If we were further away from the Sun, the gravitational influence of Jupiter would indeed become more significant. However, it's important to note that the gravitational force exerted by the Sun would still be the dominant factor determining the motion of objects in the solar system, including the planets and smaller bodies like asteroids and comets.
Jupiter is the largest planet in our solar system and has a considerable gravitational pull. Its gravity affects the orbits of other planets, particularly in terms of gravitational interactions and perturbations. However, Jupiter's influence is not strong enough to directly "pull" a planet like Earth into its own orbit.
The motion of objects in the solar system is governed by the combined gravitational forces of the Sun and other celestial bodies. The closer an object is to a massive body like the Sun, the stronger the gravitational pull it experiences. The inverse square law of gravity states that the strength of the gravitational force decreases as the distance between two objects increases.
Even if we were further away from the Sun, the Sun's gravitational force would still dominate due to its enormous mass. The gravitational pull of Jupiter would be present, but it would not be sufficient to counteract the Sun's gravity and change the overall motion of objects in the solar system significantly.
However, it is worth noting that the presence of Jupiter can have indirect effects on the stability and dynamics of the solar system. For example, Jupiter's gravity plays a role in protecting Earth from some potential impacts by attracting and deflecting comets and asteroids that might otherwise collide with our planet. This is due to Jupiter's strong gravitational influence on these smaller bodies, redirecting their trajectories away from Earth.
In summary, while Jupiter's gravity would become more significant if we were further away from the Sun, the Sun's gravitational pull would still dominate, and the overall motion of objects in the solar system, including Earth, would primarily be determined by the Sun's gravity.