Effect of Charon on Pluto Even though Pluto is not known as a planet anymore, theroetically it has/had a moon, called Charon. I've heard about something that their size are so close to each other that while Charon rotates around Pluto, it also rotates around a central point.

How does it work exactly?
Mathematically, the motion of the Pluto-Charon system can be decomposed into two parts: The motion of Pluto-Charon about the Sun, and the motion of Pluto and Charon about one another. If one sets the reference point to be the center of Pluto, the path the Pluto-Charon system would appear to follow about the Sun would be an epicycle, which is a far more complicated means of describing the pair's trajectory through space. By instead setting this reference point to be the barycenter, the trajectory followed by the Pluto-Charon system is conveniently a Keplerian ellipse.

Charon is 11.6% the mass of Pluto, and is (on average) 19,571 km away from Pluto (Source 1, 2). The barycenter is the point at which the masses of the two bodies "balance", and for the Pluto-Charon system it lies at a distance of $$\frac{m_{\text{Charon}}}{m_{\text{Pluto}}+m_{\text{Charon}}}\times\text{distance}=\frac{0.116}{1.116}\times\text{distance}=0.104\times 19,571\,\text{km}=2,034\,\text{km}$$ from the center of Pluto. As Pluto is only 1,153 km in radius, the barycenter lies ~900 km above its surface. The Pluto-Charon system is the only known (minor or major) planet for which this is the case, although the Earth-Moon system will likely satisfy this criteria billions of years in the future (see Is the Moon a Planet? on Physics SE). There are some instances of binary asteroids, however, for which the barycenter lies outside the surface of both bodies.