Darth Vader meets Enrico Fermi
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    How do you describe the energy of supernovae, the most titanic
explosions in the cosmos?


    I faced this question a week ago, as I prepared a lecture for the
course that I affectionately describe to my colleagues as
"Astronomy for the Masses." Telling students that
a supernova is a hundred million billion trillion times as powerful
as a megaton hydrogen bomb is about as useful as comparing
it to a hundred million billion trillion trillion firecrackers.
Even the asteroids and comets that are now invading Hollywood
and The New York Times do little more than dent the surface of a planet, 
albeit with unpleasant consequences for those who happen to be living there.

    The return of Star Wars to the big screen seemed to provide
just the illustration that I needed: the destruction of the planet
Alderaan by the Death Star.  At some time in their undergraduate years,
all students of physics absorb a dictum, usually attributed to
Enrico Fermi, that "a good physicist should be able to calculate
anything to a factor of two."  (It is this swaggering attitude that
leads to final exam questions at the California Institute of Technology 
like "How far can a goose fly?") Figuring myself to be at least an 
average physicist, I picked up on Fermi's challenge and set out to
calculate the explosive energy of Alderaan's demise.

    I assumed that Alderaan was a planet roughly the size of the earth and 
that the Evil Imperials, in a spirit of ruthless efficiency, would choose
to zap it with the minimum amount of energy needed to blow it up
(or, in a physicist's language, to "unbind" it, as though gently
releasing the planet from gravitational shackles).  One needs 
only high school physics to compute this energy, because all methods 
of unbinding a planet are equivalent.  For purposes of calculation, 
it is simplest to imagine peeling the planet down from the surface 
rock by rock, hurling each chunk into outer space at a speed sufficient
to escape the pull of gravity (seven miles per second in the case 
of the earth).  

    One finds the energy of this operation by squaring the planet's mass, 
dividing by its diameter, then multiplying the result by
the universal constant of gravitation, G, a number conceived by
Isaac Newton and measured in 1798 by Henry Cavendish, using
a barbell of metal spheres twisting at the end of a long, thin wire.
Plugging the earth's mass, the earth's diameter, and the gravitational
constant into this formula yields a number with many, many
zeroes in it.

    The real fun begins when one asks if such explosive power could be
achieved in a "practical" way, even by Darth Vader.  Absent a
serious loophole in our current laws of physics, the most efficient
possible scheme by which the Death Star could fuel its blasts would
be to collide matter and anti-matter, converting mass into energy
in accord with Einstein's famous formula, E = mc-squared.
With a few strokes on a pocket calculator, one finds the mass of 
matter and anti-matter required, a billion billion grams.  
About the mass of Mount Everest.

    This, I told my class, explained why the Death Star had to be so big.
Beneath its shell of spaceship bays, tractor beams, and storm troopers
must lie a vast hollow space, within which the ultimate battle station
would trundle a mountain-sized ball of anti-matter --- safely confined,
one hopes, by magnetic fields --- and its mountain-sized partner of matter, 
both poised for their cue to mate in a dance of annihilation.

    Unbinding Alderaan took roughly the amount of energy that the sun 
radiates into space in a million seconds (twelve days).  For the 
second or two that the Death Star's beam spent on its ruinous task, 
it must have shone a million times more brightly than the sun.

    All of these musings did not get me much closer to my original goal, since
even the blast that reduced Alderaan to stardust had only one trillionth the
energy of a supernova.   To equal the explosions that mark the terminal
agonies of massive stars and create the atoms of life, one must imagine
a galaxy far, far away in which a hundred billion suns are circled
by ten planets apiece, and a trillion orbiting Death Stars launch a
simultaneous attack to blow them all to smithereens.  Now THAT would 
cause a mighty tremor in the Force.

David Weinberg
Ohio State University
March, 1997