Incandescence

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.