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Universal Gravitation

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  • Univesal gravitation law: $$F = \gamma \frac{m_1 m_2}{r^2}$$
  • The squares of the periods of revolution of any two planets around the Sun are proportional to the cubes of the major semiaxes of their orbits (Kepler): $$T^2 \propto a^3$$
  • Strength $\vec{f}$ and potential $V$ of the gravitational field of a mass point: $$\vec{G} = -\gamma \frac{m}{r^3}\vec{r}, \; \phi = -\gamma \frac{m}{r}$$
  • Orbital and escape velocities: $$v_1 = \sqrt{gR}, \; v_2 = \sqrt{2} v_1$$

 

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