326 research outputs found
Dynamical Stability of Imaged Planetary Systems in Formation: Application to HL Tau
A recent ALMA image revealed several concentric gaps in the protoplanetary
disk surrounding the young star HL Tau. We consider the hypothesis that these
gaps are carved by planets, and present a general framework for understanding
the dynamical stability of such systems over typical disk lifetimes, providing
estimates for the maximum planetary masses. We collect these easily evaluated
constraints into a workflow that can help guide the design and interpretation
of new observational campaigns and numerical simulations of gap opening in such
systems. We argue that the locations of resonances should be significantly
shifted in massive disks like HL Tau, and that theoretical uncertainties in the
exact offset, together with observational errors, imply a large uncertainty in
the dynamical state and stability in such disks. This presents an important
barrier to using systems like HL Tau as a proxy for the initial conditions
following planet formation. An important observational avenue to breaking this
degeneracy is to search for eccentric gaps, which could implicate resonantly
interacting planets. Unfortunately, massive disks like HL Tau should induce
swift pericenter precession that would smear out any such eccentric features of
planetary origin. This motivates pushing toward more typical, less massive
disks. For a nominal non-resonant model of the HL Tau system with five planets,
we find a maximum mass for the outer three bodies of approximately 2 Neptune
masses. In a resonant configuration, these planets can reach at least the mass
of Saturn. The inner two planets' masses are unconstrained by dynamical
stability arguments.Comment: Accepted in ApJ. 16 pages 8 figure
The random walk of cars and their collision probabilities with planets
On February 6th, 2018 SpaceX launched a Tesla Roadster on a Mars-crossing
orbit. We perform N-body simulations to determine the fate of the object over
the next 15 Myr. The orbital evolution is initially dominated by close
encounters with the Earth. While a precise orbit can not be predicted beyond
the next several centuries due to these repeated chaotic scatterings, one can
reliably predict the long-term outcomes by statistically analyzing a large
suite of possible trajectories with slightly perturbed initial conditions.
Repeated gravitational scatterings with Earth lead to a random walk. Collisions
with the Earth, Venus and the Sun represent primary sinks for the Roadster's
orbital evolution. Collisions with Mercury and Mars, or ejections from the
Solar System by Jupiter, are highly unlikely. We calculate a dynamical
half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of
Roadster orbit realizations impacting the Earth, Venus, and the Sun within one
half-life, respectively. Because the eccentricities and inclinations in our
ensemble increase over time due to mean-motion and secular resonances, the
impact rates with the terrestrial planets decrease beyond a few million years,
whereas the impact rate on the Sun remains roughly constant.Comment: 5 pages, 4 figures, plots updated with data from 15Myr simulations,
submitted to MNRA
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