  Context. A recent observational census of Kuiper belt objects (KBOs) has
unveiled anomalous orbital structures. This has led to the hypothesis that an
additional $\sim5-10~m_{\oplus}$ planet exists. This planet, known as Planet 9,
occupies an eccentric and inclined orbit at hundreds of astronomical units.
However, the KBOs under consideration have the largest known semimajor axes at
$a>250$ AU; thus they are very difficult to detect.//
  Aims. In the context of the proposed Planet 9, we aim to measure the mean
plane of the Kuiper belt at $a>50$ AU. In a comparison of the expected and
observed mean planes, some constraints would be put on the mass and orbit of
this undiscovered planet.
  Methods. We adopted and developed the theoretical approach of Volk & Malhotra
(2017) to the relative angle $\delta$ between the expected mean plane of the
Kuiper belt and the invariable plane determined by the eight known planets.
Numerical simulations were constructed to validate our theoretical approach.
Then similar to Volk & Malhotra (2017), we derived the angle $\delta$ for the
real observed KBOs with $100<a<200$ AU, and the measurement uncertainties were
also estimated. Finally, for comparison, maps of the theoretically expected
$\delta$ were created for different combinations of possible Planet 9
parameters.
  Results. The expected mean plane of the Kuiper belt nearly coincides with the
said invariable plane interior to $a=90$ AU. But these two planes deviate
noticeably from each other at $a>100$ AU owing to the presence of Planet 9
because the relative angle $\delta$ could be as large as $\sim10^{\circ}$.
Using the $1\sigma$ upper limit of $\delta<5^{\circ}$ deduced from real KBO
samples as a constraint, we present the most probable parameters of Planet 9.

Earth and Planetary Astrophysics