In the Prologue to the Prose Edda, he seems to develop a genealogy of the Norse Gods being descendants of the Trojans. Starting with the Trojan king Priam, he develops connections, like for example Thor being son of the Ethiopian king Memnon and Tróán (the daughter of Priam). Why did he do this in the prologue, what was its purpose?
It was fashionable.
Being connected with Troy was considered prestigious. Hence Virgil claimed that Aeneas had escaped the fall of Troy to go to Rome and become an ancestor of Romulus. An unknown author claimed that a descendant of Aeneas, Brutus, had become the first king of Britain and given it its name. Snorri was working within that tradition.
Short answer: he wants to explain everything.
It was made to explain where did his non-christian ancestors' belief came from. He wants to make sense of the reason why they didn't follow christian beliefs. Snorri also links old classic names to norse names through a forced folk etymology and says that they were men from Asia (hence the name æsir (singular ás)) that were so powerful that were mistaken as gods as time passed.
I think the tree Ygg-drasil (terrible-horse) is the (wooden) Trojan horse. Perhaps this is what Snorri saw that caused him to make the connection to Troy.
terrible (adj.) late 14c., "causing terror, awe, or dread; frightful," from Old French terrible (12c.), from Latin terribilis "frightful," from terrere "fill with fear," from PIE root *tros- "to make afraid"
In Greek mythology, Tros was the founder of Troy