If light speed is always C how do rangefinders work?

[Robonewt]

Range finders can measure distances up to 5km to within an accuracy of +-10cm if reflectors are used. http://www.onsitetools.com/measuring/laser/surveying/detail/5000/

 

 

If a system were set up to measure a known distance of 5km in a north south direction somewhere using a reflector. How does the laser return to the emitter?

 

The sun and the earth with it, is travelling around the galaxy at 250,000m/s.

http://www.enchantedlearning.com/subjects/astronomy/planets/earth/Speeds.shtml

Light travels at approx 300,000,000m/s

 

Light takes 1.667e-5 seconds to travel 5000m (t=d/v, t=5000/300,000,000)

The Earth will have travelled 4.2m in that time. (d=vt, d=250,000x1.667e-5)

 

For the laser to return to the emitter it must travel 10km, which works out at 8.4m in total that the earth will have moved.

 

If you assume the laser does not carry the momentum of the emitter, and

 

If you did the experiment when the Earth was in front of the sun on its orbit, then the laser would likely hit the ground before it got back.

 

If you did it when the Earth was behind the Sun in its orbit the light would likely shoot past 8m above the emitter.

 

With the Earth running parallel the laser would pass to the left or right.

 

Surely the only way the Laser can work over such distances is that it carries the momentum of the emitter, but this could mean a variable speed of light.

[Sisyphus]

No, the Earth is not moving at 250,000m/s, because there is no such thing as absolute motion or absolute rest. There is only relative velocity, because there are no privileged reference frames. Because of this, the speed of light is constant in every reference frame. The same beam will appear to be "carrying the momentum" of whoever is observing it. Obviously, then, two observers in two different reference frames of the same event will disagree considerably about what is happening...

[swansont]

Or, putting the first phrase of Sisyphus' post another way, the laser is also travelling at 250,000m/s around the galaxy. What matters is motion of the laser with respect to the earth, and there is none. And there are no priveleged frames, etc. etc.

 

Oh, and the momentum of light is E/c. A moving source or target will see an energy (or frequency or wavelength) shift, rather than a speed change.

[Robonewt]

Yes on Earth everything is in a closed system, everything is spinning around the Centre of the Earth, Which is spinning around the centre of the Solar system, which is spinning around the Centre of the galaxy. And because everything is travelling at the same speed to start with, you can ignore these speeds in our calculations on Earth.

 

That makes sense, and if light follows the same rules as everything else, that is fine. In the closed system of Earth, the speed of light will also be measured at C. Also because it is a closed system, it can be said that the mechanism that emits light always emits it at C relative to the Emitter. However, anyone else looking in from outside, would have to consider the relative speed of the emitter to themselves.

 

The problem I have is where it says that light is measured as C regardless of the frame of reference. By saying that you are taking it outside all frames of reference and as such would have to include somehow all the relative speeds.

 

If someone was standing at the centre of the galaxy watching the rangefinder at work, then the relative speeds of the solar system round themselves, the Earth round the sun and the spin of the Earth come into play. They would measure a different speed of C that would vary depending on the time of the experiment, but they could calculate the same speed of C as us in the closed system. Relative to them, the light is not travelling at C. However using what they know about the speeds of the various components they could calculate the value of C relative to the emitter.

 

Also a speed change could cause an apparent, frequency or wavelength shift, as you are measuring the signal end on, but I suspect that statement will be knocked down by saying the maths prove otherwise.

[Klaynos]

Can special relativity be applied here? As the earth is spinning, isn't that an accelerating frame? (I'm not really sure on this)

[swansont]

Can special relativity be applied here? As the earth is spinning, isn't that an accelerating frame? (I'm not really sure on this)

 

It is, and that causes problems if you aren't careful. You get the Sagnac effect, which makes it look like the light is travelling at c+v or c-v for motion with or against the rotation, if you are analyzing things in the accelerating frame. Which tells you you aren't in an inertial frame, where you should get c. But if you account for this, and do your analysis in an inertial frame, you should be fine.

[swansont]

The problem I have is where it says that light is measured as C regardless of the frame of reference. By saying that you are taking it outside all frames of reference and as such would have to include somehow all the relative speeds.

 

But that's not what "it" says. The speed of light is constant in all inertial frames.