The center of an orbit is called the focus or the focal point. In a two-body system, such as a planet and its orbiting satellite, the focus is located at one of the two foci of the elliptical orbit. The primary body, around which the satellite orbits, is located at one focus, while the other focus remains empty.
For example, in the case of the Earth's orbit around the Sun, the Sun is located at one focus of the elliptical orbit, and the other focus is empty. Similarly, in the case of a moon orbiting a planet, the planet is located at one focus of the moon's elliptical orbit.
The concept of the focus or focal point is essential in understanding the geometry and dynamics of orbital motion. It helps determine the shape, size, and characteristics of an orbit.