A question about speed of light and sunrise time

[phinds]

Pardon while I climb off this dead horse and beat it one more time:

But, given the Earth's atmosphere's ability to refract the rays of the sun, even if the speed of light were infinite we would still see the sun slightly before it actually rises above the visible horizon.

Rob

I agree. Please stop beating this horse. It has suffered enough. RIP poor horse.

 

[rollcast]

This thread:

http://www.martaandreasen.com/wp-content/uploads/2011/08/flogging-dead-horse.jpg

 

[D H]

Pardon while I climb off this dead horse and beat it one more time:

Stop beating that horse! Your continued abuse of that poor, dead horse has nothing to do with the question at hand. Imagine that you are on the moon, or even better, an asteroid that is in more or less the same orbit about the sun as are the Earth and the moon.

The question at hand is whether the finite speed of light affects the time of sunrise or sunset. It was conjectured in the opening post that we would see sunrise eight minutes earlier were the speed of light infinite. That is incorrect. The OP was correct in that a finite speed of light does have an affect on when we see the sun rise. However the effect is in the opposite direction timewise and it is much smaller than eight minutes. An infinite speed of light would make sunrise later, not earlier, by about 1.36 seconds.

 

[sophiecentaur]

Can you explain your reasoning please? If the light beam is 'there all the time' then, afaics, the only effect would be due to the 'shadow' cast by the advancing horizon moving across the land 'just beyond' it. Any time delay/difference in the arrival of 'dawn' due to rotation would surely depend upon observer height?

 

[D H]

Can you explain your reasoning please?

I already did in post #34. Aberration of light.

The same phenomenon is ultimately responsible for the zodiacal light as seen in this photo (source: http://apod.nasa.gov/apod/ap090212.html):

The zodiacal light results from sunlight scattered by interplanetary dust that is most dense near the solar system's ecliptic plane. Aberration of light causes these small dust particles to spiral in toward the Sun via the Poynting-Robinson effect. Aberration of light also causes us to see sunrise a tiny bit earlier than we would see were the speed of light infinite.

 

[Rob D]

Stop beating that horse! Your continued abuse of that poor, dead horse has nothing to do with the question at hand. Imagine that you are on the moon, or even better, an asteroid that is in more or less the same orbit about the sun as are the Earth and the moon.

My thanks to D H for the wise counsel. Fact is, I'm relieved. It was starting to smell. I'm sure you caught at least a whiff.

Actually, I think I understand the problem and the solution. Think I'll just lay back and watch the thread play out. However, I also think I'll put the horse in the freezer. You just never know when I might need it.

Happy Sunrise,
Rob

 

[Vanadium 50]

Actually, in SR, you do not get aberration of light. In Newtonian physics with c = infinity, you also do not get aberration of light. If you want to go somewhere in between, taking pieces of both, you can get aberration. So the answer depends on exactly what is meant by changing the speed of light.

 

[D H]

Actually, in SR, you do not get aberration of light.

You do get aberration in relativity. Einstein derived it in his 1905 paper, "On the Electrodynamics of Moving Bodies." Relativistic aberration of course is not the same as classical aberration (that obtained via the Galilean transform but with a finite speed of light). Relativistic aberration does reduce to classical aberration for v<<c.

Note that I used relativistic aberration in post #34. Not that it would have made much of a difference. Classical aberration also yields a value of 1.36 seconds. The Sun's velocity relative to the Earth is about 0.0001 c, so there is very little difference between classical aberration and relativistic aberration in this case.

 

[ali297]

No. Sunrise is due to the rotation of the Earth, not due to the sun turning on and off.

Setting aside the strange question of "what would the world be like if the world weren't the way it was?"...think of this:

Regardless of whether any particular photons of light coming from the sun took 8 milliseconds, 8 minutes or 8 days to reach Earth, the photons making up the sun's rays are continuously streaming from the sun - essentially a solid line. The Earth turns and, when the spot where you are standing has a clear line of sight with the Sun, that's sunrise.

