Let
be a knot inside a torus, and knot the torus
in the shape of a second knot (called the companion
knot) ,
with certain additional mild restrictions to avoid trivial cases. Then the new knot
resulting from
is called the satellite knot . All satellite knots are prime
(Hoste et al. 1998). The illustration above illustrates a satellite knot of
the trefoil knot, which is the form all satellite
knots of 16 or fewer crossings take (Hoste et al. 1998). Satellites of the
trefoil share the trefoil's chirality, and all have wrapping number 2.

Any satellite knot having wrapping number must have at least 27 crossings, and any satellite of
the figure eight knot must have at least 17 crossings
(Hoste et al. 1998). The numbers of satellite knots with crossings are 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6,
10, ... (OEIS A051765), so the satellite knot
of minimal crossing number occurs for 13 crossings. A knot can be checked in the
Wolfram Language to see if it is a
satellite knot using KnotData[knot,
"Satellite"] (although all knots currently implemented in the
Wolfram Language are nonsatellite
knots).

No satellite knot is an almost alternating knot. If a companion knot has crossing number
and the satellite ravels times longitudinally around the solid torus, then it is conjectured
that the satellite cannot be projected with fewer than crossings (Hoste et al. 1998).