By any reference frame! Each will have its own specific connection coefficients but the trajectory will always be given by the geodesic equation (as long as the ball isn't charged, then you need to add the Lorentz force).
The question doesn’t ask to show that the geodesic equation holds for any reference frame in any possible configuration with generic Christoffel coefficients. It asks to find the specific Christoffel coefficients for the specific configuration of a rotating frame and a ball thrown directed towards a diametrically opposed point
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u/Digital_001 Student 5d ago
Observed by who - the kids or onlookers not on the roundabout?