Question

State Kepler's laws of planetary motion.

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Answer

Kepler's three laws of planetary motion are foundational principles in celestial mechanics and can be detailed as follows:

  1. The Law of Ellipses:

    • The orbits of the planets around the Sun are elliptical in shape, with the Sun located at one of the two foci of the ellipse.
  2. The Law of Equal Areas:

    • An imaginary line joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.
  3. The Law of Harmonies (or The Law of Periods):

    • The square of the orbital period ($$T$$) of any planet is directly proportional to the cube of the semi-major axis ($$a$$) of its orbit. Mathematically, this can be expressed as: $$ \frac{T_1^2}{T_2^2} = \frac{a_1^3}{a_2^3} $$
    • Here, $$T_1$$ and $$T_2$$ are the orbital periods of two planets, and $$a_1$$ and $$a_2$$ are their respective average distances from the Sun.

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