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A planet A moves along an elliptical orb...

A planet A moves along an elliptical orbit around the Sun. At the moment when it was at the distance `r_0` from the Sun its velocity was equal to `v_0` and the angle between the radius vector `r_0` and the velocity vector `v_0` was equal to `alpha`. Find the maximum and minimum distances that will separate this planet from the Sun during its orbital motion.

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To find the maximum and minimum distances that will separate the planet A from the Sun during its orbital motion, we can follow these steps: ### Step 1: Understand the problem We have a planet A moving in an elliptical orbit around the Sun. At a certain point, it is at a distance \( r_0 \) from the Sun with a velocity \( v_0 \) and an angle \( \alpha \) between the radius vector \( r_0 \) and the velocity vector \( v_0 \). ### Step 2: Conservation of Angular Momentum The angular momentum \( L \) of the planet at the distance \( r_0 \) is given by: \[ ...
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