How Many Planets Can Safely Share A Single Orbit?

Bryan Konietzko (you know, one of the guys being Avatar The Last Airbender and The Legend of Korra), is working on a new project called Threadworlds, which takes place in a solar system that has 5 planets sharing the same orbit. That got me thinking, how many planets can fit into the same orbit without there being negative side effects on the planets themselves? How would their positions relative to one another affect this?

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How Many Planets Can Safely Share A Single Orbit?

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