Can I read about this? Please show me. I am not trying to achieve anything in a thought experiment. The next step may be more interesting. Can we agree on the results?
I wouldn’t have asked the question if I knew my first thought experiment was actually done in real life! What were the results? Did it match my guess?
Time of flight has mattered for some systems. I remember when LAGEOS was launched, and the Sky and Telescope article (I’m pretty sure that was where I read it) noted that the retro-reflectors were ground with a very slightly off normal angle to account for the velocity of the satellite. But it is orbiting a few orders of magnitude closer than the moon.
Sadly a lot of the reference links for the satellite are dead.
There was a link earlier:
Sorry I still cannot find any reference to a small dot, or the location of that dot. Or even the location of a large dot. Or how it has returned to a different location. That is my thought experiment.
Sure the TOF to the moon matters in mine too. During the time the signal is going to the moon the earth rotates 1100m. A longer time, more distance rotated. But the exact time does not matter. I’m not trying to measure the precise velocity, neither of light, nor the rotation. Let’s just agree the dot comes back roughly 1km away?
I don’t see your point. The corner cubes on the moon measure on the order of a meter across. one meter out of a hundred miles is so small that the intensity is going to look uniform across it, and for many times the size of your retroreflector array. In short, you won’t be able to tell how far off perfect reflection you are, and where the center of your spot is. Maybe you could tell with a network of arrays, measuring the intensity across the bunch and interpolating to find the center. But you’re still going to have a result “fuzzed out” by the noise.
100 miles is about the right ballpark for a back-of-the-envelope estimate. a milliradian is a typical far-field angle, and the moon is about 240,000 miles away, so a ballpark spot size is 240 miles.
You decrease the far-field angle by increasing the size of the beam waist, so ironically you can make the far-field spot larger by increasing the size of the near-field spot.
Can we just pretend it works? I agree it would not easily. I promise my next thought experiment on here will be one that we could actually do in real life.
If you want to ‘pretend’, could you detail what aspects of reality should be followed (some aspects of reflectivity, apparently, but not others?) and which can be ignored?
It’s possible that selectively ignoring certain physical laws or effects can provide additional insight into the way things work, but those should be laid out as clearly as possible, which has not been done here, at least by my reading.
I think the OP is doing a thought experiment so reality need not apply.
If I can rewrite it: you send a proton from the equator on a straight line to a lunar reflector. The proton is reflected back to Earth. Where would the proton land on the Earth? I’m assuming a range based on the Moon’s distance from the Earth and orbital speed plus the Earth’s rotational speed. But to the point of the OP, it does not return to the spot where it was generated.
I also think that’s what the OP is stating, which seems obviously true, but not that insightful, right? The Earth is spinning and light isn’t infinitely fast, so obviously, it will come back at a different point if you do this at the equator.
Wonderful job Thanks! I was trying to make it a little more Real Life. Yes, that’s exactly what I meant to say…
Rittersport, I have more. This experiment is obvious but needed for the next. The reason I made it more Real Life, is because the next story could be Real Life. The above experiment is not so obvious when you consider that the earth is an inertial frame of reference, and the moon is not part of it.
It requires a second level of thinking because we are told that those reflectors return light to where it originated and street signs work while we are driving so for some people the idea that light reflects back along its path despite moving and not back to my current position may not be obvious.
When will this shoe drop?
That’s true enough. I guess is seems obvious to people who know that light has a specific speed (in a vacuum) and that the Earth is rotating.
Heh. It’s cute that you mention the street signs. This is something I’ve worked on in the patent world. Most street signs aren’t perfect corner reflectors, because if they were, they’d reflect the light back to the headlights of your car - not to the driver’s eyes. Manufacturers have spent years coming up with different skewed and tilted designs to tailor the reflection to adjust for this.
Wow really Cool! Thanks for telling me. Now I’m off on another tangent Googling…
Not necessarily. I’m on a merry-go-round and let go of a ball and it does not go straight out from me but follows my rotation so photon’s would too, right?
I know that
a) the ball does not follow my path but follows the tangent line from the point of release.
b) photons are not balls
But I could see where someone would believe balls on merry-go-rounds is an analog to light beamed to the Moon and back
Actually to where your headlights were but considering the short distance and the speed of light, close enough for government sign-building work.
It’s not always easy for people to compile a variety of factors that may or may not impact something outside of the normal human experience. The reflector cubes on the moon don’t work solely because the beam is reflected back parallel to its path, but because the beam is reflected back, AND the beam spreads wide enough that you can still detect it despite moving 1km away from your origin.
Just a non-optical note – shifts in the position of a straight line sent to the moon at the speed of light and reflected back to the earth will be subject not only to the effect of the earth’s rotation, but also to a host of other effects, including other things affecting the motion of the earth, and also to lunar libration:
I’ll point out that, even if the earth stayed perfectly still and the motion of the moon was the only factor, you’d still see a change in the position of your returning light spot (assuming a magical system in which the beam had absolutely no spread, but remained a tiny dot), because light reflected by a corner cube will be offset by twice the distance between the original beam and the apex of the corner cube. So if your corner cube moves relative to the incoming beam, your reflected spot moves by twice that distance.
I used that fact in designing a sensitive test for alignment of an instrument (located here on earth, so that the laser beam didn’t spread out very much, and you could see any positional shift).