In the extremely strong gravitational field near a large black hole, the behavior of orbits can be quite different compared to those around less massive objects like stars. The gravitational field of a black hole is so intense that it distorts space-time significantly, leading to several interesting phenomena.
Firstly, black holes have an event horizon, which is the boundary beyond which nothing can escape, including light. Inside the event horizon, the gravitational pull of the black hole becomes so strong that any object within it will inevitably be drawn towards the singularity at the center.
For orbits outside the event horizon, the shape and behavior depend on the specific conditions and the mass of the black hole. In the vicinity of a black hole, there are two types of stable orbits known as the photon sphere and the innermost stable circular orbit (ISCO).
The photon sphere is a spherical region around the black hole where photons (particles of light) can form stable circular orbits. Any other massive object, such as a planet, would not be able to maintain a stable circular orbit at this distance and would either spiral inward or outward.
The ISCO is the innermost distance from the black hole at which a test particle (an object with negligible mass) can maintain a stable circular orbit. Inside this radius, the object would inevitably fall into the black hole.
The exact shape of orbits outside the photon sphere and ISCO can vary depending on the black hole's spin and other factors. These orbits can be highly elliptical or exhibit complex patterns due to the extreme gravitational field and relativistic effects.
It's important to note that the behavior of objects around black holes is a complex subject and is still an active area of research. The precise details of orbits in the vicinity of black holes, especially those involving more massive objects like planets, require sophisticated mathematical models and simulations to fully understand.