However, if you were to somehow turn 'off' the gravitational effects of the Sun, the planets wouldn't fly off instantaneously, but rather the inner ones would fly off first, followed by the outer ones, as the gravitational signals from the Sun only propagate outwards at the speed of gravity, which ought to equal the speed of light. There is no fundamental reason why some planets are more or less eccentric than one another it's simply a result of the initial conditions from which the Solar System formed. (closest approach) and aphelion (farthest distance) with respect to the Sun.
The orbits of the eight major planets vary in eccentricity and the difference between perihelion.
