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I got the latest TLE from www.celestrak.com for a satellite. How could I convert it to osculating elements?

Please, share some links/references.

Tarlan Mammadzada
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  • Then I don't understand what you are asking at all. Those have almost nothing to do with TLEs. Also I think you are just asking about a Keplerian orbit, not an osculating orbit. There are answers here already about nodal precession, and getting the mean anomaly vs time. I'd recommend you check existing answers. – uhoh Mar 09 '18 at 15:04
  • @uhoh I mentioned TLEs because that data is available in satellite database (celestrak, space-track). I didn't find Keplerian elements for on-orbit satellites, just TLEs – Tarlan Mammadzada Mar 09 '18 at 15:40
  • I think it would be a good idea to explain with more detail what kind of data you have to start with, and what kind of values you would like to calculate from it. – uhoh Mar 09 '18 at 16:19
  • @uhoh Added some details – Tarlan Mammadzada Mar 09 '18 at 19:09
  • Perhaps this answer will help you formulate a question that is clearer to others. – Chris Mar 09 '18 at 19:32
  • If you're interested in the "Keplerian" orbit in the sense of pure, unperturbed, two-body motion, then the only changes in time will be in the fast variable (mean/true anomaly). Some of the equations you show include the secular effects of $J_2$, i.e. not Keplerian motion. – Chris Mar 09 '18 at 20:14
  • @Chris I'm considering also precession (for Sun-synchronous orbit) – Tarlan Mammadzada Mar 09 '18 at 20:20
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    "...the changes in Keplerian elements with time." is a textbook definition of perturbations, so saying "ignoring perturbations" does not make sense. According to Wikipedia's article Orbital perturbation analysis: "In reality, there are several factors that cause the conic section to continually change. These deviations from the ideal Kepler's orbit are called perturbations." The orbital perturbation equations you now show are given in there as well. Also I still think you mean *Keplerian" orbit, not "osculating" orbit. – uhoh Mar 10 '18 at 03:05
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    @uhoh Thanks. Sorry for confusing question. I accepted the answer here, and asked another question, explaining what I'm trying to do. https://space.stackexchange.com/q/25964/19219 – Tarlan Mammadzada Mar 10 '18 at 12:00

1 Answers1

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Spacetrack Report #3 provides the equations in readable mathematical format and FORTRAN code to propagate TLEs. The final output of the algorithm, denoted by X, Y, Z, XDOT, YDOT and ZDOT are the position and velocity in inertial frame, which can be converted to osculating elements by traditional methods.

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Mefitico
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  • I need also to propagate the orbit, considering the changes in Keplerian elements. Added some details to question – Tarlan Mammadzada Mar 09 '18 at 19:10
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    FORTRAN! Now we're talking! – Organic Marble Mar 09 '18 at 19:57
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    If you want to ignore all perturbations, use SGP4 (the code described in report #3) with time since epoch set to zero to obtain "initial" position and velocity, then use a keplerian propagation (also known as Two-body), this propagation however keeps all elements but the mean anomaly constant. SGP4 considers at least J2 and drag, which causes all (osculating) elements to evolve over time. I would point out however that SGP4's TLE propagation is fairly accurate and does not take that long to run, thus it could probably more adequate than Keplerian propagation for your application. – Mefitico Mar 09 '18 at 20:16
  • @Mefitico Does SGP4 consider Sun, Moon, Jupiter, Venus? – Tarlan Mammadzada Mar 09 '18 at 20:27
  • @TarlanMammadzada Sun and Moon, yes; Jupiter and Venus, no -- but it's extremely unlikely you actually need to include the effects of Jupiter and Venus in your simulation. – Chris Mar 09 '18 at 20:35
  • @Chris As I know, SGP4 works also for deep space missions – Tarlan Mammadzada Mar 09 '18 at 20:37
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    @TarlanMammadzada yes, but only for the Air Force's definition of "deep space", which is "Earth orbits with a period > 225 minutes". – Chris Mar 09 '18 at 20:40
  • For more, see How can I plot a satellite's orbit in 3D using Python and Skyfield? – uhoh Mar 10 '18 at 06:14
  • @Chris 1. What about interplanetary missions? 2. Does SPG4 refer to online sources, such as JPL horizons or space-track? – Tarlan Mammadzada Mar 10 '18 at 11:46
  • @TarlanMammadzada SGP4 is a fairly accurate propagator for 1 week in Earth Orbit (be it LEO GEO), it was not build for interplanetary orbits. You can still use patched conic techniques for low accuracy interplanetary missions within the solar system (look up Laplace's Sphere of influence) and with this you could use Kepler Elements, I'm not familiar with any semi-analytic technique for interplanetary missions and if I was responsible for such a simulation, I would likely develop some numerical method (i.e. old fashion Runge-Kutta). – Mefitico Mar 12 '18 at 03:55
  • @Mefitico The numerical methods would be a big headache, as would need lots of computational power... Does SGP4 consider Sun perturbations to be able to move on Heliocentric orbit? – Tarlan Mammadzada Mar 12 '18 at 07:57
  • @TarlanMammadzada : "Perturbations" are generally forces that create little deviation from a reference (approximate) model. For Heliocentric orbits, the sun effect is the main force, not a "perturbation". Hence SGP4 is simply not suited for heliocentric orbits, at least not as it is described in Report #3. You could adapt it for this purpose, but that would invalidate the TLE files as unnaplicable for your customization. May I suggest you try using the free version of STK for orbit propagation? – Mefitico Mar 12 '18 at 12:35