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Is the Distant Kuiper Belt Warped or Flat?

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At large semimajor axes ($a \gtrsim 50 \mbox{\;AU}$), the mean plane of the Kuiper belt is expected to be the ``invariable plane,'' which is orthogonal to the angular-momentum vector of the known solar system. However, if there were an additional unseen planet or planets in the outer solar system, the expected mean plane of the distant Kuiper belt could differ from the current definition of the invariable plane. While there is a general consensus that the mean plane of the Kuiper belt is consistent with the invariable plane for $50\mbox{\;AU}\lesssim a \lesssim 100 \mbox{\;AU}$, not much is known about the mean plane of the Kuiper belt at $a \gtrsim 100 \mbox{\;AU}$. We measure the mean plane of the Kuiper belt at semimajor axes of $100 - 400 \mbox{\;AU}$ and investigate the effects of hypothetical unseen planets of various masses and orbits on the mean plane.
Title: Is the Distant Kuiper Belt Warped or Flat?
Description:
At large semimajor axes ($a \gtrsim 50 \mbox{\;AU}$), the mean plane of the Kuiper belt is expected to be the ``invariable plane,'' which is orthogonal to the angular-momentum vector of the known solar system.
However, if there were an additional unseen planet or planets in the outer solar system, the expected mean plane of the distant Kuiper belt could differ from the current definition of the invariable plane.
 While there is a general consensus that the mean plane of the Kuiper belt is consistent with the invariable plane for $50\mbox{\;AU}\lesssim a \lesssim 100 \mbox{\;AU}$, not much is known about the mean plane of the Kuiper belt at $a \gtrsim 100 \mbox{\;AU}$.
We measure the mean plane of the Kuiper belt at semimajor axes of $100 - 400 \mbox{\;AU}$ and investigate the effects of hypothetical unseen planets of various masses and orbits on the mean plane.

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