Gravity: Conservative or Non-Conservative?

[Amin2014]

We generally take the force of gravity to be conservative, but what if the source of gravity is moving through space? Then the force would only be conservative relative to the source, correct?

As another example, consider someone in a balloon ascending with constant speed relative to earth. This person takes the balloon as his reference frame. For him a fixed point in space would be one that is fixed relative to him. If he chooses one such point, he will notice that the gravitational field at this "fixed" point is subject to change with time. Could we say gravity is non-conservative relative to this observer?

Lastly, when we say a force field is conservative, are we saying that it is conservative "relative to the source"?

 

[Nugatory]

We generally take the force of gravity to be conservative, but what if the source of gravity is moving through space? Then the force would only be conservative relative to the source, correct?

As another example, consider someone in a balloon ascending with constant speed relative to earth. This person takes the balloon as his reference frame. For him a fixed point in space would be one that is fixed relative to him. If he chooses one such point, he will notice that the gravitational field at this "fixed" point is subject to change with time. Could we say gravity is non-conservative relative to this observer?

For a force to be conservative, the potential has to be independent of time - and in both these cases the potential is not. You're better off thinking of terms of time dependency of the potential; if there is any, than the force is not conservative.

Lastly, when we say a force field is conservative, are we saying that it is conservative "relative to the source"?

Try not to think in terms of the "source" of a force. $F=ma$ defines a force in terms of its effect on the mass upon which it is acting; there's no source involved in the description.