APOD: Through a Sun Tunnel (2011 Dec 22)

[alter-ego]

Der APOD,
Do any submissions get vetted for accuracy?
How can "Halting its steady march toward southern declinations and begining its annual journey north"
Referring to the Sun as obseved from the Earth be permitted to go public?

Well, that's what the sun does.

I am disappointed that it appears if the picture looks nice, doesn't matter what, how and why, lets post it.
Lately most APODs are just time lapse, looks nice and usually not much to do with Astronomy, OK the meteorites (if any lets after the fall), do apply to APOD, but for goodness sake, we have the absolutely marveouls mathematics and physics to get MESSENGER to be engaged (soon) in a stable and close orbit of Mercury, would that not be an excellent weeks' worth of APODs?

I think these are fine pictures too! There are various levels of technical detail amongst the APODs. Carrying weeks of Messenger pictures would bore many people. I think the editors try to pick a wide variety of material to satisfy a wide variety of interests. If you are not satisfied here, and want more pure, detailed cutting-edge science, then visit other websites. NASA has great sites that you can get lost in. You can even participate in Kepler's planet hunting program!

Instead we have because of the solstice the Earth orbit is now a South to North inclination?
How can this APOD be permitted? Why confuse the many that love Astronomy especially the youth, be told the Sun is now "Halting its steady march toward southern declinations and begining its annual journey north"??

Why not? Developing early interest in astronmomy involves looking an the sun, moon and planets. It is likely that the APOD could prompt some interested, likely young, reader to ask why the sun does this. Learning comes from asking questions, and I see this APOD being a fine candidate for this.

Please, let's get back to reality, and some excellent material from NASA/ESA and many other sources, enough of time lapse and wonderful circular lines of the stars, perhaps ask those that love them to swing the camera on a string and we could have hundreds of 'scintillating' APODs.

I disagree. Sure, not every picture suits my interest either, but for what I believe the APOD is meant to accomplish, I think the editors are doing a fine job.

Am I missing something??

[owlice]

alter-ego, the only thing you may be missing is mastrulo's previous posting history (some of which isn't apparent because the posts were removed).

biddie, do you have a picture of your stained glass window? I'd love to see it!

[alter-ego]

alter-ego, the only thing you may be missing is mastrulo's previous posting history (some of which isn't apparent because the posts were removed).

Well, that certainly helps
Thanks owlice

[alter-ego]

Misconception is a much to strong of a word - I believe the assertion is true to the level we can measure solar position. I think the degree of error you are talking about does not need further discussion because it would just promote confusion here. I think the complications introduced to get at the true (most accurate) answer requires a discussion at a whole other level and not worth it here. Other than adding a comment that calculating solstice times to the minute is very complicated, leaving with the primary point that solstice timing and extreme solar declination are correlated is the right thing to do. After all, the change of declination over the timing error is extremely small at worst (essentially not measurable), i.e. the sun is at a declination extremum within our capability of knowing it (see below).

... This means that it may be a few hours off from when the sun is actually farthest north or south. Normally this doesn't really matter - but when people specifically say that is the moment the sun is at its extreme position - or that defines astronomical solstice - it is incorrect.

This is described in Astronomical Algorithms by Meeus - but in this case the source of the computation is the U.S. Naval Observatory, and they spell out the definition succinctly here:

http://asa.usno.navy.mil/SecM/Glossary.html#s

Wow! I thought I was picky

First, the variation of sol's declination about the summer solstice (worst case) is extremely small, about 0.15" (that's arc seconds!) over +/- 2.5 hours of time, and immeasurably small for +/- 10 minutes of time. For June, 2011 solstice, it looks like the timing error could be a few minutes at most.

Second, at this scale, more complicated orbital dynamics are at play. As Meeus points out, apparent geocentric longitude includes a correction for nutation and aberration. However, I did not see a specific reference or discussion by Meeus of timing error between solstice and declination extrema, but I can believe the error is not zero. That said, I'm not seeing hours.

If you have a specific reference to a multi-hour solstice / declination extrema timing error I'd like to know it. I question just how large that can be.

