The Inverse Square Law

The universal law of gravitation can be elegantly described as:

My pancreas attracts every other
Pancreas in the universe
With a force proportional
To the product of their masses
And inversely proportional
To the [square of the] distance between them

Dr. W. Albert Yankovic
(see "Like a Surgeon" for doctoral studies)

Here, we square away the Sun-Earth-Moon system.

Sun

The sun is a mass of incandescent gas

A gigantic nuclear furnace
Where Hydrogen is built into Helium
At a temperature of millions of degrees

In regions of intense magnetic activity, the surface temperature is reduced causing dark sunspots. The diameter of sunspots can be much larger than an Earth diameter. Magnetic activity peaks every 11 years.

Earth
The pale blue dot

Look again at that dot. That's here. That's home. That's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar", every "supreme leader", every saint and sinner in the history of our species lived there - on a mote of dust suspended in a sunbeam.

The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.

The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand.

It has been said that astronomy is a humbling and character-building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we've ever known.

Carl Sagan
Pale Blue Dot: A Vision of the Human Future in Space

Moon

Goodnight stars
Goodnight air
Goodnight noises everywhere

Goodnight Moon
By Margaret Wise Brown

Why is this picture not to scale?
Diameter of the sun = 109 times the diameter of the Earth

1 AU = 1 astronomical unit = 8.5 light-minutes = average distance from Earth to Sun = 108 times the diameter of the sun

There are 10¹¹ stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.

Richard Feynman

United Squares of America

"Seven squared plus one more ago, our fathers brought forth, upon this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all sides are created equal."

UNITED SQUARES OF AMERICA
The Lower 48 and the District
"From square to shining square..."

A historical note:
The District of Columbia was originally a 10 x 10 sq. mi. square, but in 1847 the southern portion was returned to the Commonwealth of Virginia.

1 pixel = 2 x 2 sq. km.


Map with state labels:

ALASKA
The Upper 1

Alaska is larger than all but 18 nations, has the combined area of the 22 smallest U.S. states, and is over 2x larger than Texas. Alaska has more than 2,500 named islands.

In this map, we preserve the scaling 1 pixel = 4 sq. km.

There are two maps: one with no text labels for the islands, and one with labels for islands with land area greater than roughly 200 sq. km. (~7 x 7 pixels)

Text labeled:



HAWAII

Hawaii is the only U.S. state that has no straight line in its boundary.




THE SQUARE-SPANGLED BANNER
a.k.a The Squares and Squares


This is the end of the geography lesson.

The World Is Square

Magellan was the first to circumnavigate the Earth.

Friedman tells us the world is flat.
Einstein found that spacetime is curved.
And Shakespeare said "All the world's a square."
Or something like that.

PANGAEA
The Supercontinent

Note: The ratio of landmass of Pangaea is to scale
to the water mass of Panthalassa, the super ocean.
(29.2 : 70.8)


THE MODERN CONTINENTS
Asia, Africa, North America, South America, Antarctica, Europe, Australia

Total land area = 149 million square kilometers
Total land area = (12,200) x (12,200) sq. km.
Total pixel area = 814 x 814 pixels
where 1 pixel = 15 x 15 sq. km.


THE WORLD IS SQUARE
The square projection

205 nations, states, and countries

From Angola to Zambia,
from the British Virgin Islands to the U.S. Virgin Islands,
from the Republic of Congo to the Democratic Republic of Congo,
and from Guinea to Guyana to
French Guiana to Papua New Guinea,
it's all squared away.


"There is One above you who combines many
Spheres in One Supreme Existence,
surpassing even the Solids of Spaceland"

- A. Square in Edwin A. Abbott's
Flatland: A Romance of Many Dimensions