Fifteen, uh, fifteen for what? In the vector setting.
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You want to work with orbital elements.
I assume you mean an orbit with an altitude of 190k km, which is 190 000 km or 190Mm?
(An orbit around Saturn at 190 km altitude will decay in a matter of minutes)
Set the semi-major axis to 250 000 km. (190Mm + ~60Mm [Radius of Saturn])
Then set the eccentricity to 0 for a circular orbit.
Inclination, longitude of ascending node, longitude of periapsis, and mean anomaly at epoch are arbitrary if all you care about is altitude. Set all of these to 0.
Depending on your reference, this will give you either an orbit in the ecliptic plane (ref ecliptic) or, as I suspect you want, an orbit around the equator in plane with the rings (ref. equator).