Date: Mon, 11 Mar 2002 15:52:42 -0800 (PST)
From: Jerry Friedman 
Subject: (urth) Leagues and gravity


--- Michael Andre-Driussi  wrote:
> Assuming that Lune Diameter = 2160 miles, and Orbit = 150,000 miles . .
> .
...

Where did you get 150,000 miles?

Anyway, you got me thinking about Green-Blue celestial mechanics.  Stop
me if this has all been done.

We're pretty sure Green is not a satellite but rather another planet
with a slightly smaller orbit, so that it comes into conjunction
every six years (if I remember correctly), right?  Also, Green has
higher gravity than the moon--otherwise the narrator would have told
us at least once how the first thing he as Horn noticed was floating
every time he tried to take a step.  I can hardly imagine Green has
less than half the gravity of Earth and the same density.  Using those
assumptions gives it 1/8 the Earth's mass.  (Calculations available on
request.)

Let's also believe Incanto quoting one Gagliardo when he says the
closest approach of Green to Blue is 35,000 leagues.  If these are
the same leagues in the afterword to _The Sword of Lictor_, namely
about three miles, then that's 105,000 miles.  For comparison,
somebody on the first visit to the Red Sun Whorl says a league is
7000 steps.  If these are half the Roman pace of which the 5000-foot
Roman mile was a thousand, then that's 7000*2.5 = 17,500 feet ~ 3.31
miles.  Using that latter number, Green's closest approach is about
1.87 x 10^8 meters.

We can now determine that the maximum force that Green exerts on Blue
at conjunction is about 8.5 x 10^21 N.  For comparison, the force the
sun exerts on the Earth is about 35.3 * 10^21 N.  In other words,
Green is going to mess up Blue's orbit something fierce--and much
more if it has more than half the Earth's gravity.  Mere storms and
tides are nothing.  Blue is going to mess up Green's orbit even more.
I doubt the system would be stable for more than one or two
conjunctions.

So did I make a mistake?  Are we supposed to infer something from this
discrepancy?  Or is this another case of Wolfe's not letting science
get in the way of the story?  The problem with the latter is that if
he can get away with anything, the kind of deductions he apparently
expects readers to make become problematic--which is the difficulty
we're having with the Blue/Ushas conjecture.

Jerry Friedman

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