Square-Cube Law?

Question

I've heard about something called the square-cube law. What is it? All I know of it is that it has something to do with mass of large objects and their gravitational influence.

Answer 1

You are probably referring to Kepler's third law, which states that the square of the period of orbit of a planet is proportional to the cube of the semi-major axis of its orbit. It can be mathematically expressed as $$ \frac{T_1^2}{R_1^3}\approx\frac{T_2^2}{R_2^3}$$ for planets $1$ and $2$ in the solar system. This equality is exact in the limit where the mass of the Sun goes to infinity.