Starship Asterisk*

by **bystander** » Mon Jan 03, 2011 3:38 pm

Havanich wrote:Thanks so much for your clear explanation. I hadn't thought about the time difference. APOD often shows us the complexity of our natural world. If the analemma moves toward vertical as you go north, would the bottom of the curve be below the horizon at the north pole?

Yes, anywhere above the artic circle, the sun never rises in the winter and so the bottom of the curve would be below the horizon.

by **Havanich** » Mon Jan 03, 2011 1:13 pm

alter-ego wrote:
Havanich wrote:I was wondering about yesterday's picture of the analemma viewed from central Europe. Does the shape of the analemma, specifically the altitude of the crossover, depend on location, time of day, or is it a constant? I thought the position of the crossover could depend on latitude, with the view at the equator being an ellipse. But perhaps not.
The Equation of Time does not depend on latitude - only on Earth's rotational and orbital parameters. The figure 8 shape likewise does not change with latitude, though parallax due to spatial separation (at differen latitudes) may change the exact RA/Declination coordinates of the Sun, the analemma shape and cross-over point (relative) location will not change.
Rising Analemma, 12 deg Latitude.JPG
However, it's not hard to see that latitude does affect the analemma's orientation, and that the orientation changes the Sun's rising and setting asymmetrically. For example, the analemma graphically shows why the Solstices aren't when the earliest/latest sunrises and sunsets occur even though they are the longest/shortes days. The plot shows a special case that I like - a rising analemma for at 12.5 deg latitude. Note the the Sun rises at the same time (within 10 seconds) over the entire month of September, while marching 15 degrees southward over the same time. For this case, the opposite side of the plotted analemma closely represents the slope on the western horizon. Over the same time interval, the sunset time changes by ~24 minutes.

Hope this helps.

Thanks so much for your clear explanation. I hadn't thought about the time difference. APOD often shows us the complexity of our natural world. If the analemma moves toward vertical as you go north, would the bottom of the curve be below the horizon at the north pole?

by **alter-ego** » Mon Jan 03, 2011 5:20 am

raindrop wrote:Thanks for explaining how the earth's axis tilt affects the analemna (sp?). At the same time you also explained why the sunset is earliest on Dec 8 and not Dec 20 or 21. I have been trying to figure this out for several years.

Your welcome. There's more to the analemma than meets the eye, and it is nice when something abstract can tie into direct experience.

I think the same causes go into moon rising time and why it rises closer together around the autumnal equinox. However, then you must be considering the moons tilt with respect to the earth?

I'm confused what you are asking. A few things I'd like to say that might help answer / clarify your question. Bottom line, I believe your association of closer moonrise times to autumnal equinox is not generally correct.

First, the lunar orbit is very dynamic compared to the Earth's orbit. Moonrises and sets are changing very quickly compared to sunrises and sunsets. Whereas Earth orbital parameters change on the scale of 10's of thousands of years, lunar orbit precession / recession cycles have ~19year and ~9year periods. Generalizing a rise / set behavior as occurring at an equinox, or other specific time does not pan out. The elliptical lunar orbit does result in a nonuniform angular velocity, and this, in turn, results in rise / set time "bunching", i.e. times of the year when moonrises are close together, and times when they are far apart. The bunching occurs at different times in the year, and not necessarily the same times, given the changing lunar orbit. On average, the moon rises 51 minutes later each Earth day. If you are comfortable looking at number tables you can find data here and maybe additional data here.

Second, if you are relating the moon's rotation axis to the "moon's tilt", there is no connection to the moonrise / set times (at least wrt a "lunar" analemma as viewed from Earth). If you were on the moon observing the Earth, the tilt of the moon's rotation axis is a key factor for the Earth's analemma. As I stated, I'd expect this analemma would constantly change orientation and shape over time. Now, back on Earth, the angle of the lunar orbital plane with respect to the Earth's equatorial plane has a key influence in the moonrise / set times. However, a practical lunar analemma analogy comparable to the Sun's analemma does not likely exist because of the everchanging orbit. So thinking of moonrise and set times using an analemma model is difficult and impractical.

