The Orbital Properties of Black Holes: Exploring the Relationship between Orbital Velocity and Distance

Abstract

This research explores the concept of black holes in the physics of general relativity, including its formation and properties. The study focuses on the relationship between the orbital velocity and orbital distance of objects around a black hole, which is measured in units of the speed of light (c) and kiloparsecs (kpc), respectively. Using observational techniques, the study produces a plot showing the relationship between orbital velocity and orbital distance, which follows Kepler's law modified by the Newtonian theory of gravity and general relativity. The study also highlights the effective potential of particles in orbit around a black hole, which combines the effects of kinetic energy and gravitational potential. The effective potential shows the gravitational and relativistic properties of black holes, such as the photon orbit radius, ISCO, and the spin parameter. The resulting plot demonstrates the characteristics of the Milky Way black hole and how its spin parameter and Schwarzschild radius affect the orbital properties of surrounding particles. The study concludes that the closer the orbital distance is to the black hole, the more the orbital velocity increases, and particles with high spin parameters and small Schwarzschild radii are unlikely to escape the black hole's gravity.