BRADFORD YORK PUKE-MARBLES:

All right!

Voices off!

Find a seat!

Science books!

Chapter Three!

Taking notes!

(Make them neat!)

Subject is . . .

Gravity!

You two there!

Move apart!

Miss Rubble-Cone?

Do it now!

Moving on!

Let me start

With the tale

Of how Sir Isaac Quickmud

Discovered the concept of Gravity . . .

Quickmud was up at the Surface one day,

Exploring the spot where his tunnel had led,

When suddenly, to his surprise and dismay,

Something bounced off the top of his head!

Quickmud said, “Ow!”

His eyes darted around.

And he noticed an apple had struck him

And dropped to the ground.

He wondered aloud

Why it hurt so much more

Than the dirt clods that fell

From the underground tunnels

He loved to explore...

And it was from pondering this question

That Sir Isaac Quickmud

Eventually discovered the concept of

Subterranean Gravity!

So -- Quickmud’s Formula!

Very simple!

Write this down:

Little ‘g’ equals big ‘G’

Times little ‘r’ over big ‘R’.

Big ‘G’ is the force of

Gravity on the Surface.

Big ‘R’ is the radius of the Earth.

And little ‘r’ is your distance

From the center of the Inner Sun . . .

Now --

Who knows what causes Gravity?

Miss Bugcruncher?

LILLIAN BUGCRUNCHER:

The Sky?

BRADFORD YORK PUKE-MARBLES:

Right!

Gravity’s caused by the Sky

Pushing down on the Earth.

Now --

Why would Gravity’s force decrease

As we tunnel away from the Surface?

Miss Cough-Cough?

HELENA COUGH-COUGH

‘Cause the Sky is blocked by the Earth!

BRADFORD YORK PUKE-MARBLES:

Good!

The Earth acts as a buffer --

Resisting the force of the Sky.

So Gravity’s force is the strongest

When you’re at the Surface!

But as you descend,

The further you go,

There’s more and more Earth

Up over your head

That’s shielding the push of the Sky!

And if you could dig your way

All the way down

To the Inner Sun’s center?

There’d be no Gravitational

Forces upon you at all!

You would be weightless!

MINNIE RUBBLE-CONE:

That would be cool!

BRADFORD YORK PUKE-MARBLES:

No -- that would be very, very hot.

Remember the myth of Icarus Flamingskin,

Who tunneled too close to the Sun . . .

All right!

Save your notes!

Ten to three!

Books away!

(Do it now!)

Tomorrow’s class?

Geology!

And the tale

Of how Lord Noah Fungalgrowth’s

Guide To The Planet was wrong . . .

The full title of this song is actually as follows:

Sir Isaac Quickmud [No. 138]

This was the hardest challenge for me so far in Masters of Song Fu.  We had to write a song about one of the 700 “mole-men” that John Hodgman listed in his book, More Information Than You Require.”  On top of that, we only had six days to write the song -- and most of those days fell during an extremely busy time for me.

The fun thing (for me!) about this song is that even though the mole-men’s concept of gravity is half-baked and inaccurate, the formula given in this song does actually work!  (At least, if we assume the Earth has a uniform density it would work . . .)

This may come as a surprise to some people.  But there is actually a linear relationship between the force of gravity and your distance from the center of a planet!  It has to do with two competing formulas . . .

The first is the equation that says that the closer you are to an object, the stronger the attractive gravitational force will be between you.  The equation looks like this:

(It’s the “r-squared” in the denominator that makes the force grow as the distance shrinks -- it’s called the “inverse square law.”)

But there’s an interesting phenomenon that occurs as you burrow towards the center of a planet.  Less and less of the planet is pulling on you as you go down!  It’s due to the fact that, if you’re anywhere inside of a hollowed-out sphere (of uniform density), the gravitational forces of the parts of the shell surrounding you cancel each other out and leave you with a net force of zero!  (Newton proved this -- for more detailed information about the Shell Theorem, you can go here . . .)

So, as you go down, the only parts of the planet that are still pulling on you are the parts of the smaller sphere still “beneath your feet.”  The volume of this smaller sphere is given by the equation . . .

(Notice that here, the radius is being cubed.)

So -- as we dig down, we’re getting closer to the center of mass of the Earth.  So the force of gravity should be growing by a factor of “r-squared.”  But -- as we dig down, less of the planet is pulling on us!  Which means that the force of gravity is simultaneously decreasing by a factor of “r-cubed”!  The net result is that the force due to gravity decreases linearly from a maximum at the surface, to a net force of zero at the center of the planet!

(But again -- this only works in any practical way if the planet were of uniform density, and if we could actually survive the trip to the Earth’s core.  But the theoretical physics is fun to think about!)

The challenge?

Write a song about a mole-man.

Download “Sir Isaac Quickmud.mp3”

(Want the sheet music?)