Solar Obliquity Induced by Planet Nine: Simple Calculation
Dong Lai

TL;DR
This paper presents a straightforward calculation showing how the hypothetical Planet Nine could cause the Sun's obliquity, explaining the 6-degree tilt between the Sun's equator and planetary orbits.
Contribution
It offers a simple, accurate method to quantify how Planet Nine's properties influence the Sun's spin orientation, clarifying the obliquity origin.
Findings
Planet Nine can induce the observed solar obliquity.
The calculation links Planet Nine's orbit to solar tilt.
The method improves understanding of solar-planet alignment.
Abstract
Bailey et al.~(2016) and Gomes et al.~(2016) recently suggested that the 6 degree misalignment between the Sun's rotational equator and the orbital plane of the major planets may be produced by the forcing from the hypothetical Planet Nine on an inclined orbit. Here we present a simple but accurate calculation of the effect, which provides a clear description of how the Sun's spin orientation depends on the property of Planet Nine in this scenario.
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