When the stone finally approached the spring-shot, Roi thought it might collide with it, but her aim hadn’t been that perfect. It was close, though. The stone passed less than half its width from the tube before continuing on around the same closed loop as before.
“I can’t believe I missed this,” Zak said. “A new periodic motion! Congratulations!”
Roi said, “What are we seeing, exactly? Is this showing us the Splinter rotating?”
“What we’re seeing is a stone in orbit, moving back and forth between its nearest and furthest points from the Hub,” Zak replied. “If we try to explain that from a Splinter’s eye-view, the motion will depend on the strength of the garm-sard weight, as well as the speed of the Splinter’s rotation. Once I would have said that those two things should combine in a very simple way, but now I’m not so sure. The two and a quarter has taught me to be more cautious.”
Roi launched another stone directly sardwards, this one faster than the first. The loop it followed was larger, but the shape was the same—about three times as long as it was wide—and the faster stone completed each circuit in the same time as its slower companion. These stones were spending half their time sard of the Null Line, moving more slowly than the Splinter, and the other half garm of the Null Line, moving faster, so over time they were keeping pace both with the Splinter and with each other. Surely that meant that each cycle they completed marked the time for all three to complete an orbit around the Hub? And surely the Splinter’s rotation around its axis shared the same period, too, as a matter of simple geometry?
Zak said, “I know what we should do.” He found an empty tube, attached it to the Null Line aligned shomal- junub, then placed a stone in its mouth and let it begin its slow fall. Now they could compare the two kinds of motion directly, without having to worry about the accuracy of their counts to time the periods.
It soon became obvious that the periods were not the same: the looping stones were taking far longer to complete each cycle than the stone falling shomal and then junub. For a while, Roi wondered if the slower cycle might be exactly twice as long as the faster one—and if some simple aspect of the geometry that she’d neglected could make sense of this—but that hope proved misplaced. The shomal-junub stone completed seventeen cycles while the looping stones completed nine. There was nothing simple about that.
Zak seemed forlorn at first, but then he proclaimed, “There’s something encouraging about the way these numbers demolish half of my assumptions, yet the whole notion of orbits seems to survive. Watching these stones, can you honestly tell me that you don’t believe they’re going around the Hub?”
Roi said, “The idea still makes sense, but we’re missing something.”
Zak regarded the shomal-junub stone. “If orbits still make sense at all, then this stone tells us how much time passes for something orbiting at a small angle to the Splinter’s orbit to come back to the same height above us each time. The stone doesn’t go wandering off along the Null Line, so the periods of the two orbits must be the same. But what if the place where the orbits are farthest apart isn’t fixed? What if that point moves around? Then this need not be telling us how long an orbit actually takes.”
He moved to the looping stones. “And when you deform an orbit so it’s no longer circular, what if the point of closest approach to the Hub isn’t fixed either? That point, too, might wander around.”
Roi struggled to picture what he was describing. “So these other orbits wouldn’t close up? The Splinter would follow a perfect circle, but these stones would be weaving up and down, or back and forth around that circle, never quite repeating their paths?”
“Yes.”
Roi was dismayed. “If the things we thought were landmarks can’t be trusted to stay still, how can we ever decide how long it takes for the Splinter to complete an orbit?”
Zak said, “Good question.”
Neither of them had the answer to it, so they set about calculating what Roi’s looping stones actually did tell them. They worked side by side until the end of the shift, slept, then worked through two more shifts.
Finally, they had templates describing the relationship between three things: the strength of the garm-sard weight, the period of the Splinter’s rotation, and the period of the looping stones. These calculations made no assumptions at all about the existence of “orbits around the Hub”; they just followed the effects of the weights directly—though they did rely on a correct understanding of how spin contributed to weight.
When Zak inserted the numbers, the template told them that the Splinter was rotating with a period about one and a quarter times the shomal-junub cycle.
If you believed in orbits, this meant that for a stone in a tilted orbit to return to its highest elevation was the fastest thing. For the Splinter to rotate around its axis took a little longer. And for a stone in an eccentric orbit to return to its greatest distance from the Hub took longer still.
Three phenomena, three different times.
“Where has all the simplicity gone?” Zak lamented.
Curiously, if he fed his original assumptions into the templates—if the shomal-junub weight was equal to the hidden rarb-sharq weight that was balanced by the spin, and if the garm-sard weight was, in total, three times as much—then all three periods would have been identical. The number three really would have made things very simple.
Roi took a break from the Null Chamber, and traveled a short way into the garmside to give herself some weight again, lest she lose too much strength. Even as she headed out of the Calm into the sights and sounds of ordinary life, she couldn’t stop thinking about motion and orbits. At the end of each shift, when her mind had once filled with the images of weeds, now she saw stones, bouncing and looping and swerving in front of her. When she woke, her first thought was always of finding a new way to check Zak’s conclusions. Their calculations deriving the Splinter’s spin from the looping stones could be flawed. Or the weight measurements they had fed into the templates could be wrong.
Zak’s simple experiment, when he’d launched a stone along the Null Line, had been compelling: it had made it obvious that the Splinter was turning while the stone was in flight. There had to be a way to measure the Splinter’s rotation directly using that effect, without allowing the complications of the garm-sard weight to intrude. If you could keep the stone moving somehow—without ever letting it go too far from the Null Line—its path would act as a reference against which the turning of the Splinter could be judged.
How could you rein it in, though, without stopping it completely?
When Roi found the answer, she turned around and headed straight back to the Null Chamber. Zak wasn’t there when she arrived, but she felt no hesitation about helping herself to his stores of material. They were a work team, now. These things were their common tools, not a lone eccentric’s hoard.
Zak arrived just as she was putting the finishing touches to her apparatus, trial and error having led to some changes in the original design. Two equally heavy stones were glued firmly to the ends of a small bar. The bar was free to pivot around its center, where it was threaded by a stiff metal wire, which was bent around into a flat rectangular supporting frame large enough for the bar to turn continuously without obstruction. Another pivot, opposite the bar, attached the frame to the wire of the Null Line; this pivot left the frame free to rotate around the shomal-junub axis.
After they’d exchanged greetings, Zak watched in silence as Roi greased the pivots, marked the initial alignment of the frame on a card fixed to the wire above it, then gave the bar a flick to set it spinning.
An earlier version—with the bar spinning around one of its ends, and a single stone at the other—had been unbalanced, shuddering mercilessly, causing the frame to slip back and forth. This design seemed to have fixed that problem. All Roi could do now was wait.
Slowly but unmistakably, the plane of the spinning bar turned. Or, stayed fixed while everything in the chamber, everything in the Splinter, wheeled around it.
Zak said simply, “Who can doubt it now?”
There was no need to measure the speed of the stones. There were no elaborate calculations to perform. One rotation of the frame corresponded to one rotation of the Splinter, if they understood anything at all.
They set up a shomal-junub stone a short distance away, to compare the motions. After a while, no doubt remained that the period of this new phenomenon agreed with their earlier calculations, based on the more complex motion of the looping stones. The plane of the spinning bar took
Roi didn’t know what to feel. She was relieved to see two lines of evidence converging on the same answer for a change, but she’d actually been hoping that this experiment might yield a different result, one that removed some of the complexity that had begun to infest the theory of orbits.
