Do gravitational systems only have one centre of gravity?

Question

I have heard that a peanut-shaped asteroid would have competing centres based around each end.

Answer 1

All gravitational systems are influenced by their nearest and strongest neighbours, even if it does not become apparent immediately, the stronest in the system exerting the most. I f your peanut shaped asteroid, presumably containing more mass at each end, had more than one larger body orbiting in its vicinity, they could both be pulling for the asteroid in an asteroidal game of 'tug of war', thus changing the centre for the peanut one, whose centre of gravity would lie somewhere between the middle of the mass at one end and the mass at the other.The combined mass of both ends, divided by the distance between them using the law of inverse square, would give you the peanut asteroid's centre of gravity.

This center fluctuates according both to its own spin, and the influence of its neighbours.

This can cause some interesting peturbations in its own orbit, and depending upon its own mass at each end, and that of the any competitors trying to capture it. The centre of gravity of the peanut shaped asteroid can change according to how much gravitational pull it was experiencing at any given time, and from which direction, as it is bein pulled by the others.

But even if it were alone out there, it would not have two separate c.o.gravity, as said, but the stabity and placement of its own centre, and its spin could affect where that centre lay at different moments, the spin and direction of motion, etc.
It may have different areas impacting on all this, but still with only one centre of gravity.
Hope I haven't repeated myself too often here....
....not sure if that is useless or helpful. So many variables...not enough time......

Answer 2

I think you're possibly being confused a little by semantics. By definition a system will only have one centre of gravity - the 'balancing point' of the system. However, if the system is made up of two or more bodies then each of those will have its own gravitational centre, and it is these which will 'compete'.

Answer 3

we have two gravity centres. 1. the earth's gravity 2. the moon has a gravitational pull on the earth, causing tides etc.

Answer 4

If the "system" is the entire asteroid, then it will have one and only one center of gravity- i.e. one point. That is the definition of the center of gravity of a system.

Answer 5

i think competing is correct