Every Day Is Special: March 8 - Kepler's Third Law Makes Its First Debut

March 8 - Kepler's Third Law Makes Its First Debut

Posted on March 8, 2018

You probably know that even ancient peoples knew that the world was spherical, but almost everybody "knew" that we - the Earth, that is - were the center of the universe.

In the 3rd Century BCE, an Ancient Greek astronomer named Aristarchus of Samos suggested that the Earth revolves around the Sun.

As early as 1514, a German/Polish astronomer named Nicolaus Copernicus began to write and talk about a Sun-centered universe, although he didn't publish his fully worked-out theory until 1543.

It took a while before the idea was generally accepted - like, a century and a half!

But in all that 150-or-so years, all along the way, various scientists tweaked the model, made more and better observations, suggested alternative explanations for the data, and inched forward in a slow-motion "Copernican Revolution."

One of these contributors was Johannes Kepler. He took Copernicus's model of the solar system, which explained observations better than did earlier models, and he made a few brilliant adjustments, so that the new model explained observations even better!

Kepler's "adjustments" were in the form of three "laws of planetary motion." He published the first two in 1609. He discovered the third on this date in 1618, and he published it in 1619.

Let's check them out:

#1 - The orbit of every planet is an ellipse (basically, an oval) with the Sun as one of the focal points.

Actually, all of the planet's orbits are ALMOST
circular. So this picture is a big-time exaggeration,
making the oval / elliptical orbit look a lot longer
than it is wide.

This exaggeration also makes the Sun look like it is
far to one side instead of, in reality, being pretty
darned close to the center!

We have to exaggerate in these sorts of diagrams,
or everybody would just say, "Oh! The orbit's a circle,
and the Sun is in the center!"

#2 - If there were a line that connected a planet to the Sun (rather like the "hand" of a clock), it would sweep out equal areas during equal intervals of time. This is because the planet moves slower when it is farther from the Sun and quicker when it is closer.

#3 - The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of the orbit.

Wh- wh- what?

This is a mathematical statement about the relationship between the distance of planets from the Sun and their orbital periods.

Remember, the closer something is to the Sun, the faster it moves. This is because the gravitational pull of the Sun is much stronger on nearby objects.

So not only does a far-away planet like Uranus have to travel a LOT farther to go aaaallllllll the way around the Sun than, say, Earth, it also travels more slowly. You can see how much longer it takes the far-away planets to travel once around the Sun in this chart:

Actually, this chart uses rounded-off measurements

of the years of the planets. To see a more accurate

list, check out this website.

By the way, if you are wondering what the semi-major axis of an orbit is, here is one more exaggerated diagram:

The major axis of an ellipse is a straight line that goes through
the widest part of the ellipse, traveling through both foci.
The semi-major axis is exactly half of that line.

Also on this date: