[Vertigo]

Ah I've found the passage! It was another SF Masterworks story: Babel 17 from Samuel Delaney. Here it is, a bit long I'm afraid even though I've cut some incidental stuff out:

"A watch," saidRydra, "and a—bag of marbles!"
"Huh?" asked Calli.
"Mar-bles?" articulated Mollya wonderingly. "Marbles?"
"One of the kids in the platoon must have brought 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.
" 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."

It's possibly a bit complicated for even older teenagers to have worked out but then on such a ship astrophysics is certainly something they would be studying. Also since the book was written in the 60s I'm not sure if the technique is a valid one.