Relativity Problem: Sweep Laser for v > c on Moon's Surface

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To achieve a light spot speed greater than the speed of light (v > c) on the Moon's surface, one must calculate the minimum angular speed using the formula V = omega x R, where R is the distance to the Moon (approximately 380,000 km). The challenge lies in the perception of distance due to the vast separation, which complicates accurate measurements. Additionally, transmitting information using a laser spot is not feasible because the spot's movement does not convey data instantaneously; it cannot be used for communication between research bases on the Moon. The limitations of light speed and the nature of angular motion prevent effective communication through this method. Thus, while theoretically interesting, practical application for information transfer remains unachievable.
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Homework Statement



You point a laser flahlight to the Moon, producing a spot of light on the moons surface. At what minimum angular speed must you sweep the laser in order for the light spot to streak across the moons surface with speed v > c? Why can't you transmit information between research bases on the Moon with the flying spot?

Homework Equations





The Attempt at a Solution



The problem is utilizing the correct length. I measure it smaller then it is, since I am so far away. but is there a way to calculate that?
 
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V = omega x R

V = c
R = about 380,000 km
omega = angular velocity in radians/s

For the second part think how you might use the laser on Earth to allow different moon bases to communicate.
 

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