Award Date


Degree Type


Degree Name

Master of Science (MS)


Physics and Astronomy

First Committee Member

Jason Steffen

Second Committee Member

Zhaohuan Zhu

Third Committee Member

Ashkan Salamat

Fourth Committee Member

Shichun Huang

Number of Pages



During the late stage of planet formation, a system is often dynamically packed with protoplanets. These bodies collide together and are ejected from the system to form the final planets. The duration of stability before these dynamical interactions occur is dependent on the initial separation of the bodies in a system. Previous works have shown that the time before a planet-planet close encounter is exponential with the initial planet spacing measured in units of mutual Hill radius. We investigate the limitations of these previous studies. We find that systems that are initially similar can have larger differences in stability times than in the limited cases of equal-mass and coplanar planets. First, we perform N-body integrations on a large number of systems with non-equal masses and equal Hill spacing. We find that the stability time relationship is heteroscedastic and best described by an increasing standard deviation with planet spacing. Second, we investigate the time until a planet-planet collision in systems with non-coplanar planets. We find that when systems with non-zero mutual inclinations experience a close encounter a significant potion do not promptly experience a planet-planet collision. Systems with significant inclinations can continue to evolve without a collision or ejection for over 1,000 times longer than the encounter time. Both of these studies and their findings influence the duration of late-stage planet formation and the stability of observed closely-packed exoplanetary systems.


dynamics; exoplanet; formation; numerical; planets and satellites; stability


Astrophysics and Astronomy

File Format


File Size

4.5 MB

Degree Grantor

University of Nevada, Las Vegas




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