Notes from Professor Boggs:
Johannes Kepler was the first to come up with a simple,
complete, and general set of “rules” that describe how
planets orbit the sun. His laws are still used today in
calculating rocket orbits! Although Einstein showed that
these “rules” are a bit inaccurate, they still give very close
approximations to how orbits really work.
The Church was still getting used to the idea that the Earth
might not be the center of the universe, and planets orbited
the Sun, when Kepler proposed that orbits might not be
perfect circles. Needless to say, the Church was NOT happy.
However, it sure explained a lot…

Verses

Tycho Brahe gathered lots of data
But someone had to show what it all meant
The church said planets gotta make round trips
Kepler said, “kiss my ellipse!”
Your epicycles gotta hit the road
Cause the orbits are all bent!
Said Kepler – said Kepler – He figured out the dance
These three little rules will be our tools
And leave not a bit to chance!

Planets make an ellipse with the sun as a focus
The other focus is just empty space
But draw two lines from the foci to the planet
You add ‘em up and the sum is constant
Works the same in every case
Said Kepler – said Kepler – He figured out the dance
These three little rules will be our tools
And leave not a bit to chance!

Planets sweep out equal areas in equal times
All those triangles add up just the same
When the planet gets too near the sun
It whips around like it’s having fun
When you’re far gotta walk when you’re close gotta run
That’s how you play that area game
Said Kepler – said Kepler – He figured out the dance
These three little rules will be our tools
And leave not a bit to chance!

The square of the period follows the cube of the distance
The average distance of planet to the sun
If your radius is two, the rule’s gonna state
That your orbital time is the square root of eight
You’d better hurry up so you won’t be late
If you’re real close in then you really gotta run!
Said Kepler – said Kepler – He figured out the dance
These three little rules will be our tools
And leave not a bit to chance!

Now Kepler’s laws were marvels of precision
Reducing orbital complexity
Then Isaac Newton came along
And said, pretty good, but your premise is wrong
You figured out the dance but I heard the song
How ‘bout one rule to replace all three
Said Newton – said Newton – that apple’s got to fall
Here’s one great law that explains what you saw
Gravity says it all!

Comments
As much of a genius as Kepler was to figure all this out, he
pales next to Newton, who had the amazing insight that
ALL objects attract each other in proportion to the sum of
their masses, with a force decreasing as the square of the
distance (gravity). From this one law, he could predict all of
Kepler’s laws exactly! Newton’s laws ruled physics for two
centuries – it took Einstein to topple him from the throne!