Kepler's Third Law establishes that the ratio of the square of a planet's orbital period (T) to the cube of the semi-major axis (R) of its orbit is a constant across the solar system, expressed as R^3/T^2. For instance, using Earth and Mars as examples, the relationship T_e^2/R_e^3 = T_m^2/R_m^3 holds true, demonstrating the consistent nature of this law. This principle applies to all celestial bodies orbiting a star, provided the forces involved decline quadratically with distance and the masses of the orbiting bodies are negligible compared to the star's mass.
PREREQUISITESAstronomy students, astrophysicists, educators in physics, and anyone interested in understanding planetary motion and gravitational interactions in celestial mechanics.
I found wikipedia's explanation quite satisfying. The relation holds for all forces that quadratically decline with distance and small masses compared to the central sun's mass.victorhugo said:How R^3/T^2 is a constant, or is it just the simple relationship between the distance between a planet to a star in a solar system and the period for that planet to orbit the star?