How does earth affect the solar system?
Out Earth is only a small planet, but anything we now call a "planet" ends up having a profound effect on the Solar System. See the explanation below.
Three words: Clearing the neighborhood.
Back in 2006 this was the most controversial phrase in all of science, as it led to Pluto being rendered "not a planet". But the implications of clearing the neighborhood are literally seen across the orbit of the planet, an effect extending far beyond the immediate region around the planet itself.
Clearing the neighborhood means the region around the entire orbit of a planet is cleared of smaller bodies that could collide with the planet; what smaller bodies remain are either controlled and trapped by the combined action of the planet and the Sun, or trapped directly as moons.
In the case of the Earth, several asteroids are known where the asteroid is held as a companion of Earth in orbit, but never in position to collide with us. The Earth acting together with the Sun has them in control. One such asteroid is 3753 Cruithne, see https://en.wikipedia.org/wiki/3753_Cruithne.
There are also Trojan-type asteroids that orbit around the Lagrange points of the planet-Sun system, points selected by the combined gravity if the planet and Sun. Earth has 2010 TK7, Jupiter has lots of them, and most planets in our Solar System are known to have at least one. See https://en.wikipedia.org/wiki/Trojan_(astronomy).
And of course, There are moons. Earth has one which is, of course, what we call just "the Moon.
Apart from these controlled objects, we see very few things hanging around Earth's orbit because of Earth clearing the neighborhood. (Most of the "potentially hazardous asteroids that are found, get "demoted when we learn more about their orbits.) So it is with Mercury, Venus, and all other planets. They leave smaller, otherwise "uncontrolled" objects confined to planet-free zones like the asteroid and Kuipet belts.
Earth is truly among the "elite" bodies under the Sun, being one of only eight "planets capable of doing this over a range of billions of kilometers. Astronomers had good reason to distinguish beighborhood-clearing bodies from other round worlds when they defined "planets" in 2006.