Nice answer.

 

[D H]

Nice answer.

Nice answer, but it is wrong. It fails to account for the Earth's orbital velocity about the Sun (or from the Earth's perspective, the Sun's orbital velocity about the Earth).

 

[phinds]

Nice answer, but it is wrong. It fails to account for the Earth's orbital velocity about the Sun (or from the Earth's perspective, the Sun's orbital velocity about the Earth).

Could you expand on that a bit? I'm not following why that has any effect on sunrise (well, OK, maybe a really tiny one)

Thanks.

 

[D H]

Multiple posters in this thread have said that the finite speed of light has no effect whatsoever on when we see the sun rise. That the Earth is orbiting the Sun does have a tiny effect on when we see the sun rise thanks to the aberration of light. The effect is small because the Earth's orbital velocity is a tiny fraction of the speed of light (about 1/10,000) and because the Earth's rotation rate is rather small (1 rev per day). Just because the effect is tiny doesn't mean it is nonexistent.

Suppose you are in a very advanced spaceship. You start at rest with respect to the Earth. As the spaceship accelerates, the stars to the left and right will appear to move in front of you. Get very close to c and almost all of the stars will appear to be in front of you. This includes even those that appeared to be almost directly behind you when you started.

 

[phinds]

Multiple posters in this thread have said that the finite speed of light has no effect whatsoever on when we see the sun rise. That the Earth is orbiting the Sun does have a tiny effect on when we see the sun rise thanks to the aberration of light. The effect is small because the Earth's orbital velocity is a tiny fraction of the speed of light (about 1/10,000) and because the Earth's rotation rate is rather small (1 rev per day). Just because the effect is tiny doesn't mean it is nonexistent.

Sounds reasonable.

Suppose you are in a very advanced spaceship. You start at rest with respect to the Earth. As the spaceship accelerates, the stars to the left and right will appear to move in front of you. Get very close to c and almost all of the stars will appear to be in front of you. This includes even those that appeared to be almost directly behind you when you started.

Yeah, I had a hard time with that when I first read it some years ago, but I finally got my head around it. I think. Maybe.

 

[lorrad]

No. Sunrise is due to the rotation of the Earth, not due to the sun turning on and off.

right answer and I read all of this

 

[SecularSanity]

Solar annual aberration applies in this case, does it not?

A special case of annual aberration is the nearly constant deflection of the Sun from its true position by κ towards the west (as viewed from Earth), opposite to the apparent motion of the Sun along the ecliptic (which is from west to east, as seen from Earth). The deflection thus makes the Sun appear to be behind (or retarded) from its actual position on the ecliptic by a position or angle κ. This constant deflection is often explained as due to the motion of the Earth during the 8.3 minutes that it takes light to travel from the Sun to Earth. This is a valid explanation provided it is given in the Earth's reference frame (where it becomes purely a light-time correction for the position of the eastward-moving Sun as seen from a stationary Earth), whereas in the Sun's reference frame the same phenomenon must be described as aberration of light when seen by the westward-moving Earth, which involves having Earth's telescopes pointed "forward" (westward, in a direction toward the Earth's motion relative to the Sun) by a slight amount.

Since this is the same physical phenomenon, simply described from two different reference frames, it is not a coincidence that the angle of annual aberration of the Sun is equal to the path swept by the Sun along the ecliptic, in the time it takes for light to travel from it to the Earth (8.316746 minutes divided by one sidereal year (365.25636 days) is 20.49265", very nearly κ). Similarly, one could explain the Sun's apparent motion over the background of fixed stars as a (very large) parallax effect.

http://en.wikipedia.org/wiki/Aberration_of_light#Solar_annual_aberration

 

[D H]

No. Sunrise is due to the rotation of the Earth, not due to the sun turning on and off.

right answer and I read all of this

That is the wrong answer. Nobody other than DaveC said anything about the sun turning on and off. If you had "read all of this" you would have seen why DaveC's answer is the wrong answer.Going back to DaveC's post,

Regardless of whether any particular photons of light coming from the sun took 8 milliseconds, 8 minutes or 8 days to reach Earth, the photons making up the sun's rays are continuously streaming from the sun - essentially a solid line. The Earth turns and, when the spot where you are standing has a clear line of sight with the Sun, that's sunrise.

