The Physics of Trojan: Creating a Fictional World.

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Spoiler Alert–If you want to figure all this physics out yourself, go read the books, Trojan Series,  and then answer the following questions [Known data about Trojan: Outer radius=5,150 Km, Inner radius=4,000 Km, Density of alloy=21.87 gm per cc., Density of crust (with quartz fibers)=14.68 gm per cc. Shafts wide enough to allow large objects (human, for example) at the North and South Poles of Trojan].If viewing this is a problem for reblogging, go here: Brian Dingle’s WordPress Blog on Trojan Physics

  1. Describe and explain the characteristics of the gravitational field inside this hollow metallic moon.
  2. Describe the motion of a man falling into the North Pole shaft, assuming no atmosphere and a clear path across the Inner Sanctum 9hollow interior) right up to the top of the South Pole shaft. What is the speed of any object falling down the shaft when it enters the Inner Sanctum?
  3. Suppose two objects passing each other within a shaft, under free fall from opposite pole shafts at the top. Show that they have the same speed but opposite velocity.
  4. Calculate the maximal kinetic energy of a five meter thick, twenty-five diameter slab of crust as which has fallen from the top of a shaft. Hint: use its speed in the Inner Sanctum.
  5. Describe in qualitative terms at steady state what the atmosphere piped into Trojan would look like (height, width, extent) when the pressure at the center of Charity (on the equator) reaches Earthside atmospheric pressures at sea level. Give some reasonable argument for how far from the equator a normal individual can comfortably walk, until they reach Earthside equivalent of 5,000 feet elevation.
  6. What is the acceleration due to gravity at the North Pole of Trojan?
  7. What rotation speed of Trojan is required that objects on the inner surface at the equator experience a force of acceleration equivalent to 9.8 meters per second per second?
  8. What is the escape velocity of Trojan, and how does that compare with the rotational velocity of Trojan surface at the Equator (surface)?

…and so it goes (judging by the rolling eyes I get, divulging this kind of information is not much of a spoiler alert). It was questions like these that I imagined to create the experience living inside a hollow moon. I sometimes think it strange I became a physician instead of a physicist, because I look at the world like this all the time.

Gravity Inside Spherical Objects

For those of you who have not read the Trojan Series, Hollow Moon of Jupiter or Nefra ContactTrojan is a large metallic moon, over 5,000 kilometers in radius or 10,000 in diameter, with a 1150 Km crust so that the Inner Sanctum, the hollow part inside, is 4,000 Km in radius. Since the crust is very dense, far denser than Earth for example, being a metal alloy, the surface of Trojan has a surface gravity that is about ten per cent higher than Earthside.

There is a shaft at the North Pole (South one too, you find out later) which starts about twenty-five meters in diameter, and spreads out to five kilometers when it opens outing the Inner Sanctum. There is a five meter metal cap over the shaft.

My original fascination with Trojan started many years ago. In my undergraduate years, in Mathematics and Physics at University of Toronto, there was a question on one of our weekly problem sets:

Consider a tunnel from Boston USA to London England (water-tight too, of course) and calculate how long it will take for a subway car on frictionless rails to make the trip.

First, you have to recognize that the car would start rolling under gravity, and it would have enough force to get it all the way to other side where it would slowly and smoothly come to a very brief stop, just like a ball peaking a high point on a trajectory. The calculation will involve trigonometry, as the force vector on the path of the car will be at an angle to the gravitation force toward the earth’s center. It will involve integration, since the force of gravity will vary with the radial depth of the car at a particular time (just like it is explained so many times in Hollow Moon and Nefra Contact) because all the mass of Trojan ‘above’ (at a radius greater than) the car contributes no force; only the mass ‘below’ (at a radius less than that of the car) has any effect.

Well, there are some pretty elegant solutions, but the curiosity, as I remember it, of that problem set in my physics class was that the transit time taken from Boston to London is the same as the transit time taken from Boston to Moscow, or Sydney, or anywhere: it’s exactly the same as the transit time from the North Pole to the South Pole, assuming no friction to muddy up the mathematics.

