In 1450, how much time would it take a traveler from Constantinople to reach Eastern India?
It would depend on what route he took, what the political situation was like in between the two areas and what time of the year he travelled. (This is just before European ships made it around Africa) To get from Constantinople to India, there were several routes. One would be to go east, crossing modern Iraq and Iran, and taking a ship from modern day Bandar-e-Abbas (then: Hormuz) either directly across the Indian Ocean to one of the Southern Indian ports (in 1450 Calicut was the most prosperous; that is where da Gama arrived) or else to take the coast-hugging route (which would take much longer, but was safer from pirates). From Southern India, it would be advisable to take another ship via Sri Lanka, or even to go through the straits between Indian and Sri Lanka (though this was a less travelled route by traders) to the East Coast of India. Of course, one could always go overland from South Western India to South Eastern India, but it necessitated travelling though a number of state