C/2012 S1 ISON
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Comet ISON was discovered on 21 September 2012 with International Scientific Optical Network (ISON) near Kislovodsk, Russia, that is a year and about two months before its perihelion passage. C/2012 S1 was a comet with an extremely small perihelion distance of 0.0125 au (about 3 solar radii). It was intensely followed by numerous observers until its decay. Sekanina and Kracht (2014) studied the disintegration process of this object in detail, suggesting that the comet fully disintegrated hours before perihelion passage. The first minor outburst occurred 16 days before perihelion (beginning of November) at a distance of 0.7 au from the Sun. However, an unforeseeable fading of the originally very active comet was reported by observers many weeks before this event.
Therefore, two orbits worth noting here are based on data taken at large heliocentric distances (more than 3.4 au from the Sun, solutions: pa, pc) and before the two-month gap starting from 9 June 2013 (see picture). The first orbit is purely GR and gives original 1/a as nearly zero, whereas the second one is an NG orbit obtained using the g(r)-like formula describing CO sublimation. Here this last orbit was taken as preffered orbit.
Comet would have its closest approach to the Earth on 26 December 2003 (0.431 au), about a  month after its perihelion passage.
See also Sekanina 2019 and Królikowska 2020.

solution description
number of observations 4056
data interval 2011 09 30 – 2013 06 08
data arc selection data generally limited to pre-perihelion (PRE)
range of heliocentric distances 9.39 au – 3.41au
detectability of NG effects in the comet's motion comet lost close to perihelion or split comet
type of model of motion GR - gravitational orbit
data weighting YES
number of residuals 8059
RMS [arcseconds] 0.36
orbit quality class 1a
orbital elements (heliocentric ecliptic J2000)
Epoch 2011 10 06
perihelion date 2013 11 28.96266068 ± 0.00032126
perihelion distance [au] 0.01246165 ± 0.00000014
eccentricity 0.99999952 ± 0.00000002
argument of perihelion [°] 345.537916 ± 0.000072
ascending node [°] 295.696606 ± 0.000100
inclination [°] 62.05178 ± 0.000566
recip semi-major axis [10-6 au-1] 38.41 ± 1.33
Time distribution of positional observations with corresponding heliocentric (red curve) and geocentric (green curve) distance at which they were taken. The horizontal dotted line shows the perihelion distance for a given comet whereas vertical dotted line – the moment of perihelion passage