Neat.

I know. I’m weird. But I do find that stuff fascinating.

Now, the Earth is solid, not hollow. Of course, while working this problem thing out, you very quickly realize that there is no gravity inside a hollow sphere that is floating in a weightless environment–like space, for example–and this is explained several times by several people in the Trojan Series, in several different ways, but in the above problems it is easy to see from the equations that there is no gravity at the center of the Earth. Nor is there in any symmetrical hollow structure; the only critical important feature is that the sphere be symmetric.

This is a well understood concept in physics, with no possible real-life example. We are not going to find a hollow moon anywhere, anytime soon.

There are parallels, of course.

The electrical field inside a charged metal sphere works on the same principle, based as it is on an inverse square law of distance, similar to gravity. The field strength is zero.

In Nefra Contact, they laugh at MacLynn, an older somewhat eccentric astronaut, but he is quick to see what will happen to Garth (the elder, James…the younger, Donald, is in Hollow Moon of Jupiter) when he falls down the hole, the North Pole shaft, into Trojan (Chapter Five, The Pit). Here, Mac is wandering out near the North Pole of Trojan, near the hole into which his colleague and co-astronaut, James Garth, has just fallen. At this point, Garth is still falling, and has not hit bottom:

Mac stood looking at the lights, entranced. Then he began his usual ramble over the transcom, forgetting the other three for the moment. “The effective mass beneath Garth’s position, the radius, from the cannon ball’s [Trojan’s] centre is proportional to the cube of that radius,” Mac muttered, “while the force between Garth and the effective mass is proportional to the inverse square of that radius. The effective mass being at the centre, of course, because we all know you can consider the mass to be centered at one point. So, the radius cubed divided by radius squared. Equals the radius. Well…for a solid sphere, but this one is hollow.”
Mac tried to scratch his head, but the helmet got in the way. “So you have to subtract the mass of the hollow part. Anyway, with the radius getting smaller, the force is decreasing, proportional to the radius, minus a bit, and thus Garth’s acceleration is decreasing too, decreasing with every meter he falls.” His friends all listened quietly now, as Mac mumbled through this, not wanting to embarrass him further by letting him know they could all hear him. “Force proportional to distance. That means the acceleration is proportional to distance.”
Mac stood still for a moment. “Acceleration is the second derivative of distance with respect to time, so…
“…Second time derivative of distance proportional to distance…

Here, Mac has figured it out. The path taken by Garth senior is a solution to a second degree differential equation of distance related to time being proportional to distance (specifically, the second derivative of distance with respect to time is equal to a constant times distance). He immediately recognizes this as the harmonic oscillator, like a spring, or a pendulum–without friction, this could go back and forth forever. The mathematical solution is a sine wave. [Substitute a sine wave into the equation. First derivative is cosine, and second derivative is back to a sine wave, differing only by the constant].

…that’s simple harmonic motion.” Squatting by the pit, he looked back at Jupiter. He thought about the south side,

Here, Mac has made an impressive intuitive leap. Not the solution to the differential  equation. Every first year physics student knows that one, and Mac is a highly trained astronaut and physician. No, if there is symmetry to this moon, there should be a shaft at the South Pole too. That is his intuitive leap. James Garth’s acceleration down the North shaft should be mirrored exactly by his deceleration up the South shaft.

It also reflects a curious logic in medicine. You don’t assume stuff that is hopeless for your patient; you instead constantly think of and prepare for what is treatable, even if unlikely. The only way to save Garth is if there is a shaft at the other end of his trip across the Inner Sanctum. So Mac needs to prepare for that, even when he doesn’t know for sure.

…but the sting of the other’s laughter made him stop muttering and kept him quiet. He got back up and returned to the LM.

MacLynn (Mac) was embarrassed earlier; he’s not going to talk about this right now. They might laugh at him again.

