Interactive Pendulum

Surprise!

How did we get from Keppler's Third Law of planetary motion: $T=2·\pi \sqrt{\frac{r^3}{G·M}}$ back to the period of a simple pendulum???

We also know: $F=\frac{G·M·m}{r^2}$ where "M" is the mass of the Sun and "m" is the mass of the Earth.

And we know: $F=m·a_{\mathrm{earth}}$

So: $a_{\mathrm{earth}}=\frac{G·M}{r^2}$

Giving us: $T=2·\pi \sqrt{\frac{r}{a}}$

Setting "r" to 1 au (the "length" of our Earth's "pendulum") and "a" to the acceleration experienced on Earth because of the Sun's gravity 1 au away takes care of the rest!!!