Hello /r/AskHistorians, I was talking with a friend and the topic of The Siege of Vienna (1683) came up. We were wondering if someone could enlighten us as to why Britian and France did not support defense troops at the Siege of Vienna at the hands of the Ottomon Empire? They seemed well enough equipped but did not help with the defense of Europe at that time. It is only speculation but were they unaware of the dangers of an encroaching Ottomon Empire in Europe or were they preoccupied (or a third possibility I had not considered)?
First, it is important to remember that all of Europe was not united against the Ottoman Empire.
When the Vatican created the "Holy League" in response to their "hereditary enemy" invading Christendom (Holy League: Holy Roman Empire, Poland-Lithuania, Republic of Venice), France and England had no interest in joining.
The Thirty Years' War had only recently ended (1648), and this had seen (among many many combatants) France and England at war with the Holy Roman Empire and Spanish Empire. These states were frequently at war with one another.
France, in fact, was an ally of the Ottoman Empire. Concerned with the situation for France in Central Europe (especially the House of Habsburg), Francis I sent a letter in 1526 requesting both an alliance and for the Ottomans to attack the Habsburgs. This was welcomed by Suleiman the Magnificent, as he had been waiting for any excuse to invade Eastern Europe, and he soon launced his campaign into Hungary. For three centuries following this, Franco-Ottoman relations were generally genial, with the two often working together towards their common interests in Central Europe.
Although relations between the two states cooled a bit by the middle of the 17th century, France still remained friendly with the Ottomans, and encouraged them to continue their campaign against the Habsburgs.
When the Holy League was formed against the Ottomans, France refused to join and in fact -- although officially neutral -- actively encouraged Ottoman victory over the Habsburgs. During the Battle of Vienna, France took this position further, and actually attempted to prevent a force of the Holy League from coming to the aid of the city.
England, for its part, was often at war with Spain (allied with the Holy Roman Empire, and under Habsburg rule for a lengthy period). The English, in general, thought highly of the Ottoman Empire during the 16th century, and often expressed admiration for its achievements and majesty. Elizabeth I sent her spymaster to enlist the aid of the Turks in her war with Spain. The English Civil War had ended just 20 years prior to the Battle of Vienna, and they were had their hands full on the home front keeping the peace. Not only this, but between 1678 and 1681, all of Britain was gripped with anti-Catholic hysteria when false-accusation were made that there was a Catholic conspiracy to assassinate Charles II -- known as the Popish Plot. Throughout the 17th century, however, public opinion was generally unfavorable towards Catholics, and often violently so. Entrance into a Catholic Holy League, sponsored by the Pope, would not have been a popular move.