The gravitational field is defined as a conservative field for small displacements of a body in the field. The potential energy of a body in the field would only be dependent on the position of the body.(adsbygoogle = window.adsbygoogle || []).push({});

Any sufficiently small displacements of the body in a closed path in this field starting at point A, going to point B, and returning to point A would yield a zero net change in energy.

But what happens if the field varies in intensity in time as the body moves in its closed path? Suppose, for example, that the mass of the earth was constantly decreasing in time. (There are continuous mass ejections at escape velocity from opposite ends of the equator.)

Would the gravitational field cease to be conservative? Would a closed loop displacement yield changes in energy not equal to zero? Could F = -dU/dx be modified to include a time-variant field U(x,t) that makes sense?

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# Conservative and non-conservative fields

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