We use an extensive suite of numerical simulations to constrain the mass and orbit of Planet Nine , the recently proposed perturber in a distant eccentric orbit in the outer solar system .
We compare our simulations to the observed population of aligned eccentric high semimajor axis Kuiper belt objects and determine which simulation parameters are statistically compatible with the observations .
We find that only a narrow range of orbital elements can reproduce the observations .
In particular , the combination of semimajor axis , eccentricity , and mass of Planet Nine strongly dictates the semimajor axis range of the orbital confinement of the distant eccentric Kuiper belt objects .
Allowed orbits , which confine Kuiper belt objects with semimajor axis beyond 380 AU , have perihelia roughly between 150 and 350 AU , semimajor axes between 380 and 980 AU , and masses between 5 and 20 Earth masses .
Orbitally confined objects also generally have orbital planes similar to that of the planet , suggesting that the planet is inclined approximately 30 degrees to the ecliptic .
We compare the allowed orbital positions and estimated brightness of Planet Nine to previous and ongoing surveys which would be sensitive to the planet ’ s detection and use these surveys to rule out approximately two-thirds of the planet ’ s orbit .
Planet Nine is likely near aphelion with an approximate brightness of 22 < V < 25 .
At opposition , its motion , mainly due to parallax , can easily be detected within 24 hours .