Question

How did the outcome of the Battle of Constantinople affect the course of history?

Answer 1

The capture of Constantinople (and two other Byzantine splinter territories soon thereafter) marked the end of the Roman Empire, an imperial state which had lasted for nearly 1,500 years

Answer 2

I would add that when the Ottomans took Constantinople, they cut off a number of trade routes from Europe to the East, leading to Europeans exploring sea routes around Africa and west across the Atlantic.

That, and the Ottomans change the name of the city to Instanbul, changing maps forever and inspiring some silly songs. =)