Task id16783

The point of the planet’s elliptical orbit closest to the Sun is called perihelion, the most distant point is called aphelion (Fig. 12.11). Let us denote the distance from perihelion to the Sun by r0, and the speed of the planet at perihelion by v0. Find the radius of curvature of the trajectory at perihelion and aphelion, the distance from aphelion to the Sun, the speed of the planet at aphelion. Prove that the movement of a planet along an elliptical trajectory is possible only if its total energy is negative.