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One of the most remarkable forces in the universe is known as
gravitation. There are other fundamental forces, ranging from the two
nuclear forces to electromagnetism, but none of them is of any
importance to anyone who doesn't want to spend their life considering
time-retarded integrals, group theory, and the horrible decor of physics
classrooms. We can see why by considering Newton's law of gravitation:
F=G*m[1]*m[2]/(r^2) : G is a proportionality constant,
m[1] and m[2] are the two masses,
and r is the distance between them.
As far as we know, G is constant at all times and at all points in the
universe. Gravity always attracts (there are no negative masses) while
electromagnetism can also repel; thus, it is extremely difficult to build
up a large amount of charge in one location. Gravity decreases with r^2,
while the nuclear forces decrease with e^r, meaning they are noticeable only
over subatomic distances.
Therefore, these other forces can be safely left to the glossy pages of
physics journals, where they won't cause any harm beyond the publication
of theoretical papers. (Physics lore claims that, asked to prove the
stability of a table, a theoretical physicist can quickly derive a solution
for a table with an infinite number of legs, and will then spend the next
thirty years trying to solve the special case of a table with a finite,
non-zero number of legs.) Gravity, on the other hand, is important to
anyone who wants to travel through space and arrive at a given point on
the first try. The various theories of gravitation lead to many interesting
results, such as bread always falling on the carpet with the butter-and-
jam side down, black holes forming, and lost change vanishing into sofa
crevices.
Unfortunately, all these really interesting gravitational phenomena require
a knowledge of General Relativity to understand. Newtonian gravity is
almost exclusively used to derive orbits, and celestial mechanics has
become a nightmare of eccentricities, tidal forces, and mathematical
techniques all invented by Frenchmen whose names begin with 'L'. Any
society needing really accurate orbital calculations is capable of building
computers able to numerically integrate them.
Therefore, in the real universe you don't have to worry about getting
actual symbolic expressions for orbital parameters; it's simpler to dump
all the masses and velocities into a suitable program and hope the
programmers responsible for the floating point routines weren't prone to
forgetting to check the carry flag.
General Relativity, on the other hand, deals with black holes, space
warps, time travel, and all the other things one finds badly mangled in
Shirley MacLaine's books. To do this, however, one is forced to use
tensor calculus, a generalization of vector and scalar calculus that is
best defined as the field where one uses every Greek letter as both
super- and sub-scripts simultaneously. Many theorems can be proved by
writing down some basic equations and manipulating them until an error
is made that lets the proof be easily completed. (Confusing the letter
zeta with anything else is frequently used. When handwritten, either
very quickly or with the greatest care, zeta always ends up looking like
a random squiggle; there is a Nobel Prize waiting for anyone who manages
to replace zeta with something simpler, like a 10-stroke Chinese ideogram.)
Errors in derivations have occasionally caused comical results; for
example, one result for the effect of emission of gravitational radiation
by two orbiting neutron stars was antidamping. The emission of the
radiation would supposedly increase the orbital velocities, and hence
increase further emission, and so on. Someone actually managed to get
that result published, thus proving that inhaling chalk dust over long
periods does indeed cause brain damage.
While a knowledge of all of the above may be useful for small talk at
cocktail parties, it probably isn't.