There might be an invisible pink teapot orbiting the Sun between Earth and Mars. Because we haven't yet disproven it, we have a reason to believe in it.
Yep, makes sense...
For the record, the orbit of Earth around the Sun is known to about 1 m, that includes the orbiting of the Sun around the solar system's barycenter. If there was a brown dwarf orbiting the Sun, with at least 13 times the mass of Jupiter, the gravitational influence would be well enough for the solar system's barycenter to shift. In fact, it would put the barycenter at 430 AU outside of the center of the Sun, where at most, with the combined influence of Jupiter and Saturn, it gets 2 solar diameters out.