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A planet travels in an elliptical orbit ...

A planet travels in an elliptical orbit about a star as shown. At what pair of points is the speed of the planet the same?

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(i) According to law of conservation of angular momentum L = mvr = constant, therefore the comet muses faster when it is close to the sun and moves slower when it is farther away from the sun. Therefore, the speed of the comet does not remain constant.
(ii) A the linear speed varies, the angular speed also varies. Therefore, angular speed of the comet does not remain constant
(iii) A no external torque is acting on the comet, therefore, according to law of conservation of angular momentum, the angular momentum of the comet remain constan.
(iv) As the linear speed of the comet changes its kinetic energy also changes. Therefore, its KE does not remain constant.
(v) Potential energy of the comet changes as its kinetic energy changes.
(vi) Only angular momentum and total energy of a comet remain constant throughout its orbit.
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