Satellites in orbit

Two identical satellites \(A\) and \(B\) are launched in equatorial circular orbits around Earth with the same period of revolution of 4.8 hours. Satellite \(A\) rotates west to east (with Earth's rotation) while satellite \(B\) rotates east to west (against Earth's rotation).

On a particular day, both satellites were seen directly overhead by an observer standing at point \(P\) on Earth’s equator. How long (in hours) will it be until both satellites are seen directly overhead again from the same point \(P?\)

Details and Assumptions:

  • The orbits are located on nearly the same circle, with just enough separation to avoid collision.

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