When we consider the elliptical orbits of the planets (Kepler's first law), we assume that the Sun is stationary at one focus of the ellipse. When does this happen? The mass of the Sun must be much much greater than the mass of the planets. But how large does the mass of the Sun need to be in order to achieve this idealized planetary motion? For example the Sun is about 1000 times heavier than Jupiter (the most massive planet) and about 100 million (108) times more massive than the least massive planet Pluto.
The 1000:1 Mass simulation, therefore, closely resembles the Sun and Jupiter system (the distance is given in Astronomical Units (AU) and the time is given in 108 seconds). The blue circle is like the Sun while the orange circle is like Jupiter. The force of attraction due to gravity is shown in the blue arrows and the relative kinetic energies are shown as a function of time in the graph (note that for this simulation the unit for the kinetic energy is not given as we are just comparing the relative amount for each object). Also note that the eccentricity of the orbit e = 0.048, the perihelion and aphelion distances, and the planet's period, match that of Jupiter.
In the 100:1 Mass simulation does the "Sun" remain motionless? What about the 10:1 Mass simulation? What do you think this means for planetary dynamics in general and in our Solar System?
For elliptical orbits, the force due to gravity changes since the separation changes. But at every instant, the forces of gravitational attraction (the force of the blue circle due to the orange circle and the force of the orange circle due to the blue circle) are always the same. This is Newton's third law. It is not too surprising that the law of universal gravitation (described by Newton) contains the third law (also described by Newton).