Morning n' Morning n' Morning!

You are in a jet plane flying along the Equator, wearing a watch that uses GPS location to update the time.

Right now, it's 8am in the morning.
One hour later, it's still 8am in the morning.
Five hours later, it's still 8am in the morning!

There is a maximum, and a minimum speed at which this feat can be accomplished. Find vmax+vmin2\frac{v_\text{max} + v_\text{min}}{2} in m/s, of course!

Assumptions and Details

  • The Earth is a perfect sphere with radius 6370 km
  • Your plane has a constant ground speed.

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