How did Jan Oort use comet orbits to propose the Oort cloud?

In 1950, Dutch astronomer Jan Oort proposed the existence of the Oort cloud by analyzing the orbital characteristics of long-period comets.12

Building on earlier work by Adrianus van Woerkom, who demonstrated that Jupiter would eventually eject long-period comets from the solar system, Oort investigated where these comets originated. He examined the "original" orbits of 19 comets—calculated by projecting their paths backward to before they entered the planetary region—and found a significant, unexpected excess of comets with orbital semimajor axes larger than 20,000 astronomical units (AU).31

Oort concluded that this concentration of orbits at such extreme distances could only be explained by a vast, distant reservoir of icy bodies surrounding the solar system. He proposed that gravitational perturbations from passing stars occasionally nudge these bodies, sending them into the inner solar system where they are observed as "new" comets. This hypothesis successfully accounted for the observed distribution of comet energies and remains the accepted explanation for the origin of long-period comets.132