I'm not getting what Kepler's Third Law is about

[victorhugo]

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?

 

[Geofleur]

It's a constant for the whole solar system. For example, suppose $R_e$ is the semimajor axis of Earth's orbit, $T_e$ is the period (i.e., 1 year in this case), $R_m$ is the semimajor axis of Mars's orbit, and $T_m$ is the period for Mars (1 Martian year). Then we have $T_e^2/R_e^3 = T_m^2/R_m^3$.

 

[fresh_42]

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?

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.