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Date: Mon, 11 Mar 2002 16:49:37 -0800 (PST)
From: Grant Peacock 
Subject: Re: (urth) Leagues and gravity

> Anyway, you got me thinking about Green-Blue celestial mechanics.  Stop
> me if this has all been done.
Yeah I once posted some similar thoughts, although I didn't do any math.

Have you considered the possibility that the narrator is accustomed to gravity
less than 1 g?  I'm assuming the whorl was designed to prepare people for Blue. 
The fliers in the whorl are perhaps more realistic in a .5g environment.

Our moon exerts a stronger force on Earth than our Sun does.  I say this because
tides are only a bit more extreme during a full moon.  (I forget the terminology. 
What are neap tides??)  So I would guess there must be something wrong in your

I think you are surely right that the orbits are unstable, even if the force
exerted by Green on Blue is a small percentage of that exerted on Earth by the
moon.  This means that the arrangement is a new one.  For those who believe the
Blue=Ushas theory, what must have happened was that the white fountain grabbed
Lune out of orbit as it came lumbering in and made into a planet.

Does the white fountain literally move through space into the system, or does it
just magically appear?

> 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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