Modified Kepler model of photophoresis - Gamier, Lance Randall C (Animo Repository, 2022)
In this study, a phenomena called ’photophoresis’ is observed on a circumstellar disk. The study is motivated by the fact that most of the details on how planetary formations on a type of circumstellar disks known as protoplanetary disks are still unknown and by studying how dust particles move in protoplanetary disks through a Kepler problem, we are able to understand the motion of dust better. Most forces such as gravity, radiation force pressure, and gas drag do not fully explain the missing details of planetary formations. One candidate that might explain the missing details is a phenomena called ’photophoresis’ would be the subject of this study, where a dust particle moves after one of its sides that is heated ends up pushing gas molecules faster that its cooler side. The purpose of the study is to observe how the photophoretic force affects the motion of dust particles that are present in the circumstellar disks. The study is conducted by comparing two mathematical models, one with photophoresis and one without photophoresis. The comparison of models would be done over a sample of 6 different masses, 6 different radii, and 15 different initial positions and velocities, giving us 540 samples of particles to compare the two mathematical models. The study is separated into three parts: A theoretical part, A computational part, and a statistical part. In the theoretical part, the Keplerian differential equations is derived from the equations describing the force experienced by the dust particle. In the computational part, the motion of the particle is simulated through a numerical computation program. In the statistical part, the data gathered from the computational part is then analyzed using an approximation error formula in order to compute the difference between the two mathematical models. The computational and statistical results shows that photophoresis has the greatest effect on the particle with the smallest mass 10^-6 g but with the largest radius 10^-1 m within the samples while having the least effect on a particle that is the complete opposite, one with the largest mass 10^-1 g but with the smallest radius 10^-6 m within the samples. Photophoresis also has the greatest effect on the particle with the highest initial position and highest initial velocity within the samples.