Velocity of laser light pt. on moon > c ?

In summary, the Earth moon distance is 3.8 * 10^8 meters and it takes 1.266 seconds for light to reach the moon. A laser pointed at the moon rotates at a speed of 10 radians/sec, covering an arc length distance of 3.8 * 10^5 meters on the moon. The velocity of the laser's point on the moon is 3.8 * 10^9 meters/sec, and it takes 1/10^4 seconds for the point to travel on the moon. However, it takes 1.266 seconds for the light to reach the moon, so the laser's point cannot exceed the speed of light. This is due to the time lag from Earth
  • #1
morrobay
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The Earth moon distance = 3.8 * 10^8 meters
Time for light to reach moon = 1.266 sec.
A laser at the origin on Earth pointed at moon rotates .001 radian
with angular speed w = 10 radians/sec.
The arc length distance described on moon ,s= (radians) (radius) =3.8*10^5 meters
The velocity of the point on the moon described by the change in direction of the laser=
v=(w)(radius) =3.8 *10^9 meters/sec
So the time it would take this point to travel on the moon = distance/rate = 1/10^4 sec as well as .001 radian/10 radians/sec at the origin, being the rotation of the laser.
Since the light takes 1.266 second to travel to moon then it does not seem possible for laser light point on moon to exceed c.
For example in this case it took 1/10^4 seconds for direction of laser point to describe the path on the moon but when the laser is in this final position after rotating .001 radian it will take the light 1.266 seconds to travel to moon.
To restate it seems that the actual velocity of the directed laser light point on the moon would not exceed c because of the time lag
from Earth to moon in light travel time .
 
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  • #2
Sure, it took the light 1.266 seconds to travel to the moon, but the light that hit the "right" edge of moon arrived just 1/10^4 seconds after the light that hit the "left" edge (assuming you swept the laser from left to right). The travel time to the moon has nothing to do with the speed of the laser "spot" across the moon.
 
  • #3
There is a fairly good discussion of this in the thread;

"Lighthouse paradox revisited"

It is three pages long, but most of the answers you seem to be looking for are on the first page.
 

1. What is the speed of light in a vacuum?

The speed of light in a vacuum is approximately 299,792,458 meters per second.

2. Can the speed of light be exceeded?

According to the theory of relativity, the speed of light is the ultimate speed limit in the universe. It cannot be exceeded by any object or particle.

3. How does the speed of light change in different mediums?

The speed of light changes when it passes through different mediums, such as air, water, or glass. This change is due to the interaction between light and the particles in the medium, and can range from slightly slower to significantly slower than the speed of light in a vacuum.

4. Why is the velocity of laser light on the moon greater than the speed of light?

The velocity of laser light on the moon appears to be greater than the speed of light because the distance between the Earth and the moon is constantly increasing due to the expansion of the universe. This creates the illusion of the laser light traveling faster than the speed of light, but it is actually just a result of the changing distance between the two objects.

5. Is it possible for an object to travel at the speed of light?

According to the theory of relativity, an object with mass would require an infinite amount of energy to reach the speed of light. Therefore, it is not possible for an object with mass to travel at the speed of light. However, massless particles, such as photons, can travel at the speed of light.

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