### Joe Philip Ninan

Shared publicly -**Inverse cube force law**

Here you see three planets. The blue planet is moving around the Sun in a realistic way: it's going around an ellipse.

The other two are moving

*in and out*just like the blue one, so they all stay on the same circle, which shrinks and expands. But they're moving

*around*this circle more slowly. In fact the red planet isn't going around at all: it only goes in and out!

In 1687, Isaac Newton published his famous book, the

*Principia Mathematica*. And one thing he did here is figure out what extra force, besides gravity, would make it move like these weird other planets.

According to Newton, gravity obeys an inverse square force law. For example, if you move a planet 3 times as far from the Sun, it feels a force that's 1/9 as strong. Figuring this out and using this to explain the motion of planets is one reason Newton is so famous.

But he also showed that if you add an extra force obeying an

*inverse cube*law, and adjust the angular momentum of your planet, you can make it planet move

*in and out*just as it did before... but make it move

*around*at a different rate!

This goes to show that Newton had intelligence to spare. He didn't just solve the important problems that made him famous, he also had lots of

*minor*ideas that still required amazing cleverness.

And turns out this strange fact he discovered is just one of several weird and fascinating things about the inverse cube force law. For example, the so-called 'centrifugal force' obeys an inverse cube law. It's not a real force; it's sometimes called a 'fictious force'. But you can still describe it using an inverse cube law, and this ultimately explains Newton's discovery.

And a

*quantum*particle in an inverse cube force behaves in a truly bizarre way, which people have been struggling to understand for decades. If you think you understand quantum mechanics, this may make you reconsider.

I recently learned a lot about these things while writing a chapter for a book called

*New Spaces for Mathematics and Physics*.

Why? Well, it's a long story. I've decided that most of what I learned doesn't belong in this paper. But I had to write it down before I forgot it! So I wrote this blog article:

https://johncarlosbaez.wordpress.com/2015/08/30/the-inverse-cube-force-law/

Go there if you're curious for more.

**Puzzle:**how many times does the blue planet orbit the Sun for each time the green one does?

The animation was made by ‘WillowW’ and placed on Wikicommons:

**If you can make a version of this animated gif that takes less than 1 megabyte, I can feature it on**

*Visual Insight***and credit you!**

But the one I really want has a green planet going

*faster*than the blue one. It's here:

https://en.wikipedia.org/wiki/File:Newton_revolving_orbit_3rd_harmonic_e0.6_240frames_smaller.gif

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