Okay, this is nothing more than a thought experiment which popped into my head while driving home from work today.
Take the case of a single body orbiting another, larger body, as in a planet and a star. The planet is in a stable, non-decaying orbit.
Now assume that the mass of the planet was noticeably increased instantaneously, that is, without any directional force applied to the planet's body, such as a meteor impact or other event would cause. So just take that the planet's mass increases without any force that would have an "equal and opposite" force that might alter the planet's velocity.
Given the starting stable orbit, and the instant increase in mass of the planet, I was trying to decide what would be the effect of the increased mass on the planet's orbit. I figured there were probably two possibilities...
- the increased mass would increase the pull of gravity between the planet and its star, thus causing the orbit to decay
- the increased mass would increase the planet's momentum, causing the centrifugal force to now exceed the centripetal force, and the planet would go flying off into space, breaking free of its orbit
I couldn't make up my mind though which might be more likely, so figured I'd ask people who would know a lot more about physics than I do.
I'm also completely comfortable with the fact that neither of my theories is correct, and the reaction of the system would be something else entirely.