Einstein's space-time-theory and wobbling stars (first detected 1995, more than 4000 detected as of may,2019) are mutually exclusive. Wobbling stars have been proven by the thousands in the last decade which makes Einstein's theory definitively obsolete. Solar systems do not rotate around the central star of the system as asserted in Einstein's space-time-theory, they rotate around the barycenter of the system. So the essence of Einstein's theory of space-time is wrong which states that the mass of the central star geometrically curves space-time ("He (Einstein) decided that (..) gravity must be (..) a geometric curvature.") so that planets follow the straightest path on their orbit around the star: "The one sentence statement of general relativity is that ‘gravity is the curvature of spacetime" Instead the central star and the planets rotate around the barycenter (or center of mass) of the system. This is a unquestionable proven fact by more than 4000 confirmed exoplanet findings till today.

Quite contrary to Einstein's  General Relativity Theory (GRT) space-time is not curved by the mass of the central star (see the picture above from woodahl.physics.iupui.edu) but stars and planets rotate around their common center of mass (symbolized by the red cross inside the star). If the mass of the planet is big in relation to his star the barycenter is even located outside the star. Same can be true if a star posseses many planets and the constellation puts all planets on one side. According to Newton's equation then less massive planets far out can even have an effect.  Even laymen can thus understand that the basics of Eintein's General Relativity Theory is wrong.

Title of the Wikipedia representation: A stylized representation of a star and a planet revolving around the common center of mass. Effects not to scale. Credit: Wikipedia: public domain

 This is today no more questioned (see for example here , deleted since this page linked to it, so alternatively see here) and has  been proven by thousands of new found exoplanet systems since 1995 (Discovery of a Planetary Orbit In 51 Pegasus (M. Mayor & D. Queloz). This news has now in 2018 finally even spreaded to the NewScientist.

If anyone should have had any doubts in the computer simulation, then the 'New Horizons' reconnaissance flyby study should have ended these doubts forever. The 'New Horizons' mission conducted a six-month-long reconnaissance flyby study of Pluto and its moons in summer 2015, culminating with Pluto closest approach on July 14, 2015. Here the world could see in 'real life' pictures that Einsteins theory is wrong. Everyone  who has eyes to see can see here Pluto and Charon rotate around their common center of mass.

Students: Please tell your prof that Einstein's theory of general relativity (GRT/GTR) is disproven by this movie (this is not a simulation, not an animation, this is filmed reality!). Most prof's haven't got the time to always know the latest science news.

 Pluto and Charon rotating around their common center of mass

"The Pluto-Charon Dance: This close up look at Pluto and Charon, taken as part of the mission’s latest optical navigation (“OpNav”) campaign from Jan. 25-31, 2015, comes from the Long Range Reconnaissance Imager (LORRI) on NASA;s New Horizons spacecraft.

The time-lapse frames in this movie were magnified four times to make it easier to see Pluto and Charon orbit around their barycenter, a mutual point above Pluto’s surface where Pluto and Charon’s gravity cancels out – this is why Pluto appears to “wobble” in space. Charon orbits approximately 11,200 miles (about 18,000 kilometers) above Pluto’s surface." https://www.nasa.gov/content/the-view-from-new-horizons-a-full-day-on-pluto-charon

Compare this to the following pictures, where the earth (and thus pluto) should be rocksteady fixed in the skies according to Einsteins theory (in Einsteinian diction: The mass of the earth (or Pluto) geometrically curves space-time so that satelites (or moons) follow the straightest path on their orbit around the earth/Pluto) There simply is no center of mass or barycenter in Einsteins theory and hence no rotation around the center of mass or barycenter. Einsteins theory of relativity therefore is not in conformance with the laws of physics.:

 http://news.stanford.edu/news/2005/may11/gpb-051105.html

http://science.nasa.gov/science-news/science-at-nasa/2005/16nov_gpb/