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The Sun certainly is the primary mass in our Solar System. The Earth orbits the Sun in a very stable manner. There are no other stars near enough to Earth to affect its orbit in a measureable way.
Jupiter affects Earth's orbit, of course. In fact, the orbits of the planets in the Solar System are interrelated, yet the primary influence is the Sun. Gravitational influences between the gas giant planets is the way that Uranus and Neptune were discovered ... both were "calculated to exist" before they were first seen and reported.
It is possible that other stars have passed near the Sun in the past and affected planetary orbits, but we have no direct way of knowing that.
Our entire Solar System orbits the Milky Way galaxy (within the galaxy), and as near as we can measure it is a stable situation.
The universe is not only stranger than we imagine, it's stranger than we CAN imagine. --- JBS Haldane
Come visit me at Comanche Springs Astronomy Campus (we're on Google Maps) in Texas.