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As in the title, it is possible to have a repeatable Sun-synchronous orbit but with an elliptic eccentricity?

If yes, which equations I have to consider to determine its classical orbital elements?

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    $\begingroup$ You used the term "classical orbital elements". Do you mean "Keplerian orbital elements" or "osculating orbital elements"? There is no such thing as a Sun-synchronous orbit in classical/Keplerian/osculating orbital elements because the right ascension of ascending node is fixed (as are all of other classical orbital elements except for mean anomaly). You'll need to use some non-classical orbital element set, or an orbital element set in which right ascension of ascending node, argument of periapsis, inclination, semi-major axis length, and eccentricity can change. $\endgroup$ Commented Jun 28, 2022 at 20:49
  • $\begingroup$ Thank you for your answer, I mean Keplerian Orbital Elements which in commercial softwares (such as STK) are called classical orbital elements. In fact I want a set of equations that allows me to calculate the sma, ecc, inc, RAAN, Aop and TA. I already have ones for the case of a circular repeating SSO, with which I computed a set of elements and defined an orbit which works well in simulations with simple approximation of only J2 Perturbation. However the ground track is not regular when I try to do the same with an elliptic orbit. And that's the reason behind the question. $\endgroup$
    – Frank
    Commented Jun 29, 2022 at 7:23
  • $\begingroup$ PS I disagree about the fact that the keplerian elements remain constant for a SSO cause for definition a SSO has a mean RAAN rate (due to J2 perturbation) which is equal to the one of the Sun. Maybe I didn't understand what you mean for fixed orbital elements. $\endgroup$
    – Frank
    Commented Jun 29, 2022 at 7:30

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This paper might help answer your question. They look at repeating ground tracks and sun synchronous orbits. The seem to limit their discussion mainly to circular orbits, because they say perigee is too close to the the earth for some elliptical orbits, but then go on to discuss some elliptical orbits in the context of MEO at the end of the paper.

Paek, S., Kim, S., Kronig, L., & De Weck, O. (2020). Sun-synchronous repeat ground tracks and other useful orbits for future space missions. The Aeronautical Journal, 124(1276), 917-939. doi:10.1017/aer.2020.21

The paper includes some derivations with equations that might help with the second part of your question.

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  • $\begingroup$ Thank you for your answer and for the paper, I'll check it out. $\endgroup$
    – Frank
    Commented Jun 29, 2022 at 7:32

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