The mods at r/AskScience suggested this would be a better place, so anyone with Science History knowledge, I'd love to know more:
My understanding is that Uranus and Neptune were only discovered recently (post 1700) in Western science. But Wu Cheng-en's "Monkey" mentions "the nine planets". Being written in the mid 16th century, does that mean the Chinese had already discovered them? Or were they referring to other celestial bodies? If so, what would be the likely ones?
Just to be clear, you're talking about Arthur Waley's abridged translation of Journey to the West into English, and the line "nine planets" occurs in Waley's translation?
If that is the case, the first step would presumably be to check the actual translation - it could easily be that Waley (writing in the 1940s) chose to translate a line like "all the heavenly globes" into "the nine planets". If you don't have an original-Chinese version of Journey to the West, perhaps you could specify where in the story this line occurs so that it is easier for someone to track down the original phrase?
Edit: Thanks to /u/Jetamors and /u/Usedpresident for the references/translation. Based on the rest of the passage (the four kings, the twenty-eight celestial houses, etc), this seems to be an overall reference to Sanskrit/Vedic astrology, much of which also eventually spread (in part, with its own variations) to China. In that case, the "nine planets" of Arthur Waley's translation may be referring to the nine Graha - The Sun, The Moon, Mercury, Venus, Mars, Jupiter, Saturn, Rāhu and Ketu. These aren't "planets" in the modern sense of the word - they're (speaking very vaguely here) the nine bodies/forces which move across the sky (in a particular manner) - so that may not be the best choice of word for the translation.
That's as far as I'm comfortable answering, but should give you a good start towards if you want to try and verify whether that passage is indeed referring to the Graha, or to pursue some further independent research of your own into what the Graha are, or even the adoption of Vedic astronomy/logy in China.