HOWEVER, you can generate an interesting "lunar" analemma snapshot (as seen in this APOD) by taking a picture of the moon (from the Earth) at time intervals increasing by 51 minutes each day to remove the mean lunar angular motion. This analemma reflects the higher-eccentricity lunar orbit by the significantly assymetric figure 8. Although the closer two adjacent moon images are in annlemma time (horizontal axis) also means that risetimes are closer, but remember that for this analemma, if images are parallel to the horizon then their risetimes are multiples of 51minutes apart (unlike the Sun's analemma where it would mean the same rise / set time).

I hope this is helpful.

by **raindrop** » Sun Jan 02, 2011 5:38 pm

Thanks for explaining how the earth's axis tilt affects the analemna (sp?). At the same time you also explained why the sunset is earliest on Dec 8 and not Dec 20 or 21. I have been trying to figure this out for several years. I think the same causes go into moon rising time and why it rises closer together around the autumnal equinox. However, then you must be considering the moons tilt with respect to the earth? raindrop

by **alter-ego** » Sun Jan 02, 2011 6:52 am

Havanich wrote:I was wondering about yesterday's picture of the analemma viewed from central Europe. Does the shape of the analemma, specifically the altitude of the crossover, depend on location, time of day, or is it a constant? I thought the position of the crossover could depend on latitude, with the view at the equator being an ellipse. But perhaps not.

The Equation of Time does not depend on latitude - only on Earth's rotational and orbital parameters. The figure 8 shape likewise does not change with latitude, though parallax due to spatial separation (at differen latitudes) may change the exact RA/Declination coordinates of the Sun, the analemma shape and cross-over point (relative) location will not change.

However, it's not hard to see that latitude does affect the analemma's orientation, and that the orientation changes the Sun's rising and setting asymmetrically. For example, the analemma graphically shows why the Solstices aren't when the earliest/latest sunrises and sunsets occur even though they are the longest/shortes days. The plot shows a special case that I like - a rising analemma for at 12.5 deg latitude. Note the the Sun rises at the same time (within 10 seconds) over the entire month of September, while marching 15 degrees southward over the same time. For this case, the opposite side of the plotted analemma closely represents the slope on the western horizon. Over the same time interval, the sunset time changes by ~24 minutes.

Hope this helps.

by **quattroman** » Sun Jan 02, 2011 6:10 am

annoymous wrote:I'm confused - how is the photographer's shadow in the picture? And doesn't that look more like a front yard then the backyard?

Because the pictures of the Sun used to create the analemma is photographed with a filter. To get one image of the scenery from the spot where the analemma pictures are taken, the photographer has to take one image with the sun out of the picture to avoid bakclight (in order to get a better picture).

by **Havanich** » Sat Jan 01, 2011 2:30 pm

I was wondering about yesterday's picture of the analemma viewed from central Europe. Does the shape of the analemma, specifically the altitude of the crossover, depend on location, time of day, or is it a constant? I thought the position of the crossover could depend on latitude, with the view at the equator being an ellipse. But perhaps not.

by **Beyond** » Sat Jan 01, 2011 3:54 am

Boomer12k wrote:"TO INFINITY AND BEYOND!"

Why - Thank you, Boomer12k.

YEE-HA!!

by **alter-ego** » Sat Jan 01, 2011 1:56 am

Guest wrote:
Please explain why the lower loop of the analemma is longer than the upper one.
When the earth is moving faster in its orbit, the amount of time by which its position varies from that of a circular orbit is at its greatest. If the orbit was perfectly circular, the analemma would simply be a vertical line. It is the difference in speed during the ellipitical orbit that creates the lobes. The faster speed creates the larger lobe. It is explained in much greater detail (and mathematical precision) in the link I cited above.

