# Conservative forces intuition

Take a gravitational field (with all the field lines pointing inwards) and a perfectly circular curve as an object's trajectory. To find the work exerted by the force on the object, compute the line integral $\oint_C\overrightarrow{F} \cdot \overrightarrow{v}=Work=0$; which is to be expected as there is no tangential component to a conservative force, and $\overrightarrow{F} \cdot \overrightarrow{v}=0$ everywhere.

However, work is being done on the planet as it isn't moving in a straight line, and $\overrightarrow{F}$ is the only force around to provide this work.

Therfore, is perfect circular motion unphysical? Is the real motion more like Newton's 'infinitesimal pulling in' model pictured below, the downward pulls being the points where $\overrightarrow{F} \cdot \overrightarrow{v} \ne 0$, for instance? Have I misunderstood something?

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