It requires less delta-V to create a large change in inclination when the object is far from the Sun, because the orbital speed in a more or less circular orbit varies as (orbital radius)^(-1/2).

▲

JoeAltmaier 4 hours ago | parent [-]

Yes, imagine a highly elliptical orbit and you've just reached the furthest point , like the roller coaster at the top of the hill, almost stationary. At that point you could pretty much boost the object in any direction you wanted, and it would then assume that orbit.

	▲	pfdietz 4 hours ago \| parent [-]
		Yes. In that situation, where the perihelion is at the minimum tolerable distance from the Sun, the speed at apohelion is proportional to 1/(distance to sun) (this follows from conservation of angular momentum).