Unusual Faster-Than-Speed-of-Light Situation

A physics student attaches a laser pen to an ultra-fast robotic arm, pointing it at the moon. Consider a spherical moon, in which the laser is visible as a dot. A single rapid flick of the arm moves the dot from point $$A$$ to point $$B$$ in a 120 degree arc through the lunar surface. Calculate the maximum interval of time $$\Delta t_{\text{max}}$$, in milliseconds, in which the movement of the arm could take place so that the laser dot moves twice as fast as the speed of light $$c$$ in the lunar surface.

Details and assumptions

1. Lunar radius is $$= 1737.1 \text{ km}$$.
2. Speed of light is $$c = 3 \times 10^{5} \text{ km/s}$$.
3. Take $$\pi = 3.14$$.
4. The result is a single digit integer
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