Say that one day the sun vanishes. Or, for a scenario just marginally more physically possible, say a giant pool cue moving near the speed of light approaches the sun perpendicular to the orbital plane; knocks it far, far away; and then quickly retreats whence it came.
Ignoring for the moment what happens to life on earth, how would the sudden loss of the sun affect the orbits of the planets? Would they continue to revolve around an empty central point? Would they stop moving altogether? Would they fly off on the tangents to their orbits? In the long term, would the planets take up new orbits around the next-most massive object in the solar system (i.e., Jupiter)?
My WAG is they fly off on tangents.
If the Sun simply winked out of existence, the planets would simply shoot away at their speed of orbit in a more or less straight line, affected by whatever other gravity might pull them in various directions (e.g. if we happened to fly in the general direction of Jupiter, eventually that would be pretty bad for the Earth.)
Jupiter isn’t nearly large enough for the other planets to take up orbits around it unless by some awesomely long-shot chance they were in perfect position to be flung into Jupiter’s path at the moment the Sun vanished. The Earth, for instance, in much further from Jupiter than it is from the Sun and Jupiter is a very small fraction of the Sun’s mass, so at this distance the effect of Jupiter’s gravity is negligible.
Planets orbit the sun because the sun’s gravity pulls them in. They are essentially constantly falling towards the sun, but moving fast enough sideways that they never hit it - just keep swinging around it.
Gravity propagates at the speed of light. So, if the sun disappeared, the planets would continue orbiting the now-empty central point in the solar system for however many minutes it takes light to travel from the sun to the planet. On earth, that’s about eight minutes.
After that, without the sun’s gravity keeping them in freefall around it, each planet would stop orbiting and simply continue traveling in a straight line tangent to its orbit. That’s ignoring the gravitational effects of the planets on each other, which, at these distances, would be minimal, I think.
If the sun vanished, all planets would fly off on tangents after a few minutes time. Moons would continue to orbit their planets. Planetoid pairs like Pluto / Charon would continue off on a tangent based on the motion of their center of gravity.
If a giant pool cue struck the sun at nearly the speed of light, the sun would probably explode, ejecting solar mass in all directions.
If a giant pool cue gravitationally moved the sun away, all the planets would also be gravitationally affected by the pool cue.