Savchenko Problem 2.6.2

Physics · mechanics · thermodynamics

Problem

Some planets in the Solar System have a near-circular orbit centered on the Sun, and they orbit the Sun almost uniformly. How is the acceleration of these planets directed? How does it depend on the distance between them and the Sun, if it is established that the square of the period of rotation of the planets is proportional to the cube of the radius of their orbit? (Imagine that you don't know the law of universal gravitation yet.)

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