Where in the sky is the sun?

[Duplex]

Sunlight takes eight minutes to reach Earth. Meanwhile the sun and Earth have moved/rotated.

Suppose that the sun emitted two types of light, the 8-minute light and a spooky “zero-time light”. Where in the sky would we see/measure the second spooky sun - the real position of the sun?

The approximate angle or distance in sun diameters?

 

[dacruick]

Well that depends on the time of year, and probably slightly on atmospheric condition (refraction is dependent on moisture and angle).

There are equations easily available online which can calculate the position of the sun. You would simply have to find the difference in angle between a point now, and a point 8 minutes from now.

 

[russ_watters]

That's not what the question asked...

Duplex, given that the Earth rotates in 24 hours, how far (in angle) does it travel in 8 min? That is not a difficult calculation...

 

[dacruick]

You would simply have to find the difference in angle between a point now, and a point 8 minutes from now.

how far (in angle) does it travel in 8 min? That is not a difficult calculation...

I'm sorry but I don't see a huge distinction between our two answers. The Earth rotates every 24 hours but the elevation angle changes depending on the time of the year. In the winter the change in elevation angle over a full day is much less than in the summer, and peaks at solar noon.

In other words, there are two angles to account for, the azimuthal and elevation angles. simply dividing 360 degrees by 24 hours and using that ratio with 8 minutes will not suffice.

 

[russ_watters]

Sorry, I read the first 3/4 and missed the last sentence!

However, the OP just said angle, not elevation angle. So I wouldn't go more complicated than a time ratio calc.

 

[dacruick]

Sorry, I read the first 3/4 and missed the last sentence!

It's okay . I might be getting a little defensive today too. You're not the first PF Mentor to give me a hard time today haha.

 

[russ_watters]

Er..sorry, late edit

 

[Duplex]

Could it be a difference if the Earth rotates or the sun revolves around the Earth? A sort of three-body problem?

1. The sun is stationary in the sky and sends its parallel light as a laser beam towards the Earth.
Eight minutes before sunrise, it emits light that reaches me at sunrise. As the sun and solar direction coincide, the 8-minute light and the zero-time light coincide, i.e. the sun is really where I see it.

No matter the angle where I see the sun in the sky, there is only one sun in which the 8-minute position and the real position are identical.

2. The sun revolves around Earth. The medieval approach.
Don’t we then "see" two suns, the eight minutes old position and the sun's actual position?

I guess this question is somewhat simple, maybe I'm suffering from brain-fag but it was a baffling spin-off from a FTL discussion among some friends a year ago. If we had a measurement instrument for a hypothetical FTL-effect where would we find the sun in the sky.

 

[dacruick]

I don't understand what you are saying.

The sun's position in the sky is always moving relative to an observer on Earth. That's about all I can say.

 

[A.T.]

1. The sun is stationary in the sky and sends its parallel light as a laser beam towards the Earth.
Eight minutes before sunrise, it emits light that reaches me at sunrise. As the sun and solar direction coincide, the 8-minute light and the zero-time light coincide, i.e. the sun is really where I see it.

No, you will see two suns. The 8-minute light will be subject to aberration:
http://en.wikipedia.org/wiki/Aberration_of_light
For the zero-time light aberration is zero.

2. The sun revolves around Earth. The medieval approach.
Don’t we then "see" two suns, the eight minutes old position and the sun's actual position?

Yes, here we also see two suns. But in this frame we attribute it to delayed signal from an outdated source position for the 8-minute light.

 

[jetwaterluffy]

There is 360 degrees in a full circle. There is 1440 minutes in a day. Work it out.

 

[sophiecentaur]

No, you will see two suns. The 8-minute light will be subject to aberration:
http://en.wikipedia.org/wiki/Aberration_of_light
For the zero-time light aberration is zero.


Yes, here we also see two suns. But in this frame we attribute it to delayed signal from an outdated source position for the 8-minute light.

This thread has me confused. What can you possibly be implying when you say that you can see "two suns"? It is either a wind up (never on PF, I'm sure ) or a novel / alternative attempt to consider what is going on. But there is no paradox involved.

The only light that will reach Earth has taken 8 minutes to get here - by which time the Earth has rotated 360X 60/1440 degrees since it was emitted. How can you suggest that you could 'see' the light earlier than that? You could draw a diagram with lines on it to show two paths, possibly, but the one path would represent an impossible journey for the light (the no-time delay path doesn't exist)

 

[Drakkith]

I'm not sure why this is so complicated. IF there was this "FTL" light from the sun that reached you, you would see 2 suns, one of them, the FTL light, would be slightly ahead of the normal one. Since FTL doesn't exist this does not happen. To see where the sun "really" is you would predict its location based on the knowledge of how far the Earth is from the Sun and how fast light travels.

 

[sophiecentaur]

Doesn't all this boil down to frames of reference?
People are trying to introduce a problem where there isn't one.

 

[TGlad]

Blimey, here's the simple answer:
The zero-delay sun will be where the sun you see is in 8 minutes time.
Which is probably about a four sun diameters.

The speed of the sun through the galaxy etc doesn't make a difference as the Earth goes the same speed.

 

[Duplex]

Thank you guys.
I have considered all your answers, and I can not find anything but the problem arises if I look at the sun's apparent journey across the sky as equivalent to Earth's rotation with a stationary sun.

I think there is a difference. In the first case we have two suns, the illusory one we see with eight-minute delay with our eyes and the real position is slightly ahead in the direction of travel. It's like a jet in a perpendicular motion, where the light reaches us first and then the slow sound is lagging behind.

In the second case, our 24 hour rotation, we see the sun in its real position, where the sunlight that reaches us consists of two components: the old 8-minute light and a hypothetical fresh FTL-light.

I hope my basic problem has been to understand how my academic friends (no physicists) who discussed this subject at a party could have such different views.

Now, it is far past midnight here and it's time to sleep…

 

[A.T.]

Duplex, given that the Earth rotates in 24 hours, how far (in angle) does it travel in 8 min? That is not a difficult calculation...

...wouldnt go more complicated than a time ratio calc.

There is 360 degrees in a full circle. There is 1440 minutes in a day. Work it out.

So you guys seriously think that the visible position of the sun is about 2° off the actual direction to the sun, because the Earth rotates 360° per 24h?

What if I stand on the north pole (during the summer there)? Same offset? What if I stand on the north pole and start spinning faster than the Earth? Will the offset increase?

 

[sophiecentaur]

So you guys seriously think that the visible position of the sun is about 2° off the actual direction to the sun, because the Earth rotates 360° per 24h?

What if I stand on the north pole (during the summer there)? Same offset? What if I stand on the north pole and start spinning faster than the Earth? Will the offset increase?

Wherever you stand, the azimuth error will be the same because the Earth is rigid and rotates at the same rate around its axis all over the surface (forget tides). The actual position in the sky will not be shifted by the same amount but that is only a detail of geometry (not time and c) and doesn't really help in the philosophy of this discussion.

 

[A.T.]

the problem arises if I look at the sun's apparent journey across the sky as equivalent to Earth's rotation with a stationary sun.

The only thing that causes an offset between the visible and real direction, is the component of relative velocity (between source & detector) that is perpendicular to the real direction. The dominating effect here is the orbital velocity of the Earth, but the offset from it is very small probably not visible with the naked eye. The rotation of the Earth plays a tiny role, and that only if you are not one of the poles, so you have some tangential velocity from that rotation.

 

[A.T.]

So you guys seriously think that the visible position of the sun is about 2° off the actual direction to the sun, because the Earth rotates 360° per 24h?

What if I stand on the north pole (during the summer there)? Same offset? What if I stand on the north pole and start spinning faster than the Earth? Will the offset increase?

Wherever you stand, the azimuth error will be the same..

- What exactly is "azimuth error" ?
- What is its value?
- If I don't stand still on the pole, but start to rotate will the "azimuth error" be different?

