Rocket
The world over that has been an obsession with immortality and the desire to live forever, in China this desire manifested in alchemy and many countless individuals over the thousands of years toyed with compounds to create the elixir of eternal life and like a infinite number of monkeys with an infinite number of type writers they envitable created something that would change the world when somebody combined sulfur, charcoal saltpeter and created black powder.
However, despite the modern name "gunpowder", guns were not the first thing to be invented using the new stuff, which make sense if you think about it. in order to make a gun you need to have A: powder that will explode all at once not slowly burn, and B: Metal working to contain the explosion. Rockets on the other hand work by having a material that burns relatively slowly rather then blowing all up when you light it on fire and they don't need to be as well built since your only directing a lower pressure constant flame rather then one big blast.
A (very) Brief History of Rockets
400-100BC: the first, sorta, rocket we know of came about in Greece. A roman named Aulus Gellius wrote of how a Greek would entertain the people of the city of Tarentum with a wooden pigeon on a wire propelled by steam, 300 years later Hero of alexander made the Aeolipile, a metal ball on a water kettle. when the kettle was heated the water turned to steam, went up some pipes and spun the ball around by escaping two L shaped nozzles. These may not sound like rockets but they work the same way, speedy hot gas goes out one end, and creates movement. Obviously the Greeks never expanded on this concept so these remain only a footnote in rocket, and indeed world history.
1000s to 1200s: At this point the Chinese are believed to have invented the rocket proper, though it's not until 1232 that we have solid evidence when the Chinese attacked invading Mongols with "Arrows of flying fire". these "Fire arrows" were regular arrows with rockets attached or rockets with primitive warheads. Rockets also make an appearance in Europe around this time and Arab writings talk about Mongols rockets which they usedto help capture Baghdad, which the Arabs picked up on and used against the French during the Seventh Crusade.
1300s: some time in the 14th century that Huolongjing was written in china, a tactical book about the use of black powder or "fire weapons". included were 10th century fire arrows, rocket lunchers, two stage rockets, winged rockets, land mines, naval minds, triggers for them, proto-guns such as fire lances, match lockes, early bombards, poisonous gunpowder extra. What makes this book important for rockets is that it talks about the first multi stage rocket the "fire-dragon issuing from the water" Or it's proper name the Huo Long Chu Shui. The Fire dragon was a tube lifted on by rockets, with more rockets inside of it. Once lunched it would fly out and the booster rockets would ignite and fire the rockets out of the front of it. The Fire dragon was used mostly by the Chinese navy.
1400 Military Rockets make there way to Europe it self rather then Europeans coming to the mid east and getting rocketed for there trouble thanks to Ottoman Empire when they lay siege to Constantinople, of course the Ottomans got flamethrowered for there trouble so it perhaps all balanced out in retrospect.
1500s: the earliest experiments with multistage rockets in Europe were made.
1600s: The "Artis Magnae Artilleriae pars prima" ("Great Art of Artillery, the First Part", also known as "The Complete Art of Artillery") was printed in Amsterdan and it was used as a Artillery manual and included instruction on production and properties of Rockets, including multi-stage rockets, batteries, and rockets with wing stabilizers rather then big sticks.
1700s: the first all metal rockets are developed in India in the Kingdom of Mysore. the Mysore rockets were used very successfully against the British East India company (East India Company brief summery: think a cyberpunk mega corporation only more racist) and the British were surprised by what these rockets could do. There all metal nature allowed more fuel meaning they had a lot more range (2 kilometers) then what the British had seen a rocket do, and so like any good British man, they stole a few and sent them back home so that they could learn how to make more.
1800s: The British invent the Congreve rocket from there study of the Mysore rockets. The Congreve was very effective for it's day, true it did not out range a cannon but you could fire it a lot faster, it was lighter so you needed half as many horses to pull a rocket unit around, and the had a major advantage over period cannons: they had payloads. Thanks to slower speeds rockets could have warheads such as incendiary compounds to light a town ship on fire, it's why there were relatively ineffective against fort Henry during the war of 1812 and allowed the US to sing about how there flag was still there, despite the rockets red glare. in 1844 William hale came up with the Hale Rocket, a much more accurate version of the Congreve without the need of a stick to stabilize it self since it was able to spin it self like a rifled bullet.
1900-early 1945s: now things get interesting. Up to now humans had only experience with solid rocket engines, mostly of gunpowder, but the early 20th century the first liquid fuel rockets started to be developed and a lot of rocketry groups were started but military rockets had died off by the time world war one began. The reason was that everything a rocket could do a howitzer could do better since we had gotten a handle on making shells by this point. Rockets had some uses during the war though mostly as a anti Zeppelin device. Still over the course of the war much research was done into rockets. After the war though Germany found it self with a problem, the treaty of Versia ended the war, the German army could have any artillery to allow long range fire such as the Railway guns they used to shell Paris with in first World War, but like a good rule lawer there found a loop hole and funded rocket research.
Rockets were similar to the older rockets, some what inaccurate but you could fire lots of them very quickly and as lessons from the first world war showed: the best way to use artillery was as a quick, short intense barrage to disorinatate the enemy just before you attacked and Artillery were very, very good at that. Rockets thanks to there lightness thanks to the lack of gun needed for them also became the gold standard in manportable anti tank weapons with the US bazooka being among the first. Germany of course invented the V1 and V2, a flying bomb and a the first missile respectively, during the war, but like other such weapons Germany would have honestly done better to build a few dozen more Panzers then invest in such relatively ineffective weapons.
late 1945s-2000s: Following the second world war missiles would quickly come to dominate the way all nations would deliver atomic weapons and missiles soon got bigger then anything that had come before becoming some of the largest machines ever built. Missiles also would come to dominate air weapons as well, for awhile the US thought it did not even need to put cannons on it's aircraft and It could use missiles for everything, they were wrong of course but with ranges far beyond any gun and the ablity to chase an enemy it's not hard to see why they thought so. Anti tank missiles continue to be highly effective and anti air missiles are also very, very useful. incidnetly: the difference between a Missile and a Rocket is more then semantics, a rocket is unguided a missile is not. Once you shoot a rocket of nothing controls it but gravity, physics and fate, while with a missile something is still controlling it.
Unlike firearms which have the Railgun of Damocles hanging over there future, Rockets and Missiles always seem to stick around in how we picture future wars thanks to there traits, lightness compared to guns, and ability to carry explosive payloads to delicate to be shot out a gun that make them useful now.