I would like to compute the distance between a satellite and a specified orbit. For instance, for an orbit at 897 km altitude, 0 degree eccentricity, 99 degree inclination, and RAAN of 0 degrees on Jan 01, 2023 00:00:00 GMT (Sun Synchronous Orbit), is there a way to calculate the distance from the International Space Station to the closest point on that orbit?
I can imagine converting a bunch of points on that orbit to ECI coordinates and then computing the distance between them and the ISS and choosing the smallest. I could further interpolate points between the two closest points on the orbit if I needed finer granularity.
I'm wondering if there is a clever geometry trick that I can use instead of calculating all of those distances. If I could convert the Keplerian components of the orbit to the parametric equation of an ellipse, I could use this but the conversion to the ellipse seems to be less than straightforward (see here).