A space station orbits the Earth on a circular orbit with a period of \(120\) minutes. 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 small steel balls 1.0 m forward and 1.0 m backward from the center of mass of the spacecraft (\(x_1=-1.0 \) m, \(x_2 =1.0\) m, \(y_1=y_2=0\) and \(z_1=z_2=0\) m), so that they are perfectly at rest relative to the space craft. He watches them floating in their "weightless" state. How far will the two balls be from each other 120 min later? Give your answer in meters, rounded to the nearest integer.

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