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Curious about gravitational sluing detail

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Let's say a big rock is headed toward a small moon, impelled only by existing momentum and gravitational pull. The rock is not rotating or tumbling at all, leastwise not in relation to the local time/space norm. The rock is sped up by the moon's gravity and it falls ever faster and faster. But the rock just misses crashing into the planetoid, which BTW has no atmosphere, and the diving rock gets slued around the much bigger entity and careens (slingshots) off on a greatly altered trajectory. My only question is, wouldn't such a momentous encounter tend to impart some spinning/tumbling feature to the runaway rock? (And can you prove it?)

Many thanks.

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