How does the non-mechanical waves move through the space?

Non-mechanical waves(radio waves) which are sent into space are nothing but electromagnetic waves similar to light waves.Unlike sound waves or water ripples(waves) which require a medium to propagate in,electromagnetic waves are self-sustaining waves.We know that a moving charge causes a magnetic field and a moving magnetic field induces an electric field.Since an electromagnetic wave comprises of both electric waves and magnetic waves which are caused by each other,therefore they dont require a medium for propagation.