Satellite knot as a splice
= Satellite knot as a splice
Let $P$ be a knot in the exterior of an unknot $U$. Splicing the exterior of a companion $C$ to the $U$-boundary of the two-component exterior exchanges their peripheral curves and leaves the $P$-boundary. Meridian filling that remaining boundary gives $S^3$, and its filling core is the satellite $P(C)$.