Your first statement is true, but deviation from a circular orbit / constant orbital velocty contributes only about 1/3 of the time variation magnitude. Less obvious, but significant, is the affect due to the tilted axis alone. This is likely created by Earth's rotation plane not parallel to orbital plane. For a circular orbit (eccentricity = 0) the figure 8 still exists, but is symmetrtic. Years ago I wrote an analemma program which cross-checks very well with the downloadable program available via the Other Analemmas tab. Below are interesting screenshots using the linked program:

: Axis tilt explains about 2/3 of the time variation
(click to enlarge)

Only as the axis tilt => 0deg does the figure 8 converge to a point, but a simple line analemma does not ocurr. Unfortunately the linked program does not take inputs = 0, so if you want to explore really small tilts and eccentricities you can, but you'll get varied shapes.

by **Boomer12k** » Sat Jan 01, 2011 12:09 am

"TO INFINITY AND BEYOND!"

by **Guest** » Fri Dec 31, 2010 10:01 pm

Please explain why the lower loop of the analemma is longer than the upper one.

When the earth is moving faster in its orbit, the amount of time by which its position varies from that of a circular orbit is at its greatest. If the orbit was perfectly circular, the analemma would simply be a vertical line. It is the difference in speed during the ellipitical orbit that creates the lobes. The faster speed creates the larger lobe. It is explained in much greater detail (and mathematical precision) in the link I cited above.

by **neufer** » Fri Dec 31, 2010 9:17 pm

raindrop wrote:
Please explain why the lower loop of the analemma is longer than the upper one. Since earth is at perihelion in January and moves faster then, the loop closer to the winter solstice should be shorter than the upper near the summer solsticeone. Earth is moving slower when at apehelion in August. This is going to bother me until someone explains it.

The sidereal rotation period of the earth is 23h 56m 4.1s but an extra 3m 55.9s is required (on average) to catch up with the apparent (59.14' long/day on average) longitudinal angular velocity of the sun around the earth.

However, the apparent longitudinal angular velocity of the sun around the earth is not a constant (54.23' long/day) for TWO different reasons.

Assuming the earth went around the sun in a circle then the sun would appear to go around the earth at a constant speed of 109.72km/day (40,075km/365.2422). However, at the equinoxes the ecliptic crosses the longitude lines at an angle of 23.5º so that the apparent longitudinal angular velocity of the sun is slowed down to ~54.23' long/day. At the solstices the ecliptic not only crosses the longitude lines directly (at zero angle) but the physical distant between longitude lines on the ecliptic is very short such that the apparent longitudinal angular velocity of the sun is speeded up to ~64.49' long/day. This explains the figure 8 pattern.

However, since the earth goes around the sun in a ellipse with perihelion around the northern winter solstice the apparent longitudinal angular velocity of the sun is especially fast [(54.23 + 12.43)' long/day] at this time whereas at aphelion around the northern summer solstice the apparent longitudinal angular velocity of the sun is only moderately fast [(54.23 + 8.16)' long/day]. The earth's slight elliptical orbit hence makes for an unsymmetrical figure 8. Mars's extreme elliptical orbit makes for a teardrop analemma. Pluto's extreme elliptical orbit is trumped by its extreme axial tilt and therefore has a figure 8 analemma.

by **raindrop** » Fri Dec 31, 2010 7:55 pm

Please explain why the lower loop of the analemma is longer than the upper one. Since earth is at perihelion in January and moves faster then, the loop closer to the winter solstice should be shorter than the upper near the summer solsticeone. Earth is moving slower when at apehelion in August. This is going to bother me until someone explains it.

by **neufer** » Fri Dec 31, 2010 7:18 pm

dmbeaster wrote:
Other planets (except Mercury an Venus) have their own analemma based on their own unique characteristics of tilt and elliptic orbits.

http://en.wikipedia.org/wiki/Analemma wrote:

http://antwrp.gsfc.nasa.gov/apod/ap061230.html
http://antwrp.gsfc.nasa.gov/apod/ap050713.html
<<On Earth, the analemma appears as a figure eight, but on other solar system bodies it may be very different because of the interplay between the tilt of each body's axis and the elliptical shape of its orbit.

