In this talk I investigate transverse knots in the standard contact structure on R^3. These are knots for which y>dz/dx. The name "transverse" comes from the fact that these knots are positively transverse to the contact planes given by the the kernel of the 1-form dz-ydx. The classification of transverse knots has been long investigated, and several invariants were defined for their distinction, one classical invariant is the self-linking number of the transverse knot, that can be given as the linking of the knot with its push off by a vector field in the contact planes that has a nonzero extension over a Seifert surface. Smooth knot types whose transverse representatives are classified by this classical invariant are called transversaly simple. In this talk I will talk about how transverse simplicity is inherited for positive braid satelites of smooth knot types.