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My understanding is as follows. Due to the distance involved and the fact that they are not all disturbed in exactly the same way due to having separate initial velocities, there would be considerable difference in the impact on any two bodies by a given force. It would take a very long time for an object at the distance of the Oort cloud to reach the Sun (up to and including millions of years), giving these slight variations in motion time to make huge differences in orbit and arrival time.
As for the shape being a sphere rather than a plane, that would be due to the diminishing impact of the Sun's gravity on the objects as distance is increased. The closer objects in the cloud would like closer to the plane of the solar system, while further objects would be more spread out due to the higher ratio of gravity from extra-solar objects impacting their orbits. It is postulated that all the objects originated in the solar plane, but that the outer ones have migrated in their orbits over time due to those extra-solar forces. The overall shape of the positional probability of the objects would probably look more like two balloons pressed together inside another balloon than a sphere.
As for detecting a companion star at a distance of 25,000-50,000 AU, the extremely long orbital period would make the wobble imperceptible to an observer sitting inside the system riding around on a planet which is itself spinning and experiencing precession.
Regards,
Eric
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