Final answer:
Celestial objects orbit around an imaginary point called the barycenter, the common center of mass for a system. In the Solar System, this point is influenced by the positions of massive planets and typically lies within or just outside the Sun. Historically, models like Ptolemy's used points like the equant to account for observed celestial motions, which have been replaced by the understanding of elliptical orbits and gravitational laws.
Step-by-step explanation:
The planets and other celestial objects technically orbit around an imaginary point known as the barycenter, which is the common center of mass of a system of bodies. In the Solar System, this barycenter can be within or outside of the body of the Sun, depending on the positions of the planets.
For example, when massive planets like Jupiter or Saturn are on the same side of the Sun, the barycenter of the Solar System can be located outside the physical Sun. However, when considering individual planet orbits such as the Earth's orbit around the Sun or the Moon's orbit around the Earth, it is more common to refer to these objects as orbiting their larger host body (the Sun or Earth, respectively) due to their overwhelming mass compared to the planet or moon.
Historically, systems like Ptolemy's involved deferents and epicycles with orbits centered not directly on Earth but on a point offset from Earth called the equant. This was to account for the observed retrograde motion of planets, which is now known to be an effect of their elliptical orbits and our perspective from Earth.
Kepler's laws later described planetary orbits as ellipses with the Sun at one focus, and Newton's law of universal gravitation provided the underlying principles for why these orbits occur.