A Binary star system
A system of stars orbiting a common center of gravity where there is no mass at the center of gravity is known as a Kepler Rosette. Such an arrangement is theoretically possible but is unstable. No such an arrangement has (yet) been observed in the real universe.
All objects in a Kepler Rosette have to have identical mass and exactly the same kind of orbit (differing only in their phase angle) and must be evenly spaced on some multiple value of their phase angle. If the orbit of such a Rosette is eccentric then the system will pulsate in diameter on the period of the orbit.
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A binary star system consists of two stars orbiting a common center of mass. The center of mass, or barycenter, is the point around which both stars orbit due to their gravitational interaction. This system is common in the universe and helps astronomers study various aspects of stellar evolution and dynamics.
Two stars orbiting a common center of gravity is known as a binary star system. The center of gravity, or barycenter, is located at a point between the two stars based on their masses and proximity. The stars will appear to be in orbit around this point as they move through space.
Gravity keeps the planets in orbit around the sun and the stars and the stars in orbit around the center of the galaxy. Gravity also holds the stars together against their own internal pressure.
The stars we can see are all within our galaxy (the Mikey Way). In general all the stars are orbiting the center of the Mikey Way.
Moons orbit planets. Planets orbit stars. Some stars orbit other stars, or orbit their mutual center of gravity. Stars orbit the center of the galaxy. Galaxies may orbit the center of the "galactic group".
No stars orbit the Sun. The Sun is a star itself, and it is at the center of our solar system, with planets such as Mercury, Venus, Earth, and Mars orbiting around it.