[Paper Review] Orbital evolution of the P/1996 R2 and P/1996 N2 objects

С. И. Ипатов, Gerhard Hahn|arXiv (Cornell University)|Dec 17, 2024

Astro and Planetary Science7 citations

TL;DR

Numerical integrations study how orbits near P/1996 R2 (a Jupiter-crossing object) and P/1996 N2 evolve over time, showing sensitive dependence on initial conditions, possible Earth-crossing, and quasi-periodic changes for P/1996 N2.

ABSTRACT

A numerical integration of the equations of motion of the Sun-planets-an object system is used to study the evolution of orbits close to the orbit of the P/1996 R2 object, which is a Jupiter-crossing object, and to the asteroidal orbit of the P/1996 N2 object, which, at the moment of its detection, had a tail similar to a cometary one. Small variations in the initial data considerably affect the evolution of orbits close to that of the P/1996 R2 object. The time elapsed up to the ejection of the object into a hyperbolic orbit varied from 3*10^4 to 2.7*10^7 yr. Some objects were in resonances with Jupiter and Saturn for a long time. For about 20 percent of the runs, objects reached the Earth's orbit during evolution. Orbital elements of the P/1996 N2 object changed quasi-periodically over the considered time span of 200 Myr. Variations in the semimajor axis, eccentricity, and inclination were equal to 0.04 AU, 0.11 deg, and 3.5 deg, respectively.

Motivation & Objective

• Investigate how small variations in initial conditions affect the long-term evolution of orbits near P/1996 R2 and P/1996 N2.
• Assess the stability and resonance involvement of these orbits under Sun-planet gravitational dynamics.
• Determine the likelihood and timescales for transition to hyperbolic or Earth-crossing trajectories.

Proposed method

• Numerical integration of the Sun–planets–object system to simulate orbital evolution.
• Propagation of orbital elements over timescales up to 200 Myr.
• Analysis of resonance occupancy with Jupiter and Saturn and tracking ejection times to hyperbolic trajectories.

Experimental results

Research questions

• RQ1 Do orbits near P/1996 R2 remain stable or do small initial differences lead to divergent outcomes?
• RQ2 What fractions of simulated evolutions reach Earth-crossing orbits, and on what timescales do ejections occur?
• RQ3 How do the orbital elements of P/1996 N2 evolve over hundreds of millions of years, and are they quasi-periodic?

Key findings

• Ejection times vary widely, from 3×10^4 to 2.7×10^7 years, depending on initial conditions.
• Some simulated objects resided in resonances with Jupiter and Saturn for extended periods.
• About 20 percent of the runs resulted in the object reaching Earth's orbit during evolution.
• P/1996 N2 showed quasi-periodic changes in orbital elements over 200 Myr, with semimajor axis variation of 0.04 AU, eccentricity variation of 0.11, and inclination variation of 3.5 degrees.