Curved space 1

Classical Mechanics Level pending

A space station orbits the Earth on a circular orbit with a period of $$T=120$$ minute. The station is stabilized in such a way that its main window always faces the Earth and otherwise the space craft is not rotating. All jets are off.

We set up a local system of reference so that the velocity vector of the space craft is parallel to the $$x$$axis (forward/backward), the vector pointing from the center of the Earth to the space craft is parallel to the $$z$$axis (up/down) and the $$y$$ axis (left/right) is perpendicular to these two. The origin of the system of reference is in the center of the space station.

An astronaut carefully places two very small steel balls $$1.0m$$ to the left and $$1.0m$$ to the right of the center ( $$x_1=0.0m$$, $$y_1=1.0m$$, $$z_1=0.0m$$ and the $$x_2=0.0m$$, $$y_2=-1.0m$$, $$z_2=0.0m$$ ) so that their velocity relative to the spacecraft is zero. How far will the balls be from each other 30 minutes later? Give your answer in meters to one decimal space.

See variations on this problem here and here and here .

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