A stated in another answer, significant is a relative concept, as it depends on the degree of precision required by the question made.
Keplerian orbits, the solution of the inverse square law for a central force or two body problem, are perturb by several much smaller forces that, nevertheless, change the trajectory a bit.
Here are the relative strength ...
When calculating the future orbit of an artificial (Earth) satellite, is the moon's gravity significant or insignificant?
It's a great question!
Of course everyone's definition of "significant" will be different.
Gravity is a long range force, it never goes to zero, and decreases only as $1/r^2$. Nothing blocks it either, so basically everything pulls on ...