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Let's say in 1793, Catherine the Great is convinced by her lover to make an attempt to conquer China. Russia mobilizes 40,000-50,000 men and storms Outer Manchuria. Qing totally underestimates the Russians and only send a small army and it is wiped out. By then Qing's military was in severe decline due to the Banner system becoming decadent, widespread corruption, and loss of military morale. Not to mention Heshen was strangling the state with his mass endemic corruption and the state had become inefficient, unresponsive and in the hands of incompetents.

Qing send two large armies of "elite banner troops" to Manchuria, both of which are defeated. Rebellions then break out all over China due to Qing losing their aura of military superiority. Large parts of the country slip out of their control. Due to the turmoil and political risks, Qianlong doesn't abdicate in 1796. When he dies in 1799, Heshen launches a coup and takes out the heir Jiaqing, promoting a favourite to rule as puppet emperor.

Meanwhile Russians begin to colonize Manchuria (which is largely empty before large scale Han immigration), attracting local recruits into their army due to their superior military weapons and the promise of victory and spoils. Russians begin manufacturing cannon and muskets in Manchuria. In 1802, they march on Beijing. The Great Wall fortifications by this time are a joke both due to corruption and China not expecting a northern threat since the Manchus themselves invaded. The Russians capture Beijing and loot it. Heshen and the Qing emperor flee to Nanjing. China is now split between warlords, the Russians, and the southern Qing dynasty.

Working with Confucian officials, the Russians declare a new dynasty and place a Romanov on the throne. They build a Han army equipped with European weapons and manage to defeat the other dynastic contenders and win over the local Han populations whereas before Russian troops were too prone to looting and atrocities. Once they take Nanjing, they execute Heshen and all his lackies thus earning the respect of the Confucian officials. They do not attempt to impose their Orthodox religion and decide to rule China largely on Confucian lines and customs under a new Mandate of Heaven, though introducing new European technology, science, education, ect. Manchuria is annexed by Russia, while Qing territories in Central Asia, Mongolia, Tibet go independent as vassal states of both China and Russia.

Is this realistic? Militarily feasible? Can 50,000 Russians defeat 200,000 Qing army in the 1790s?
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