In the following list, "day" and "year" refer to the synodic day and sidereal year of the particular body:

* Mercury: Because the day is exactly two years long (due to orbital resonance), the method of plotting the sun's position at the same time each day would yield only a single point. However, the equation of time can still be calculated for any time of the year, so an analemma can be graphed with this information. The resulting curve is a nearly straight east-west line.

* Venus: There are slightly less than two days per year, so it would take several years to accumulate a complete analemma by the usual method. The resulting curve is an ellipse.

* Mars: teardrop

* Jupiter: ellipse

* Saturn: technically a figure 8, but the northern loop is so small that it more closely resembles a teardrop

* Uranus: figure 8

* Neptune: figure 8

* Pluto: figure 8 >>

http://en.wikipedia.org/wiki/Anna_Karenina wrote:
<<Anna Karenina (Russian: Анна Каренина) is a novel by the Russian writer Leo Tolstoy, published in serial installments from 1873 to 1877 in the periodical The Russian Messenger. Tolstoy clashed with its editor Mikhail Katkov over issues that arose in the final installment; therefore, the novel's first complete appearance was in book form.

Tolstoy considered Anna Karenina his first true novel, when he came to consider War and Peace to be more than a novel. The character of Anna was likely inspired, in part, by Maria Hartung (1832–1919), the elder daughter of the Russian poet Alexander Pushkin. Soon after meeting her at dinner, Tolstoy began reading Pushkin's prose and once had a fleeting daydream of "a bare exquisite aristocratic elbow", which proved to be the first intimation of Anna's character.

Although Russian critics dismissed the novel on its publication as a "trifling romance of high life", Fyodor Dostoevsky declared it to be "flawless as a work of Art". His opinion was shared by Vladimir Nabokov, who especially admired "the flawless magic of Tolstoy's style", and by William Faulkner, who described the novel as "the best ever written".>>

by **dmbeaster** » Fri Dec 31, 2010 6:08 pm

For those interested in the details of the shape of the analemma, this website is great. http://www.analemma.com/Pages/framesPage.html

The shape and positioning of the analemma is a composite of the effects of the earth's tilt and its elliptic orbit, as well as the position on earth and time of day that you record the images. The tilt stretches the image north/south and also introduces some east-west movement of the curve. The elliptic orbit also stretches the image east/west and creates the different sized lobes of the curve. Where you are on earth determines the degree to which the analemma is tilted from vertical.

Other planets (except Mercury an Venus) have their own analemma based on their own unique characteristics of tilt and elliptic orbits.

by **BMAONE23** » Fri Dec 31, 2010 5:59 pm

neufer wrote:
WildGuruLarry wrote:
jrjanzen wrote:
Obviously concocted. The shadows in the picture are in a direction NEVER achieved by any of the solar positions on the analemma!
Question: How could you believe that a photo with 36 suns in it could NOT be "obviously concocted"?

http://www.universetoday.com/wp-content/uploads/2010/12/Santa-Maria-with-Figures-to-scale.jpg wrote:
Santa Maria Crater Exploration

WOW Neufer,
That picture is just loaded with Asternuts

by **cmflyer** » Fri Dec 31, 2010 4:49 pm

Polaris never changes position from a given point on Earth. But if you create an afternoon analemma it will have a different angle in the picture from a morning analemma, because the camera is facing in different direction. This one was in the morning.

neufer wrote:
beyond wrote:
I think the last time i saw this, it was tilted the other way. Well, no matter which way it is, it still looks neat.
Analemma's lie on the celestial equator with the little loop end pointed towards Polaris (the celestial north pole).