[zloq]

Well you seem to agree with my main point - that the moment of solstice is not defined as an extreme declination of the sun, but as a specific longitude along the ecliptic. One reason to do that is the motion of the sun is fairly steady in longitude, whereas when it is near an extreme point its behavior is dictated by higher order effects that would be hard to include accurately. A good example is the time of earliest sunset - which many people think happens on the winter solstice. But precisely because the sun is fairly stationary in dec. at that time, its changing apparent longitudinal speed is the dominant effect to determine sunset time - and the earliest sunset occurs many days earlier. At the top of a peak of a curve, highly magnified, it is completely flat - so even a slight perturbation could induce tilt at the main peak that has a big magnifying effect in laterally shifting the new peak.

As Meeus describes, an error of 1" in the solar longitude induces a 24s change in the time of a solstice. So - even if higher order effects (mainly due to the changing ecliptic latitude of the sun, which never exceeds 1.2") cause a tiny, sub arc-second change in declination, it can result in a relatively huge shift in longitude where that peak occurs - and therefore a big shift in time. It's not the *magnitude* of the shift that counts, but its rate of change, which causes a tilt of the top of the peak and offsets the lateral position of the new peak. I think these are all motivations to avoid defining events in terms of an extreme value - because the resulting time will be very sensitive to higher order effects.

As for 0.15" being "immeasurably" small - in many applications it is huge. Meeus points out that solstice is defined based on the unperturbed sun (including the effects of aberration and nutation), which ignores effects below 0.01". That is the level of simplification that is allowed in the definition that produced the time cited in the APOD caption. He also points out that even at the equinox, by the definition in use, the sun can be as far as 1.2" off the equator. But since the ecliptic is at an angle relative to the equator at the equinox, this has little impact on the time it crosses the equator, in contrast to the solstice where the sun is moving parallel to the equator.

I think it's good to know how these terms are defined - especially when the numbers are cited. If you say the number is based on one thing, and then you ask the person who did the calculation, who responds, "That's not what I did" - I think that's not good. The true definition of astronomical solstice is counter-intuitive - so when people speak of that moment as being a point of extreme declination - I can only assume they have never been exposed to the details spelled out by Meeus and the Astronomical Almanac. I just prefer to go by what something is rather than what it isn't.

I personally would have said the sun reaches its extreme point on the day of the solstice - to get the main idea across - and then separately talk about the moment of solstice and how it's defined. I enjoy learning about how these terms are actually defined - especially when they are somewhat surprising - and when there are in fact good reasons for them to be defined that way.

zloq

[Chris Peterson]

I personally would have said the sun reaches its extreme point on the day of the solstice - to get the main idea across - and then separately talk about the moment of solstice and how it's defined. I enjoy learning about how these terms are actually defined - especially when they are somewhat surprising - and when there are in fact good reasons for them to be defined that way.

In a one paragraph APOD caption, the reasonable thing to do is to say that the solstice is the time where the Sun reaches its southernmost declination, and then provide a link to a more detailed discussion (assuming one is readily available to the editors).

[alter-ego]

In a one paragraph APOD caption, the reasonable thing to do is to say that the solstice is the time where the Sun reaches its southernmost declination, and then provide a link to a more detailed discussion (assuming one is readily available to the editors).

Certainly this is a good solution. Unfortunately, with a reasonable amount of effort, I was not able to find such links. I believe Meeus provides enough fundamentals that one could, in polynomial form, probably approximate the timing deviation between the June solstice and maximum solar declination. Instead, I followed up with an empirical mapping of these times. In hindsight, I'm not sure if I saved any time, but I saw there was a definite path at least.

As for 0.15" being "immeasurably" small - in many applications it is huge. Meeus points out that solstice is defined based on the unperturbed sun (including the effects of aberration and nutation), which ignores effects below 0.01".

Ok, I can now speak more definitively about the nature and magnitude of this timing deviation. I used a (complete) VSOP87 code to obtain solar coordinates and times over three lunar nutation cycles (a JPL ephemerides may be more accurate, but VSOP87 meets the accuracy requirements for this discussion). I looked at one cycle interval between 1000 and 1019 AD and two consecutive cycles between 1982 and 2020 AD. Here is what I found:

• 1. All three cycles showed the timing / declination differences fell on the same parabolic curve => Declination difference is quadratic with the timing difference.
  2. The maximum timing difference appears to occur 4 times during each nutation cycle, and the greatest value is approximately +/- 550 seconds. I.e. the time of maximum declination is symmetrical about the solstice, and occurs ~550 seconds before and after a (different) solstice within each nutation cycle. Note: The solstice time (apparent geocentric longitude = 90°) was determined to ±1 millisecond, and the maximum declination timing to <±3 seconds.
  3. The maximum difference in declination between solstice and greatest declination ≈ 550 microarcseconds. This is ~1/20 of the 0.01" accuracy limit Meeus talks about, and may be well below the best position precision that can be claimed today.

