The orbital mechanics seem relevant as, why provide such a detail otherwise; but perhaps it's merely in the collective consciousness because of certain recent videos.
If we say it's a spool of wire instead, then it all gets much simpler, indeed.

For which, testing impedance across far ends of the cable (it doesn't much matter whether either end is connected to the core or shield: the core simply adds Zo to the shield impedance at each end), is just some manner of, somewhere between a wire over ground plane (for whatever length of the wire is laid out on the ground*), to a spooled inductor (all the wire wound up in a more compact package).
The smaller it is, of course -- and for that matter, if it's doubled back on itself, in a "noninductive" manner for example -- the less sensitive it will be to ambient fields. So, depending on if you have this laid out maximally, like, literally looping around the Earth multiple times -- you'll have quite a lot of gain to ambient fields, particularly at very low frequencies (mains, submarine communcations, Schumann resonance, even daily ionospheric cycles I suppose), so, still some things to account for in addition to its own self-impedance; or, if in a small package and cancelled out to ambient fields, maybe not much of anything besides what's applied to it.
*Not that ground is very well defined, for short lengths; a wire in free space may be a better approximation. Which amounts to a higher Zo for that segment. Of which, a relatively large fraction of that impedance might be due to radiative loss rather than self-impedance. Depends on how good the ground is (soil? metal building?), what all is inbetween (wood or concrete floors?), etc.
In any case, that much wire, spooled up, will certainly have quite some inductance. A meter might not notice much impedance at all between the ends, at least until it charges up -- the time constant could be, fairly unsurprisingly: many seconds!
Tim