Super Planetary-Motion Smackdown: Kepler v. Newton


Science is always an unfinished project. That’s what makes it so much fun. The process—collecting data, building models to explain how the world works, and then topping them with new models—is just plain exciting. The history of science is full of epiphanies, civil wars, and revolutions, but perhaps the very best stories come from astronomy. So let’s look at part of this story, the episode where Isaac Newton got up on Johannes Kepler.

Of course, you first need the backstory. The ancient Greeks studied the Earth and the sky, but their basic model had all the objects (sun, moon, and planets) moving in circles around Earth. Later, Nicolaus Copernicus said, “Hey, if you put the sun in the center, then you can explain this weird motion of Mars.” After that, Kepler came up with his model for planetary motion. There was lots of fighting and crying in the middle of this, but I will leave that up to your imagination.

Kepler’s model has three main ideas. (These are usually presented as “Kepler’s three laws of planetary motion,” but taking them together, it’s really just a model.)

  • Planets orbit the sun in elliptical (not circular) paths.
  • As a planet gets closer to the sun, it moves faster.
  • The orbital period (T ) is related to the orbital distance (a) by the expression T 2 = a 3 (where T is measured in years and a is measured in units of the Earth-sun distance).

A couple of comments: First, this model is just based on the observational evidence available at the time—but it fit this data quite well. This was no easy task. Imagine just trying to plot the orbits of the planets. You’d do that by observing their location in the sky over the course of a year (or more). But then you had to account for the fact that the spot from which you were measuring was also spinning through space.

There is another important thing to notice. The relationship between period and orbital distance gives a “1 = 1” equation for Earth. It takes Earth one year to orbit the sun, and it has an orbital distance of 1 AU (astronomical unit—distance from Earth to sun). It wasn’t until much later that someone was able to actually determine the distance from Earth to the sun. This is crazy if you think about it.

Just so we’re all on the same page, here is a numerical model for some random planet orbiting the sun. It’s just a gif below, but here is the code if you want to see it.

This is the best model of planetary motion we had before Newton. And, really, it’s a fine model. You could even use it to find some new object orbiting the sun or to model the motion of a comet. But could it be more general? Is there a more fundamental model that could explain both the motion of a planet orbiting the sun and the motion of the moon orbiting Earth? Maybe even one that could also explain the motion of an apple falling from a tree?



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