Consider our solar system, in the frame of the sun (i.e. "the sun is stationary"), with a simplified 5 planets and nothing else. Suppose that for a brief moment, all of the planets aligned (doomsday) perfectly along the same axis, with velocities perpendicular to the position vector of them drawn from the sun.
In this situation we may find the centre of mass of the solar system, it's somewhere on the line of the planets. We may also find the velocity of the centre of mass, it is non-zero, and will be moving perpendicular to this line of planets. Since no force acts on the solar system as a whole, this velocity of the centre of mass will remain unchanged, and so the solar system as a whole will drift further and further away from its initial position (the centre of mass will at least). How is this possible? in real life, in the frame of the sun, the solar system doesn't drift? or does it? What am I missing?
This question arose out of a coding project for simulating a solar system using newton's laws and numerical integration techniques. When I "start" the solar system, I align all the planets, and thus give the centre of mass a net velocity, that should remain unchanged, but the solar system does not "drift out of frame" during the simulation, but I would have expected it to- perhaps the effect I speak of is simply very small.
