetary Transport Network." – PM 2Ring Feb 18 '22 at 13:12
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    @PM2Ring A google search for "LTOOL site:nasa.gov" yields lots of hits. One of the earliest says "This software is available for commercial licensing." JPL oftentimes does not quite grok the concept of open source. That applies to NASA as a whole. There is a lot of software I've written for NASA that an ordinary person cannot get their hands on. – David Hammen Feb 18 '22 at 15:19
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    @David I don't think uhoh is expecting to find the details of the algorithm they use to do the Lagrange point calculations. He just wants to know how JPL define them. – PM 2Ring Feb 18 '22 at 19:12
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    @uhoh On second thoughts, they probably don't ignore everything else, since they want a point that sits on the line connecting the two mass centres and which has zero effective potential in the rotating frame. – PM 2Ring Feb 18 '22 at 19:17

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