# Illustration Orbital velocities and angles in a circular motion

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Two velocity vectors $$\boldsymbol{v}_1$$ and $$\boldsymbol{v}_2$$ at two different times of a body moving on a circular path. The vector ($$\boldsymbol{v}_2$$ was parallel shifted here. The magnitude of the two vectors is equal: $$v_1 = v_2$$. The direction, on the other hand, has changed due to the motion on a curved circular path. This change of direction results in the change $$\Delta \boldsymbol{v}$$ of the velocity vector:$$\Delta \boldsymbol{v} ~=~ \boldsymbol{v}_2 - \boldsymbol{v}_1$$

The two right triangles (green and blue) with the corresponding angles were used to derive the centripetal acceleration. It can be shown that $$\Delta \varphi = \Delta \theta$$.

The velocity change $$\delta \boldsymbol{v}$$ is the cause of the centripetal acceleration acting on a body moving in a circular orbit.