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We detect planets elsewhere by either them passing in front of the star or star wobbling IIRC. How come we can't detect this hypothetical big outer body by Sun wobbling a bit? We are pretty close to see minute changes. If its there it must have some effect, no?

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My understanding is that radial velocity detection only works when you’re watching the entire system from afar. Since Earth is part of the solar system, we’re inside the moving frame. We can’t measure the Sun’s wobble relative to the solar system barycentre without comparing it to some external fixed reference.

2 big reasons, first is that wobbles which we normally observe require that the star move enough to be detected on a shorter time scale. IE: if the orbit takes 100 years and we look twice in 5 years, the planet will have only moved 5% of an orbit and the wobble will be near 0. Second is the less mass and further the planet is away, the less noticeable the wobble. Something at 500 au is going to produce no measurable wobble in our lifetime.

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