The satellite (or adjunct) is a syntactic function. All non-obligatory constituents that are situated at the clause level, and therefore depend on the predicate, are included in this category.
While some satellites can occur with any type of state of affairs, others are limited in their distribution by their semantics and those of the predicate which they depend on. For example, satellites expressing the instrument typically occur with controlled states of affairs, since they are to be manipulated by the agent in order to achieve a certain goal.
 The term satellite is sometimes used in a more specific sense. E.g. Harm Pinkster (2016: 25) uses it as a general term for non-obligatory constituents, independently whether they are clause-internal (i.e. satellites sensu stricto, which he calls adjuncts) or extra-clausal (i.e. disjuncts).
τῷ with the infinitive signals an instrument, cause or manner as a satellite.
The infinitive, preceded by a preposition and an article, signals a satellite. The semantic role of the satellite depends on the meaning of the preposition in question.
The participle, usually accompanied by ὥστε, signals a result as a satellite agreeing with an argument.
The participle, sometimes accompanied by ἅτε or ὡς, signals a cause as a satellite agreeing with an argument.
The participle in the future (rarely in the present) signals a goal as a satellite, agreeing with an argument. This is usually the case with verbs of sending, going, commanding, preparing, etc.
The participle, if necessary preceded by the negation μή, signals a condition as a satellite agreeing with another constituent.
The genitive absolute, often accompanied by ἅτε or ὡς, signals a cause as a satellite.
The genitive absolute, often preceded by the negation μή, signals a condition as a satellite. The subject of the genitive absolute is never the same as that of the main clause (meaning that coreferential situations are impossible).
The genitive absolute, often preceded by περ or καίπερ (or καί or καίτοι), signals a concession as a satellite.