Final answer:
The orbits of nearby objects in the solar system are most directly affected by a planet's gravitational field, which was exemplified by the prediction and discovery of Neptune based on Uranus's orbital deviations.
Step-by-step explanation:
The characteristic of a planet that would most directly affect the orbits of nearby objects in the solar system is its gravitational field. This is because the gravitational pull from a planet can influence the trajectory of other bodies nearby. The discovery and prediction of Neptune's existence is a prime example of this phenomenon, as Neptune's gravitational field was responsible for the unexpected orbital deviations of Uranus. It was these deviations that led to the mathematical prediction of Neptune before it was directly observed.