How can one prove, based on the concept of work, that when a planet moves from aphelion to perihelion, its linear velocity

How can one prove, based on the concept of work, that when a planet moves from aphelion to perihelion, its linear velocity increases, and when it moves backward, it decreases?

When the planet moves from aphelion to perihelion, the gravitational force of the Sun does a positive work, which, according to the kinetic energy theorem, leads to an increase in the planet’s speed. When it moves from perihelion to aphelion, on the contrary, the gravitational force performs negative work and the planet’s speed decreases.

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