Gravitation and Kepler's Laws Notes

Newton’s Law of Gravitation

  • Mutual force of attraction between particles of matter.

  • Limitation of gg?

  • Formula: F=Gm<em>1m</em>2r2F = G \frac{m<em>1 m</em>2}{r^2}

Centripetal Force

  • Force acting on a body moving in a circular path, directed towards the center.

  • Formula: F=mv2rF = \frac{mv^2}{r}

Kepler’s Laws

  • 1st Law (Law of Orbits): Planets move in elliptical orbits with the Sun at one focus.

  • 2nd Law (Law of Areas): A line connecting a planet to the Sun sweeps out equal areas in equal times.

  • 3rd Law (Law of Periods): The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.

    • Formula: T2=4π2GMr3T^2 = \frac{4\pi^2}{GM}r^3