According to Eq. (7), the velocity vector of a planet as a function of the angle θ is

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(2 Use this to explain the following statement: As a planet revolves around the sun, its velocity vector traces out a circle of radius k/J with its center at the terminal point of c (Figure 11). This beautiful but hidden property of orbits was discovered by William Rowan Hamilton in 1847. B v(0) k ) = 1 / 0 + c D Planetary orbit v(0): A v(0) B Velocity circle D -X