Amazing Speed Traversing the Inner Sanctum

When Garth senior falls down the North Pole shaft, he achieves an unbelievable speed, 13,393 kilometers per hour in just over eight minutes of falling under the variable acceleration of falling through the crust of the moon. This may seem ridiculous to those of us experienced with free fall on Earth, where maximum velocities achieved are in the range of 122 miles per hour, or about 200 km per hour. The part we are ignoring is resistance due to atmosphere. Buoyancy of the air around us has a much greater effect than we ever realize.

The appendix on Gravitational Analysis at the end of Nefra Contact addresses and explains this. The problem could not be calculated algebraically because the hollow interior weightlessness complicates the equations too much. It is a relatively simple procedure, though somewhat tedious, to create a computer spreadsheet to iteratively crunch out these numbers. What’s his speed after one second, what’s the speed after two, and so forth.

Trojan is a symmetrical sphere that is hollow, with relatively small (25 meters external opening to 5 kilometers internal opening) bore at both the North Pole and the South Pole. The axis of rotation runs exactly through these pole shafts. In order to achieve the physical characteristics required of Trojan, the following is given:

Outer radius 5,150 Km
Inner radius 4,000 Km
Density of metallic alloy 21.87 gm per cc
Density of crust (with quartz fibers) 14.68 gm per cc.

Here is an example of the calculations for the first seven seconds of free-fall that I did for Nefra Contact.

Time position r(1-ri^3/r^3) acceleration speed distance speed (Km/hour)
0 5.1500E+06 2.7370E+06 1.1192E+01 0.0000E+00 0.0000E+00 0.0000E+00
1.0000E+00 5.1500E+06 2.7369E+06 1.1192E+01 1.1192E+01 5.5959E+00 4.0291E+01
2.0000E+00 5.1500E+06 2.7369E+06 1.1192E+01 2.2384E+01 1.6788E+01 8.0581E+01
3.0000E+00 5.1499E+06 2.7369E+06 1.1191E+01 3.3575E+01 2.7979E+01 1.2087E+02
4.0000E+00 5.1499E+06 2.7368E+06 1.1191E+01 4.4767E+01 3.9171E+01 1.6116E+02
5.0000E+00 5.1499E+06 2.7367E+06 1.1191E+01 5.5958E+01 5.0362E+01 2.0145E+02
6.0000E+00 5.1498E+06 2.7366E+06 1.1190E+01 6.7148E+01 6.1553E+01 2.4173E+02
7.0000E+00 5.1497E+06 2.7364E+06 1.1190E+01 7.8339E+01 7.2744E+01 2.8202E+02

Of course, the spreadsheet goes on for 496 seconds (first column) not just the seven shown, until James Garth emerges into the Inner Sanctum (the funny term in the head of the third column is the only thing that varies apart from time, and it is derived from the equations of motion standard for this problem, rearranged a bit to reduce calculation errors which can add up in an iterative process like this; r refers to position and ri is the fixed inner radius).

This is essentially the spreadsheet that Phil Crinshaw Sr. develops ‘on the fly’, in the Landing Module on Trojan’s surface, showing that James Garth will take 496 seconds (8 minutes and 16 seconds) to fall the distance of the shaft through the crust of Trojan, at which time he will be traveling about 13,393 km per hour, and will have travelled a total distance of 1,150 km!

13,393 km per hour versus 200 km per hour, after eight minutes of free fall. That is the difference air resistance makes! On Earth, that eight minutes of free fall would be through a gravitational field that is essentially constant at 9.8 meters per second per second. On (or in) Trojan, the gravitational field at the surface is 11.2 meters per second per second, ten per cent more than Earth (diets, folks, everybody is ten per cent heavier), but the field strength drops almost linearly down the crust to the inside of Trojan where it is zero. Nevertheless, eight minutes and sixteen seconds of free fall through the crust, with no friction, gets you going this fast because there is no buoyancy or resistance of atmosphere.

Now, imagine what it would look like to pass through the Central Structure (the older term for the Carousel), that 3 kilometer round donut like structure in the middle of Trojan, where the Ortho Burn Unit, Trojan Governance, Euler Laser Constructions and the military are housed, not to mention ‘Saggies’ or Sagitarius Bar and Grill. Remember, as is described in Hollow Moon of Jupiter, there is a channel through the middle of the Carousel where nothing is allowed to be, just in case something falls down the North Pole (or South Pole, by now, when it’s metal cap is removed) shaft.

