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For the last two decades we have been observing a huge increase indiscoveries of long-period comets (LPCs), especially those withlarge-perihelion distances. We collected data for a full sample of LPCsdiscovered over the 1801-2017 period including their osculating orbits,discovery moments (to study the discovery distances), and original semimajoraxes (to study the number ratio of large-perihelion to small-perihelion LPCs infunction of 1/a-original, and to construct the precise distribution of an1/a-original). To minimize the influence of parabolic comets on thesedistributions we determined definitive orbits (which include eccentricities)for more than 20 LPCs previously classified as parabolic comets. We show thatthe percentage of large-perihelion comets is significantly higher within Oortspike comets than in a group of LPCs with a<10000 au, and this ratio oflarge-perihelion to small-perihelion comets for both groups has grownsystematically since 1970. The different shape of the Oort spike forsmall-perihelion and large-perihelion LPCs is also discussed. A spectaculardecrease of the ratio of large-perihelion to small-perihelion LPCs with theshortening of semimajor axis within the range of 5000-100 au is also noticed.Analysing discovery circumstances, we found that Oort spike comets arediscovered statistically at larger geocentric and heliocentric distances thanthe remaining LPCs. This difference in the percentage of large-perihelioncomets in both groups of LPCs can probably be a direct consequence of awell-known comets fading process due to ageing of their surface during theconsecutive perihelion passages and/or reflects the different actualq-distributions.

Discovery statistics and the 1/a-distribution of long-period comets detected over the 1801-2017 period