Satellites appear to be in the same place in the sky due to their specific orbits around the Earth. There are primarily two types of orbits that allow satellites to seemingly remain fixed in the sky from the perspective of an observer on the ground: geostationary orbit and Molniya orbit.
Geostationary Orbit: Satellites in geostationary orbit (GEO) are positioned approximately 35,786 kilometers (22,236 miles) above the Earth's equator. They orbit the Earth at the same rotational speed as the planet itself, completing one orbit in 24 hours. This synchronization with Earth's rotation enables them to remain stationary relative to a specific location on the ground. From an observer's perspective, the satellite appears to be in the same position in the sky at all times. Geostationary orbits are commonly used for communication, weather, and television broadcasting satellites.
Molniya Orbit: Molniya orbit is another type of highly elliptical orbit used by certain communication satellites. Satellites in Molniya orbit have high inclinations and spend most of their time over high latitudes, particularly the northern latitudes. They have a highly eccentric orbit that brings them closer to the Earth during part of their orbit, allowing for longer periods of visibility from the ground. Molniya satellites spend more time near their apogee (farthest point from Earth), resulting in a slower apparent motion across the sky. This makes them appear to be relatively stationary for extended periods when viewed from specific ground locations.
It's important to note that most other satellites, such as those in low Earth orbit (LEO) or medium Earth orbit (MEO), do not remain fixed in the sky. They have orbital paths that take them across different parts of the sky as they orbit the Earth. Only satellites in specific orbits, like geostationary and Molniya orbits, can maintain a fixed position relative to an observer on the ground.