along a bag of marbles. Get it and meet me in G-center."
She jumped over the ruined skin of the bubble seat and leapt up the hatchway, turned off at the radial shaft seven, and launched down the cylindrical corridor toward the hollow spherical chamber of G-center. The calculated center of gravity of the ship, it was a chamber thirty feet in diameter in constant free fall where certain gravity-sensitive instruments took their readings. A moment later the three Navigators appeared through the diametric entrance- Ron held up a mesh bag of glass balls. "Lizzy asks you to try and get these back to her by tomorrow afternoon because she's been challenged by the kids in Drive and she wants to keep her championship."
"If this works she can probably have them back tonight."
"Work?" Mollya wanted to know. "Idea you?"
"I do. Only it's not really my idea."
"Whose is it, and what is it?" Ron asked.
"I suppose it belongs to somebody who speaks another language- What we've got to do is arrange the marbles around the wall of the room in a perfect sphere, and then sit back with the clock and keep tabs on the second hand."
"What for?" asked Calli.
"To see where they go and how long it takes them to get there."
"I don't get it," said Ron.
"Our orbit tends toward a great circle about the Earth, right? That means everything in the ship is also tending to orbit in a great circle, and, if left free of influence, will automatically seek out such a path."
"Right. So what?"
"Help me get these marbles in place," Rydra said. "These things have iron cores. Magnetize the walls, will you, to hold them in place, so they can all be released at once." Ron, confused, went to power the metal walls of the spherical chamber. "You still don't see? You're mathematicians, tell me about great circles."
Calli took a handful of marbles and started to space them—tiny click after click—over the wall. "A great circle is the largest circle you can cut through a sphere."
“The diameter of the great circle equals the diameter of the sphere," from Ron, as he came back from the power switch.
"The summation of the angles of intersection of any three great circles within one topologically contained shape approaches five hundred and forty degrees. The summation of the angles of N great circles approaches N times one hundred and eighty degrees." Mollya intoned the definitions, which she had begun memorizing in English with the help of a personafix that morning, with her musically inflected voice. “Marbles here, yes?"
"All over, yes. Even as you can space them, but they don't have to be exact. Tell me some more about the intersections."
"Well," said Ron, "on any given sphere all great circles intersect each other—or lie congruent."
Rydra laughed. "Just like that, hey? Are there any other circles on a sphere that have to intersect no matter how you maneuver them?"
"I think you can push around any other circles so that they're equidistant at all points and don't touch. All great circles have to have at least two points in common."
'Think about that for a minute and look at these marbles, all being pulled along great circles."
Mollya suddenly floated back from the wall with an expression of recognition and brought her hands together. She blurted something in Kiswahili, and Rydra laughed. "That's right," she said. To Ron's and Calli's bewilderment she translated: "They'll move toward each other and their paths'll intersect."
Calli's eyes widened. "That's right, at exactly a quarter of the way around our orbit, they should have flattened out to a circular plane."
"Lying along the plane of our orbit," Ron finished.
Mollya frowned and made a stretching motion with her hands. "Yeah," Ron said, "a distorted circular plane with a tail at each end, from which we can compute which way the earth lies."
"Clever, huh?" Rydra moved back into the corridor opening. "I figure we can do this once, then fire our rockets enough to blast us maybe seventy or eighty mites
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