The applet simulates the motion of a planet around the sun assuming there are no other planets that exert forces on the given planet. In reality, the presence of other planets causes slight perturbations of the motion simulated by the applet.
In the applet, the sun is assumed to be fixed in an inertial frame while the planet is revolving around the sun. This is a very good approximation since the mass of the sun is much greater than that of any planet. (The sun's mass is about 1000 times greater than that of the largest planet, Jupiter.)
In reality, both the sun and all of its planets are revolving around their common center of mass, which is at rest in an inertial frame, the center-of-mass frame. Since the sun is so much more massive than its planets, the center of mass of the solar system is much closer to the sun than to any of the planets so that the small motion of the sun around the center of mass can be neglected to a very good approximation.