Why do people think there is a giant “hidden” planet somewhere in the depths of our solar system?
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This have actually happened several times in the past two hundred years and is generally how discoveries of new planets start. For example Neptune was discovered from theories and calculations first and then we pointed our telescopes at it. Not all the theories of planets have panned out though. Vulcan is the most famous planet which never was but there was also a theory of a ninth planet orbiting beyond Neptune which was based on calculations that assumed the theory of relativity was false. They did find a dwarf planet, Pluto, during this search but it turned out not to fit their calculations.
The current leading theory for a ninth planet is based on observations of the comets. We have already found some patterns in them leading us the theory of the Oort cloud. However as we have collected more data and do the calculations again the orbits are even less random then first thought. And there is a high chance that the comet orbits are caused by a planet disturbing their stable orbit. We can calculate roughly where it would be but it still gives us a lot of sky to look through and we do not have telescopes good enough to observe it yet. So we can only collect more data and build bigger and better telescopes.
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