This thesis studies the formation of planets and the destruction of stars that explode as supernovae. To understand planet formation and recreate the diversity of exoplanets that we see in our galaxy, we need a better understanding of protoplanetary disks. We develop a time-evolving model for the solid particles in these disks, tracking maximum particle size and surface density in their outer regions. This time dependent particle modeling shows us that disks pass through several regimes as more particles drift inwards, lowering maximum particle sizes and surface densities. By combining this model with our model for pebble accretion, we are able to estimate growth rates for injected protoplanetary cores. Applying our models to a sample of seven disks, we find that planetesimals should grow rapidly, particularly early in the disk's lifetime before it has drained too much. To reproduce observed planetary masses, we find that protoplanetary cores must reach planetesimal sizes before the ages of typically observed disks.
Turning our attention to smaller particles, we develop a new model for pebble accretion to explore the growth of lower mass protoplanetary cores. We apply full gas effects to the dynamics of small cores, finding that their new velocities play a crucial role in understanding their growth. Additionally, we model full probability distributions for the relative velocities of interacting particles, rather than simply studying the mean velocity. As we extend the model down to cm scales, we find that gas interactions play the dominant role in setting relative velocities for inter-particle collisions. At these small scales especially, particles in the low velocity tail of the velocity distribution can be accreted particularly rapidly, enhancing growth. In examining these rare growth interactions, our model suggests a path for solid body growth across the meter-scale barrier, up to planetesimal masses.
Finally, I also present my work statistically modeling the ages of Type Iax supernova progenitor stars. In this study, we use Hubble Space Telescope photometry of the stellar regions around Type Iax supernovae explosion sites to estimate ages for these regions. This is performed by statistically rigorous fitting of theoretical stellar models to our multi-band photometry. We are ultimately able to generate probability distributions for the ages of each supernova we consider, generating strong constraints on the formation channel for these events.
