Saturday, March 6, 2010

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.

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.

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
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


  1. I recognize some constellations.
    The square dipper, squarion and squared gemini.
    Are there more?
    Also, may be you should consider making the earth a cube to explain the day-night cycle.

  2. Clock-wise: Big Dipper (Ursa Major) + North Star, Virgo (apparently the beta star is missing!), Hercules, Orion, Sagittarius.

    Shall we also show the ripples in four-dimensional space-time to describe the small ripples due to the slight wobble of the sun? Perhaps we should include the gravitons popping in and out of the 10 or 11 or 26 dimensional branes of string theory?

    It's a square world after all...