13,393 km per hour is 3.7 kilometers per second. How far away can you see the Central Structure? In Nefra Contact it is described as 500 meters on each side. It has grown to about 3 kilometers in diameter by the time of Hollow Moon of Jupiter, some forty years later in 2065.

The resolution of human vision is about one arc minute, or about 50 cm at one kilometer distance, or about 500 meters at a thousand kilometers (can we see a window in the side of a house mile away–just, perhaps, depending on lighting, and lighting in Trojan is not all that good). Thus the Central Structure might be visible for about three minutes–as a dot or blob in the sky–until one is about fifteen seconds away. The width of a steel girder may not be apparent until one is about 500 meters away, a distance which will be covered in 0.13 seconds by anything falling through the center. Don’t blink!

The Carousel, at 3 kilometers diameter, might be just visible from the inner surface of Trojan, 4,000 kilometers away, especially when it crosses the solar bulge, but probably not through the equatorial atmosphere…one probably has to get out of atmosphere, in a tranpod or up the inner surface, say to the 80th parallel in latitude.

There is no sensation of speed, of course, traversing through Trojan–it is, after all, relative. There is only ‘sensation’ of acceleration. But what exactly is that? When we accelerate in a car, we feel it because it is being resisted. When we jump off a cliff, we are accelerating at the speed of gravity, 9.8 meters per second per second. On Trojan, near the surface, like on Earth, it would be 11.2 meters per second per second, or about ten percent heavier than on Earth.

Falling down the shaft at the North Pole of Trojan is free fall, and it feels like we do jumping off a cliff–nothing. Slowing down going up the South Pole has got to be the exact opposite of falling down the North. Negative 0, instead of positive 0. In other words, nothing.

Acceleration in a fast car or spaceship feels like something, because we are being pushed. Acceleration in a uniform gravitational field, like jumping off a cliff, or rising to a peak of a trajectory through the air after being shot from a cannon, has no real sensation at all. That is because every molecule of our being is under the same force field, not just those being pushed into it by others.

We imagine we would feel deceleration, but that is because our experience is always in an atmosphere, or in a car or other vehicle that is pushing you. Actually falling in free fall, whether accelerating or decelerating, feels like nothing. (Not convinced? Remember that astronauts doing a space walk are in a constant gravitational field around the Earth that is keeping them in orbit, always falling toward the center of the Earth, as well as lateral velocity forming the usual orbital circle.)

Now, we are used to accelerating in free fall as we jump off a cliff into a lake, for example. Our experience of decelerating in free fall is rare indeed (falling up!), certainly very brief when it occurs, and feels again like–nothing. Like ski-jumping or roller-coasters at the top of the curve, or a mountain bike achieving a brief moment of liftoff.

So, in Chapter Fifteen, One’s Tether, in Nefra Contact, about mid-chapter, the following paragraph is puzzling:

The deceleration now was roughly a fifth of gravity on Earth. It felt good after an hour of weightlessness. It felt like more control. He could feel which way ‘up’ was, or perhaps down, depending on how you looked at it. Garth turned on his head lamp, but the surfaces were still too far away. He thought as he looked up that he might just see some point of light, from the Xenon lamps Princeton had put out.

No. It didn’t feel different. It felt like nothing. This is James Garth’s imagination playing tricks on him, or my lack of concentration because I don’t spend a lot of my time free falling in an upward direction.

“Garth, it’s two minutes, your speed is down to a mere 4,744 kilometers per hour, and you’re 80 kilometers away. Your deceleration is almost maximal.”
“Yeah, I can feel it. I’m slowing my rotation with the pole. Not quite sure what to do with it, but I guess it will slow down too. I see the light.” Hands are sweaty. Cold sweat. No mist or leaks, but why am I so cold?