It's clear why the maximum solar declination is associated with the June solstice. In fact it's safe to say that, at solstice, the sun is at it's maximum declination within the uncertainty of predicting it's position. However, as was zloq's point, the most accurate method for determining the solstice time is using the sun's apparent geocentric longitude, not the sun's declination.

[zloq]

Hi-

I didn't know you were studying this - there is a JPL web interface for custom ephemerides at:

http://ssd.jpl.nasa.gov/horizons.cgi

You can enter different locations on the earth and request different types of output - and the key items for this would be the geocentric coordinates of the sun, and the topocentric coordinates - without refraction. I agree that the geocentric shift of the minimum looks to be around 10 minutes, but even that is enough to make it incorrect to say 5:30 is when the sun "stands still" or reaches its most southern declination. But there is still a possible shift of hours if you use the topocentric location of the sun, still without refraction, for a place like Tehran, where the sun is rising in the east at the time of geocentric extreme. It's because the sun is near its extreme declination that other small factors enter in, and in this case just the parallax caused by the observer's rotation around the earth will make the sun push further south during the day than as seen from the center of the earth. So the true minimum is dependent on the observer's location - and solstice by the "minimum" definiton is different for everyone - and different by hours.

So I agree that the geocentric time will be pretty near - but still many minutes off - so it is triply wrong to say 5:30 is when the sun was most south. That time is based on a different definition of solstice, the actual time based on geocentric coordinates would be around 9 minutes off, and the actual time for an observer on the rotating earth could be hours off.

As I said earlier, I would have said something like:

The sun reaches its extreme southern position on December 22 UT, the date of solstice for 2011. The time of astronomical solstice is 5:30 UT based on the moment the geocentric sun reaches 270 degrees ecliptic longitude - not its minimum declination as is commonly thought.

No need to cite an ephemeris - just cite the USNO definition of solstice that I provided a link for - which is the one used to calculate the 5:30 value.

I think this would have been good to say because it is correct rather than incorrect, and it is informative both to people with little knowledge of astronomy and to the millions who are somewhat knowledgeable but are not aware of the definition of astronomical solstice - and would appreciate learning this fact since it is counter-intuitive. If a time is given *to the minute* for something - then it should be described in terms of how it was calculated when the operative definition is fundamentally different.

If people do play with the JPL page - beware that it will calculate values for night time, which is when the sun is not visible. If you include those points you will see multiple minima or "solstices" where the sun "stands still" - because its declination near solstice is dominated by factors as small as the observer's spinning around the earth 93 million miles away. I think it should be possible for a location to have two such solstices even in daytime, but I'm not sure.

zloq

[.::makc::.]

MAGRATHEA!!

Click to view full size image

[alter-ego]

I didn't know you were studying this - there is a JPL web interface for custom ephemerides at:

http://ssd.jpl.nasa.gov/horizons.cgi

Hi zloq,
Yes, thanks. I've used this one before, but for this I like other tools better only because I wanted time increments smaller than a minute. It was easier to use other programs than trying to access a more powerful version of the JPL ephemerides. In the world of modeling and predictions, I prefer higher accuracy than what may be verifiable - a 1-minute time increment was just to chunky for me.

So the true minimum is dependent on the observer's location - and solstice by the "minimum" definiton is different for everyone - and different by hours.

This is an interesting point, but I didn't think there was confusion over topocentric v. geocentric coordinates. I didn't see this as a reference point in the APOD description.

No need to cite an ephemeris - just cite the USNO definition of solstice that I provided a link for - which is the one used to calculate the 5:30 value.

I'm not questioning the formal solstice timing definition - your point is a good one. I wanted to know the actual expected magnitudes of multiple timing and declination differences over multiple nutation cycles to gain some confidence in the trends and their repeatablitly. Any earlier references to these were weak and speculatory.

[alter-ego]

MAGRATHEA!!

I first thought you were exclaiming MARGARITA!!, and I thought hot chocolate would be better. But if that's an Earth-building Magrathea engineer in the picture, I doubt that's a cement sewer pipe he/she is sitting in.