 

[Duplex]

The only thing that causes an offset between the visible and real direction, is the component of relative velocity (between source & detector) that is perpendicular to the real direction. The dominating effect here is the orbital velocity of the Earth.

There is an interesting factor.

http://en.wikipedia.org/wiki/Earth's_orbit

“The orbital speed of the Earth around the Sun averages about 30 km/s (108,000 km/h), which is fast enough to cover the planet's diameter (about 12,700 km) in seven minutes”

Seven minutes...

 

[sophiecentaur]

- What exactly is "azimuth error" ?
- What is its value?
- If I don't stand still on the pole, but start to rotate will the "azimuth error" be different?

Look up the meaning of Azimuth angle. It relates to angle around the polar axis and is one of the parameters used to specify the position of an astronomical object. It would be better to look at a proper diagram than to have me give some lame verbal description.
The azimuth angle is independent of the latitude of the observer.


Of course if you turn around then the sun will appear to be going round Earth at a different rate. I don't see how that's relevant, though. It's only like assuming the Earth rotates at a different rate.

 

[A.T.]

There is an interesting factor.

http://en.wikipedia.org/wiki/Earth's_orbit

“The orbital speed of the Earth around the Sun averages about 30 km/s (108,000 km/h), which is fast enough to cover the planet's diameter (about 12,700 km) in seven minutes”

Seven minutes...

Yes, so while light goes from the Sun to Earth, the Sun moves(from the Earth's perspective) about one Earth diameter (1/109 of the Sun's diameter). As I said, barely visible.

 

[russ_watters]

Ahhh, carp - you're right. Sorry for that, guys.

 

[sophiecentaur]

There are two effects at work (in the very simplest model). There is a 2 degree rotational error due to rotation and a 13(+)k km positional error. The 2 degree error is the larger one by far.
But either way, there is only one visible image of the sun and that is how it looked about 8 minutes ago.

 

[A.T.]

Of course if you turn around then the sun will appear to be going round Earth at a different rate. I don't see how that's relevant, though. It's only like assuming the Earth rotates at a different rate.

Exactly. And would that different rotation rate change the angular offset between the visual and actual sun position (seen from the pole)?

 

[A.T.]

There is a 2 degree rotational error due to rotation.

Please explain how you arrived at this 2 degree error due to rotation. What if the Sun was further away, so it's light needs 12h to Earth. What would be the rotational error between the visible and actual Sun position?

 

[sophiecentaur]

I think we are talking in different frames of reference here, I think. If you are talking of azimuth angle (which is usual) then yes it would.
Imagine if the Earth were neither rotating nor in orbit around the Sun (sky hooks), it would see the Sun in the same position in the sky all the time. Erect a stick, pointing at the Sun and put it on a rail track around the equator. Start the Earth rotating (24hr period) but keep the stick pointing in the same direction (in space) that it was pointing. The Sun will no longer appear to be in line with the stick but will appear to be 2 degrees behind where the stick is pointing (which will still be directly at the 'actual' position of the Sun).

 

[A.T.]

Erect a stick, pointing at the Sun and put it on a rail track around the equator. Start the Earth rotating (24hr period) but keep the stick pointing in the same direction (in space) that it was pointing. The Sun will no longer appear to be in line with the stick but will appear to be 2 degrees behind where the stick is pointing (which will still be directly at the 'actual' position of the Sun).

How did you arrive at those 2 degree?

What if the Sun was further away, so its light needs 12h to Earth (which still has a 24hr rotation period). What would be the angle between stick (pointing at the 'actual' position of the Sun) and the visible position of the Sun?

 

[sophiecentaur]

Please explain how you arrived at this 2 degree error due to rotation. What if the Sun was further away, so it's light needs 12h to Earth. What would be the rotational error between the visible and actual Sun position?