Can he feel it? I don’t think so. It’s like bouncing off a diving board, how you feel at the top of the curve. If you shut your eyes, can you really feel it? If you shut your eyes, can you really tell when you reach the top? Or do you just key off the sensation of breezes on your skin.

And a moment or two later Phil makes the same mistake, when Garth has to take the oxygen cylinder from the crew at the South Pole (they can’t make a hole big enough to get Garth out, but they can give him more oxygen for the round trip):

“Garth,” Phil called, “Garth, are you with us?”
The pain this time was real, but not so bad. He had the cylinder, followed closely by five meters, not twenty five, of tether, with no clasp.
“Garth, you have to clip on.”
“No, I don’t, ‘cause I didn’t let go.” Garth hugged the cylinder as the walls of the shaft sped by at increasing speed, widening out as he dropped back into Trojan.

Phil is briefly forgetting that the cylinder of oxygen will fall at exactly the same rate as James Garth, and is worried that it will drift away, wrenched from Garth’s hands by the differences in acceleration between the cylinder and Garth. But there is no difference.

Potential Energy

Throughout James Garth’s trip through Trojan, he is reminded occasionally that in order to get back to the top of the North Pole shaft, he cannot lose any energy at the South Pole shaft. If he hits the South Pole cap with his feet, for example, he must shove off hard. He worries, too, about hitting the walls, as any small amount of friction might be enough to prevent him getting back up the other side at the North Pole.

Of course, it is not worst case scenario, but it is a bad case scenario, when this happens:

He grabbed the cylinder shifting his body again ready for the taut tug that might wrench the cylinder away. He wrapped his body around the cylinder and grit his teeth. He started to drop, but the cylinder wasn’t coming with him, so he gripped it harder. It was slipping slowly, the tether slipping through the rock cut, snagged on something on the other side. He worried he had to clip the end of the tether but something was different than planned. His swing was slowly extending out, as the tether played out, and he swung back and forth increasingly slower than the previous cadence of Princeton’s ‘Left, right—’ Suddenly, with a jerk, the tether stopped coming through the metal cut.
“Hang on Garth,” Princeton said. Garth was frantic. Somehow he knew if he dropped from this height, at the end of the full twenty five meters of tether, he wouldn’t make it, but he couldn’t remember why. Something was wrong with dropping from this height.

James Garth is frantic, because he knows his potential energy from twenty five meters below the Trojan surface is only just enough to get him back to–twenty five meters below the Trojan surface at the North Pole. And they can’t get him out at the North Pole from twenty five meters down in the pit.

Princeton searched the line and found the clip at the end snagged on the tripod.
She commanded her crew to pull Garth up to the top of the shaft.

Now that is quick thinking, or she planned for this.

“We can’t get him out,” they panicked at her order, and froze.

They aren’t as quick-thinking as Princeton. They don’t realize why she wants them to pull him up.

“Do it!” she screamed. They did it, not understanding why. Princeton told Garth to hold on. She knew he was hanging on, the cable was taut. The crew yanked him up to the top, up the twenty five meters that he had fallen before the tether snagged.
Garth’s shoulder where the cylinder had hit him screamed in pain, and he resisted the temptation to feel it with the other hand, to see if it was dislocated again. It felt the same, but he dare not let go of the cylinder. He swung back and forth under the surface of the South Pole of Trojan, the pain waning his strength, and the wall of the shaft scraping against his injured shoulder with each swing. Perspiration ran into his eyes, and moistened the crusting vomit, resurrecting the stench of fear and nausea.
Princeton pulled out a laser cutter for the cable, and pausing long enough to tell Garth he was about to drop, she cut the cable. The frayed cable disappeared into the surface and Garth was gone. 

Of course, there is still five meters to make up, the thickness of the crust up at the poles near the surface. The hole at the South pole was not big enough (they hadn’t enough time) to get Garth out, so they gave him an extra oxygen tank and sent him back. But the snag that almost cost twenty five meters of potential energy was now only five. And five meters, like ‘a miss is as good as a mile,’ might also be too much. Garth’s trajectory down the South Pole shaft is going to be exactly mirrored by his trajectory up the North Pole shaft, because his total energy, kinetic and potential, has to be the same.

