Kepler's Third Law of Planetary Motion

Kepler's Third Law of Planetary Motion

  • Statement of the Law: The square of a planet's orbital period ($T^2$) is proportional to the cube of its average distance ($r^3$) from the Sun.

    • This can be expressed mathematically as:
    • T2∝r3T^2 \propto r^3
    • This means that if you take a planet further from the sun, its orbital period will increase disproportionately.

  • Definitions:

    • Orbital Period (T): The time it takes for a planet to complete one full orbit around the sun.
    • Average Distance (r): The average distance between the planet and the sun during its orbit, typically measured in Astronomical Units (AU).

  • Implications:

    • Kepler's Third Law shows the relationship between a planet's distance from the sun and the time it takes to orbit, highlighting that planets further from the sun take longer to orbit due to their increased distance.
    • This law can be utilized to calculate the orbital period of planets if the average distance is known, and vice versa.