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