Neat, eh?

Atmosphere in Trojan

I confess, for quite a long time I thought that when atmosphere inside Trojan reached something comparable to Earthside, that the Inner Sanctum would be full, and there would be concern that excessive atmosphere would be lost up the North and South Pole shafts and that it would be necessary to support an atmosphere on the surface.

With that in mind, falling down the pit would be limited to terminal velocity because of the buoyancy effects.

No, I don’t think so anymore. Remember, Trojan revolves once every 67 minutes, so there is ‘gravity’ on the inner surface, well, acceleration anyway.

Consider one molecule. This argument appears in Hollow Moon of Jupiter, Appendix A:

“Byron, listen,” the undergraduate pleaded.
“Huh?” Byron said, re-establishing eye contact with the student.
“Thought experiment: introduce one molecule into Trojan, anywhere. Say oxygen. Eventually it hits a wall, picks up rotational energy and angular momentum which plasters it up against the inner surface. If not right on the equator, it slides out to the equator, where it continues to interact with the spinning wall.”
The TA nodded equivocally, raising his eyebrows in a gesture that said he understood and agreed.
“Now add more molecules,” the student said. “Keep adding them; they either pick up rotational angular momentum from the under surface of Trojan, and slide down to the equator, or they get shoved along by the molecules already there, already spinning.”
The TA frowned. “You can’t expect much buildup. The layers of molecules would start slipping back, and each successive layer would rotate more slowly.”
The undergraduate locked eyes with the TA. “Like Earth?” he asked.
The TA’s eyes darted down to the left, then around the room, then back to the undergraduate.
“There isn’t that much slipping on earth,” he said, quietly. “The whole atmosphere moves around with the Earth. If the atmosphere didn’t move, and the earth spun underneath it, there’d be a hell of a wind—1,000 miles an hour.”
The undergraduate sat down on a stool in front of his TA, while the party became a little more raucous in the background. The co-ed had stepped away from the TA’s view.
“Earth’s atmosphere moves with the earth; the frictional forces between layers of atmosphere are sufficient to force it so, and the same would happen in Trojan. Trojan atmosphere would accumulate along the equator, spinning with, and within, the undersurface of the hollow moon.” The undergraduate’s speech was gaining speed. “The resulting pressure buildup would be due to the apparent weight of the atmosphere spinning with Trojan, and when it got to one atmosphere right at the undersurface, it would be a strip a couple of hundred kilometers wide and maybe ten kilometers high before molecules became so rarified as to be insignificant.”
“The numbers that made their way to the centre of the sphere, let alone up one of the shafts, would be tiny in comparison to the total atmosphere contained,” the TA said.
“Damn near zero, I surmise,” the undergraduate added.
The TA shrugged. “It’s like, what’s the concentration of atmosphere 4,000 kilometers above the Earth? Isn’t that what we could expect in the centre of Trojan?”
“A molecule per cubic foot?” the student asked.
The TA had slowly lost, and then even more slowly, regained his smile. He started nodding his head. “Neat. Very neat.”

I agree with the undergraduate. The atmosphere would smear itself along the equator, spread out above and below (in terms of latitude) and Earthsider type atmospheric pressures to a livable degree would exist in a range of about 200 kilometers on either side. This means that the rest of the Inner Sanctum would be relatively low level vacuum. Like outer space. I am unsure as to whether atmosphere at the center would be exactly like 4,000 kilometers above the Earth, but I am quite sure it would be unbreathable, and unable to provide buoyancy, or air friction. It would be pretty close to a vacuum, and I wish I could figure out what it would be. It also means there would be very little loss out either North or South Pole shafts.

Light Inside Trojan

It is difficult to imagine light on the surface of Trojan, being five times the distance from the sun, compared to Earth. Clearly the sun would appear smaller, and the photons from the sun would be 1/25 the intensity, simply because of the distance. Jupiter is 5 Astronomical Units away from the Sun, to Earth’s one.