In the northern hemisphere Polaris is
off to the upper left in the morning:

http://antwrp.gsfc.nasa.gov/apod/ap101231.html
http://antwrp.gsfc.nasa.gov/apod/ap061223.html
http://antwrp.gsfc.nasa.gov/apod/ap071204.html
http://antwrp.gsfc.nasa.gov/apod/ap070617.html
http://antwrp.gsfc.nasa.gov/apod/ap030320.html
and off to the upper right in the afternoon:

http://antwrp.gsfc.nasa.gov/apod/ap091220.html
http://antwrp.gsfc.nasa.gov/apod/ap081221.html
http://antwrp.gsfc.nasa.gov/apod/ap040621.html
What APOD lacks is a southern hemisphere analemma with the little loop end pointed
down to the lower left in the morning or down to the lower right in the afternoon.

by **skippy** » Fri Dec 31, 2010 4:40 pm

These type of pic here make me want to vomit

by **Chris Peterson** » Fri Dec 31, 2010 3:21 pm

jrjanzen wrote:Obviously concocted. The shadows in the picture are in a direction NEVER achieved by any of the solar positions on the analemma!

The images of the Sun were collected in the morning. The landscape image was recorded in the afternoon. The latter needed to be done when the Sun wasn't in the field-of-view, or it would have completely ruined the view of the sky.

by **chainsaw** » Fri Dec 31, 2010 2:50 pm

I think a solar analemma makes a good visual image to keep in mind when trying to understand the women in my life. Just when I think things are consistant every day something comes up which demonstrates that I really don't know which direction they're coming from. I'd bet if I had a fixed camera which rendered images of my lovely wife's emotional state each week, I'd come up with an analemma which would give me a much better understanding of what's really going on! I only hope that the little and big ends of it would have nothing to do with latitude: at approximately 42 degrees north I might have to lie a little bit when asked if her butt looked big.

Just sayin'...

by **biddie67** » Fri Dec 31, 2010 2:37 pm

Oh!! And a mighty hoorah of CONGRATULATIONS to Opportunity, et. al., for reaching the Santa Maria Crater!!

And, finally, a Hearty Happy New Year to all !!!!!

by **biddie67** » Fri Dec 31, 2010 2:26 pm

Congratulations, Tamas Ladanyi !! An excellent job of precise perserverence !!

I agree with "Brewer" above - what a great project to collect a set of analemmas from 5 positions on the Earth - the North and South poles, 45 degrees North and South and at the Equator for AM, Noon and PM .....

by **Sweetwater Tom** » Fri Dec 31, 2010 2:21 pm

What is the significance of the cross-over point in the figure-8? When does it occur?

Thanks.

by **Brewer** » Fri Dec 31, 2010 2:15 pm

Wouldn't it be wonderful to see a set of these with a Northern Hemisphere (say 45 degrees north), an equatorial and a Southern Hemisphere versions! Impressive.

And shouldn't one be able to figure out the latitude, north or south, of the photo(s) by the placement of the crossing in relation to the midpoint?
Some fun!

I have always been so impressed with the effort and discipline needed for these! Wonderful!!

by **neufer** » Fri Dec 31, 2010 2:00 pm

WildGuruLarry wrote:
jrjanzen wrote:
Obviously concocted. The shadows in the picture are in a direction NEVER achieved by any of the solar positions on the analemma!
Question: How could you believe that a photo with 36 suns in it could NOT be "obviously concocted"?

http://www.universetoday.com/wp-content/uploads/2010/12/Santa-Maria-with-Figures-to-scale.jpg wrote:
Santa Maria Crater Exploration

Starship Asterisk*

APOD: Analemma 2010 (2010 Dec 31)

Post a reply

Expand view Topic review: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)

Re: APOD: Analemma 2010 (2010 Dec 31)