OK. Take a star that is 100LY away. What direction would you say it was when you are looking at it? You have to bear in mind that the Earth has rotated about 36525 times since the light left that star. By the time it reaches us, we have no idea where that star is, as viewed by a remote observer. It could have blown up 99 years ago and we would be none the wiser. It is only because we 'know' where the Sun is and because it is so close that the question in the OP arises, I think.

If you were to be controlling a probe, heading for the centre of the Sun and had to press a button at the right time to be sure it would be heading in the right direction, you would need to take into account the offset in the observed position .

I just realized that this introduces the idea of Sidereal and Solar Days and where we see planets. The Moons of Jupiter were seen to be in the 'wrong' places as Jupiter's orbit, relative to ours, took it to different distances away. This was an early clue that light is not instantaneous.

 

[A.T.]

OK. Take a star that is 100LY away.

No, I said 12 light hours. Why can't you answer this simple question:

If the Sun's light needed 12h to Earth (which still has a 24hr rotation period): What would be the angle between stick (pointing at the 'actual' position of the Sun) and the visible position of the Sun?

Alternatively you can tell me how you arrived at those 2 degree for 8 light minutes distance. Then I will compute it myself for 12 light hours.

 

[sophiecentaur]

See my post no12- but I can repeat:
360 degrees rotation per day
24X 60 minutes in a day
8minutes represents
8/24X60th of a day
or 360X8/24X60
=2 degrees of rotation

Imagine you did this the other way round. Shine a laser upwards at the equator as the Earth rotates. The beam will not be straight, will it? No, it will form a spiral which spreads out at c.
If you want two objects to appear in the same place in the sky, they will have to lie on a similar spiral - not on a straight line. The Sun - and your proposed Sun that is 12 light hours away will not be aligned either, as viewed by some celestial mapmaker but will appear to be aligned from Earth.

I really can't see how my arguments have a flaw.

Remember, our whole view of the Universe is affected by the speed of light. Nothing is fixed. It all depends upon who is looking and where they are.

 

[JeffKoch]

I think there is a difference. In the first case we have two suns... In the second case, our 24 hour rotation, we see the sun in its real position, where the sunlight that reaches us consists of two components: the old 8-minute light and a hypothetical fresh FTL-light…

I do not have the vaguest idea what you are attempting to say but it sounds like utter nonsense. The only answer that matters: The sun is exactly where you see it in the sky, right now, end of story. It does not make sense to ask where it is *now*, because now is now and the only contact you have with the sun's light and therefore apparent position is through that 8 minute gap. Where it is *now* is really where it will appear 8 minutes in the future, defined by the distance to the sun and the speed of light - we can try to predict where it will appear, and we'll probably get it right, but then again the Earth might get knocked out of it's orbit and flung into interstellar space by a random passing relativistic black hole between now and then. Who knows.

 

[A.T.]

See my post no12- but I can repeat:
360 degrees rotation per day
24X 60 minutes in a day
8minutes represents
8/24X60th of a day
or 360X8/24X60
=2 degrees of rotation

So for 12h light travel time we would get an angle of 180° between the visible sun position and the stick that points to the 'actual' sun position. Correct?

That means, when we would see the Sun directly overhead, the stick would point directly into the ground, indicating that the sun is 'actually' on the other side of the planet. Is that what you are saying?

What happens if we suddenly stop the Earth's rotation in that very moment, with the visible Sun directly above us and the stick pointing into the ground? Would the visible Sun suddenly disappear?

 

[sophiecentaur]

What happens if we suddenly stop the Earth's rotation in that very moment, with the visible Sun directly above us and the stick pointing into the ground? Would the visible Sun suddenly disappear?

Of course not. It would appear to set in the normal manner (as the last twelve hours worth of light arrived at us from the positions it had occupied during the last twelve hours) and then not appear again in the 'morning'. It would be the other side of the Earth and invisible.

I really don't think you guys are thinking in terms of light taking time to get anywhere.
Are you actually disagreeing that light from a laser would travel outwards in a spiral? Is it INSTANTANEOUS? If the argument applies for one direction then it has to apply for the other.