From the Earth, the angular diameter of the Sun is about 30 arc minutes (about half a degree). From Jupiter, it is about 6 arc minutes, one fifth that of the Sun from Earth. The angular diameter of the Carousel as seen from Trojan inner surface is 2.5 arc minutes, just within our resolution, but it’s precursor in Nefra Contact, the Central Structure, is only about 0.4 arc minutes. You could see it with good binoculars, but that’s about it.

Close as it is to being a star, Jupiter is not quite big enough to generate its own radiation.

Is the sky totally dark?

No, clearly not. Consider being far from a light generating city on a night when the moon is on the other side of the Earth. Dark, sure. Black, no. Star light does something. Even 1/25 of the sun is a fair bit.

Light inside the hollow moon is difficult to imagine, and here I have invoked Nefra know-how. Quartz fibers, like waveguides, might generate considerable light, especially when realizing that what is captured on the outside is concentrated by a ratio of 25/16 when one considers the surface area of Trojan on its outer surface (~5,000 kilometer radius), compared to the under-surface (4,000 kilometer).

As indicated in the books, however, ambient lighting is increased by industrial and domestic lighting, and shutters of windows being controlled by timers to simulate a twenty four hour day, timed with UNSA Headquarters at New York, Earthside.

Periodically, the light penetrating the crust via quartz fibers will be largely covered by the Great Ocean. The Ocean is full of ice in Nefra Contact, water in Hollow Moon, where it provides water for the two towns via the Syrin River (Nefra Attack, not yet published). The water of the Great Ocean is stained with the metallic surface of Trojan, the crust dust, producing a harmless inky darkness, but covering the light source for 5 to 7 minutes every 67 minutes, the Trojan day. The Trojans call this ‘On Eclipse’, and not too many remember what this means (is it English, or French?).

A longer period of darkness occurs once a week (Earthside week) as the orbit of Trojan around Jupiter takes it behind the shadow of Jupiter for something over three hours. This is referred to as J’Eclipse, for Jupiter Eclipse, although this phrase is more clearly recognized as potentially French. Some deep thinkers wonder if James Garth had named these originally (Garth is Canadian and knows both official languages well enough), but the history of it’s naming has been lost.

But take this passage, mid-way through Chapter Fifteen, The Rescue, from Hollow Moon of Jupiter:

“…But once a week—essentially a Trojan week, but close to an Earthside week—at varying times of the usual Trojan day, the lights go out. And for three to four hours, a number which also varies slightly, about 227 minutes, the place goes almost dark, but for the street lights, houses and industrial buildings. Many artificial lights are programmed to dim down or go out during j’eclipse, to add to the…romantic effect.”…
“Though not many of us can manage that,” the Ensign said. There was a lascivious smirk to his voice, which in the EVGs, no one could see, but everyone could hear. The co-pilot chuckled again, and Crinshaw heard Garth sigh.
“What?” Crinshaw said. “I missed something.”
Garth snorted softly. “The Ensign is referring obliquely to the other colloquial meaning of j’eclipse.”
“Ah, la français,” the Ensign sighed. Garth stiffened. Crinshaw furrowed his brow, but no one could see.
“Traditionally, j’eclipse is a time for lovers…”

In Nefra Attack, (not yet published) the light of the Sun dances through the shallow waters of the Syrin River, already cleaned of much of the metal staining by water treatment plants at the Farm Project Proximal, and is enhanced by external lighting and fine refraction grids engraved into the polished metal surface of the Senator’s lavish backyard. The subsequent marvelous display of rainbow light shows every hour (minor), and the fantastic displays once a week during J’Eclipse (major, at beginning and end), always attract Frankie Keller, the Senator’s daughter, to sit on the balcony inside the mansion with a view of the back, with her Margarita, and enjoy the show, unfortunately to her peril (sorry, you gotta wait of it).

Well, that’s enough for now. There are many other fascinating features of this fanciful Hollow Moon, some I am sure, I have thought out incorrectly, and some I have not yet thought of at all. I guess I’ll just keep writing, living in a world of Science Fiction. But I invite you to help!

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