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How do Jupiter and Saturn change the paths of some comets?

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Illustration showing the eight planets of the solar system in order from the Sun-Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune-depicted to scale by size, with labeled diameters in miles and kilometers. The Sun is partially visible on the left for comparison. — Solar system The planets (in comparative size) in order of distance from the Sun.

Jupiter and Saturn, as massive planets, exert significant gravitational influence on comets that pass through the planetary region of the solar system. This process, known as gravitational perturbation, alters the orbits of these comets in several ways:12

Orbital Energy Changes: Jupiter’s gravity can scatter a comet's orbital energy, which results in either increasing or decreasing its orbital period and size.2
Capture and Ejection: These gravitational interactions can capture comets into shorter-period orbits—often referred to as Jupiter-family comets—or, conversely, perturb them into hyperbolic orbits that eject them from the solar system entirely into interstellar space.2
Uniform Distribution: Repeated passages through the planetary region allow the giant planets to spread comets across a range of orbital energies, leading to a more uniform distribution of long-period comets over time.2

Essentially, when comets from the Oort cloud enter the inner solar system, the gravity of Jupiter and Saturn takes control of their paths, determining whether they remain in the system or are cast out.2