How does Jupiter change the orbits of comets?

Jupiter exerts a significant influence on the orbits of comets through its powerful gravitational field. As comets pass through the planetary region, Jupiter’s gravity acts to perturb their orbits, leading to several distinct outcomes:1

• Energy Scattering: Jupiter can scatter a comet's orbital energy, which changes its orbital period and size. This process can either capture a comet into a shorter-period orbit or increase its energy, potentially ejecting it from the solar system on a hyperbolic orbit into interstellar space.1
• Orbital Evolution: Repeated passages through the solar system allow Jupiter to redistribute the orbital energies of comets. This interaction is a primary mechanism for the evolution of short-period comets, often referred to as "Jupiter-family comets," which have orbits that are typically concentrated near the ecliptic.21
• Tidal Disruption: In extreme cases, such as with Comet Shoemaker-Levy 9, a comet passing too close to the planet can be captured into orbit around Jupiter. The intense tidal forces from the planet's gravity can then break the comet's nucleus into multiple fragments, which may eventually impact the planet.3

Astronomers use the Tisserand parameter to identify and track these periodic comets, as this value remains approximately constant even after their orbits have been altered by Jupiter's gravitational influence.2