Could the Ottomans have conquered Europe?

Say if Sultan Suleiman the Magnificent had been able to make it to Vienna before coalition forces and been able to lay siege to the city and cut off outside forces, would Austria have fallen or would they continue to fight on? The one huge advantage the Ottomans had was the rest of Europe was so engaged in their petty little squabbles that they would rather their mortal enemies fall then unite against the Moslem threat.
 
If the letters from the Pasha of Buda to the Austrians are anything to go by, the Ottomans were having a difficult enough time holding on to Hungary. They could have taken Vienna and damaged the Habsburgs, forstaling the fall of Hungary, but holding Vienna would be something else entirely.
 
Romans did it. Why can't the turks?

Different demography, the Roman conquest happen at a point in time where agricultural advanced had resulted in massive increase in a population on the Italian peninsula, while these hadn’t spread west and north yet. A power on the Italian peninsula couldn’t have done the same 500 year earlier.
 
Say if Sultan Suleiman the Magnificent had been able to make it to Vienna before coalition forces and been able to lay siege to the city and cut off outside forces, would Austria have fallen or would they continue to fight on? The one huge advantage the Ottomans had was the rest of Europe was so engaged in their petty little squabbles that they would rather their mortal enemies fall then unite against the Moslem threat.
At best the balkans and hungary, Italy with luck and effort but not more or less.
 
Say if Sultan Suleiman the Magnificent had been able to make it to Vienna before coalition forces and been able to lay siege to the city and cut off outside forces, would Austria have fallen or would they continue to fight on? The one huge advantage the Ottomans had was the rest of Europe was so engaged in their petty little squabbles that they would rather their mortal enemies fall then unite against the Moslem threat.

Even if he managed to do this, there is no guarantee that Vienna is falling: siege with the relieve force coming from outside tended to be a risky scenario for the besieges (Padua, Turin, 2nd Vienna, Narva, etc.).
 
Even the absolute best-case scenario for the Ottomans where everything goes right and snowballs with zero issues would not be enough to get them past the Alps IMO

The absolute best-case scenario for grabbing as much land as unreasonably imaginable would be a no Timur invasion scenario that sees the Ottomans go all-out on an Italian adventure resulting in a ridiculous navy being established to supply this invasion and maintain supply lines. This shifts the Ottoman perspective on military expansion to be way more naval-oriented. The Ottomans succeed in overunning Italy and as a side consequence, establish absolute naval supremacy in the Eastern Med. Additionally, the Papacy's authority gets shattered in the process when the Ottomans set up a puppet Pope. Between the Western Schism analogue and the puppet Pope in Rome, a de facto division of the Catholic Church occurs eventually giving rise to national churches and increasing hostility between Western states on the basis of religious doctrines.

Tl;dr because I'm not about to write out a full wank scenario the Ottomans end up doing their OTL shenanigans in the Middle East, manage to overrun Persia while it's still fractured, and otherwise establish lots of local vassals and puppets to govern the more tribal regions of Eastern Persia/Afghanistan, Arabia, and North Africa under the guise of holding the authority of Caliph. The Ottomans establish a complimentary military system to the Janissaries that's basically Muslim Crusaders to capitalize on the Middle East's manpower. Meanwhile in the Med. the Ottomans are pulling out all the stops claiming to be the 3rd Rome and implementing Roman-inspired institutions in their conquered Christian provinces. Backing up this claim is their holding of Rome and Constantinople, Pax Ottomana in the Mediterranean, and the supposed completion of Justinian's reconquest of the Mediterranean with the magnum opus of of alt-Mehmed II, the subjugation of Hispania and ripping Iberia apart into a large number of feuding tributaries with the 'Caliphate' of Cordoba as the primary vassal and chief enforcer of Iberian subjugation

This is pretty much as good as it theoretically gets for the Ottomans in Europe. Unlike the Romans they're not facing horribly demographically outclassed tribes but organized, densely populated states and their administrative core is based out of Thrace and Western Anatolia. Best-case scenario for the Ottomans, they've got the navy to lock down the entire Mediterranean and can expand their reach to the Western Mediterranean coast. In theory Iberia is conquerable thanks to it's large coastlines, isolation from the rest of Europe thanks to the Pyrenees, and they have a full lockdown on Italy letting them leverage their resources in Italy, North Africa, and Southern Spain to overrun Iberia. So they've done Roman things, but there is NO way they ever overrun France. Too defensible, no allies to leverage, too much land that can't be resupplied from sea, a large, hostile local populace and so on. Trying to march to Lyon would be 10x worse than trying to march on Vienna as far as Ottoman supply lines are concerned.
 
The problem with a Ottoman conquest of Italy should be pretty obvious, Italy was the battle ground of HRE/Germany, France and Aragon/Spain, the Ottomans successes against the Habsburg in OTL heavily depended on the Habsburg being busy fighting France and France cooperating with the Ottomans. Here the Ottoman do the equivalent of walking into a bunch of rapid dogs and try to take the pierce of meat they’re fighting over. In OTL Ottoman expansion was helped by the fact they could mostly take on one enemy at the time. First the Byzantine, then the Serbs, then the Hungarians and then the Austrians.
 
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