Centre of mass interactive activity part 2
In this slightly modified interactive application, the arithmetic is spelled out for you for any available combination of mass choices. The laws of physics mean that the centre of mass is always positioned so the value of two ratios, the ratio of the masses and the ratio of the distances from the centre of mass, multiplied together is exactly 1. This comes from the fact that was illustrated in Figure 2. (The figure 1047 that appears in the calculation is the mass ratio of the Sun and Jupiter, MSun/MJ. This is a slightly more accurate figure than 1050 that was displayed on screen in the previous part.)
Play with choices of masses, and watch how the position of the centre of mass and the values of the ratios change. One of the most beautiful mysteries of the Universe is the fact that it can be described by mathematics that can be written down and understood.