I study the interaction between orbiting stars and stellar mass black holes with the gas disk of Active Galactic Nuclei (AGN). By establishing a geometric relationship between the orbital plane of the orbiting object with the plane of the disk I can determine the fraction of the orbit spent in the disk based on the semi-major axis and inclination angle of the orbiting body. Once in the gas disk the orbiter is subject to a drag force by the gas which results in a loss of energy of the orbiter leading to a decrease in semi-major axis and decrease in inclination angle. Using mechanics and conservation of energy laws an equation can be formulated for the time spent in the disk. Our objective is to calculate what we refer to as the capture time which is when the orbiter is fully embedded in the gas disk which occurs when the inclination of the orbiter has reached what we refer to as the critical angle which occurs when the entire orbit is contained in the gas disk.

Below is just some simple code showing I have been messing around with in order to show that accretion does not play a role in the capture time of stellar objects. I have neglected the effect of the drag force in order to focus just on the contribution to the energy loss from the process of accretion. It clearly shows that it is completely negilgible.