Question 83
A Geostationary Earth Orbit is situated directly above the equator and has a period equal to the Earth's rotational period. It is at the precise distance of $22,236$ miles above the Earth that a satellite can maintain an orbit with a period of rotation around the Earth exactly equal to $24$ hours. Because the satellites revolve at the same rotational speed of the Earth, they appear stationary from the Earth surface. That is why most station antennas (satellite dishes) do not need to move once they have been properly aimed at a target satellite in the sky. In an international project, a total of ten stations were equally spaced on this orbit (at the precise distance of $22,236$ miles above the equator). Given that the radius of the Earth is $3960$ miles, find the exact straight distance between two neighboring stations. Write your answer in the form $a+b \sqrt{c}$, where $a, b, c$ are integers and $c\gt 0$ is square-free.