Holding Orbits Up to the Light

In science class the story arrives pre-packaged: Ptolemy drew circles on circles, retrograde motion embarrassed everyone, Kepler straightened the orbits into ellipses, Newton explained why, Einstein explained it better, and then somebody pointed a telescope at a galaxy and the math stopped adding up.

It’s a tidy story. It is also a story I have never actually checked. So let’s check it — not with adjectives, but with data.

The claim, and a machine to break it

Here’s the model on trial — call it M₁: a planet moves on a perfect circle, centred on the Sun, at constant speed. It’s the picture you carry in your head. It’s the one Galileo carried to his grave.

I’ve done all the hard parts for you. No tables of logarithms, no years of hand-computation. Below is the best modern orbit (the data) with M₁ (the model) laid over it, and a single number — R² — telling you how well the circle predicts where the planet actually is. Flip between planets and watch it move:

—eccentricity —circle model R² —RMS error —

Start on Venus: the circle is almost perfect, R² a hair under 1. Now flip to Mars, then Mercury. The red line is the gap between where the model says the planet is and where it is. So here’s the only question this post asks:

If this were your data — clean, free, undeniable — would you throw the model out? Or would you start looking for a reason the wiggle doesn’t count?

Because that second instinct has a name, and a 1,500-year history. It’s called an epicycle.

(the rest is coming)

This is where the planetary position data goes — residuals, error bars, and the moment a 400-year-old equation either survives or doesn’t.