http://arxiv.org/abs/2004.14913
In this paper we investigate whether Uranus’s 98$^{\circ}$ obliquity was a byproduct of a secular spin-orbit resonance assuming that the planet originated closer to the Sun. In this position, Uranus’s spin precession frequency is fast enough to resonate with another planet located beyond Saturn. Using numerical integration, we show that resonance capture is possible in a variety of past solar system configurations, but that the timescale required to tilt the planet to 90$^{\circ}$ is of the order $\sim 10^{8}$ years; a timespan that is uncomfortably long. A resonance kick could tilt the planet to a significant 40$^{\circ}$ in $\sim 10^{7}$ years if conditions were ideal.
We also revisit the collisional hypothesis for the origin of Uranus’s large obliquity. We consider multiple impacts with a new collisional code that builds up a planet by summing the angular momentum imparted from impactors. Since gas accretion imparts an unknown but likely large part of the planet’s spin angular momentum, we compare different collisional models for tilted, untilted, spinning, and non-spinning planets. We find that two collisions totaling to $1\,M_{\oplus}$ is sufficient to explain the planet’s current spin state. Finally, we investigate hybrid models and show that resonances must produce a tilt of $\sim$40$^{\circ}$ for any noticeable improvements to the collision model.
Z. Rogoszinski and D. Hamilton
Fri, 1 May 20
1/54
Comments: 31 pages, 17 figures, submitted to a AAS journal