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Universal Gravitation

  • Univesal gravitation law:
    $$F = G \frac{m_1 m_2}{r^2}$$
  • 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:
    $$\vec{f} = -G \frac{m}{r^3}\vec{r}, \; V = -G \frac{m}{r}$$
  • Orbital and escape velocities:
    $$v_1 = \sqrt{gR}, \; v_2 = \sqrt{2} v_1$$
Keywords: 
gravitation, potential, periodic, revolution, orbit, Kepler, escape velocity
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