It is that last sentence that is erroneous. Here is a corrected version: The Earth turns and, when the spot where you are standing has a clear line of sight with where the Sun was 8.3 minutes ago, that's sunrise.

Due to the finite speed of light we don't see what is. We see what was. Those "what is" and "what was" positions of the Sun would coincide if either the speed of light was infinite or if the Earth and Sun were not moving with respect to one another. However, the speed of light is finite, and the Earth and Sun are moving with respect to one another. There is a slight angular deviation, about 20.5 arcseconds, between those "what is" and "what was" positions of the Sun.

This angular offset, aka the solar annual aberration, makes sunrise occur a tiny bit earlier (note: not later) than it would if the speed of light was infinite.

 

[phinds]

That is the wrong answer. Nobody other than DaveC said anything about the sun turning on and off. If you had "read all of this" you would have seen why DaveC's answer is the wrong answer.


Going back to DaveC's post,

It is that last sentence that is erroneous. Here is a corrected version: The Earth turns and, when the spot where you are standing has a clear line of sight with where the Sun was 8.3 minutes ago, that's sunrise.

Due to the finite speed of light we don't see what is. We see what was. Those "what is" and "what was" positions of the Sun would coincide if either the speed of light was infinite or if the Earth and Sun were not moving with respect to one another. However, the speed of light is finite, and the Earth and Sun are moving with respect to one another. There is a slight angular deviation, about 20.5 arcseconds, between those "what is" and "what was" positions of the Sun.

This angular offset, aka the solar annual aberration, makes sunrise occur a tiny bit earlier (note: not later) than it would if the speed of light was infinite.

I agree that your statement is correct but ONLY if the speed of light is what it is. Dave's statement, unlike yours, is correct REGARDLESS of whether the speed of light is c or infinite. Your statement does not answer the OPs question.

 

[DaveC426913]

Those "what is" and "what was" positions of the Sun would coincide if either the speed of light was infinite or if the Earth and Sun were not moving with respect to one another. However, the speed of light is finite, and the Earth and Sun are moving with respect to one another. There is a slight angular deviation, about 20.5 arcseconds, between those "what is" and "what was" positions of the Sun.

For my own edification, this angular deviation is due to the Earth's movement in its orbit around the sun, correct? In 8 minutes the Earth has moved almost 9,000 miles around its orbit, (this is unrelated to its own axial rotation).

I accept this will have an impact on the time of sunrise (which changes over the course of a year).

I discounted this as it did not seem to be what the OP was asking.

 

[sophiecentaur]

IS there any point in taking a non-ideal model for this? Surely the case of a regular rotation and a circular orbit is the one to sort out first. Here, the speed of Earth through space wrt c may be looked on as relevant because the path of the light that is seen will not be a straight line, as drawn on a map of the situation. However, the apparent sunrise event will still be regular.
Other effects (elliptical orbit etc) may be of interest but I don't think they can involve any paradoxes.

 

[D H]

For my own edification, this angular deviation is due to the Earth's movement in its orbit around the sun, correct? In 8 minutes the Earth has moved almost 9,000 miles around its orbit, (this is unrelated to its own axial rotation).

That's correct. That angular deviation results from the aberration of light, and this is a function solely of the relative velocity of the Sun with respect to the Earth.

Annual aberration is something for which astronomers need to account when they aim their sub-arcsecond telescopes. Certainly the stars don't really move by ±20 arcseconds over the course of a year. That motion is a relativistic optical illusion. That same illusion applies to the Sun, but for the Sun the annual aberration is a nearly constant ±20 arcsecond angular deviation.