APOD: At the Shadow's Edge (2021 Nov 25)

[APOD Robot]

At the Shadow's Edge

Explanation: Shaped like a cone tapering into space, the Earth's dark central shadow or umbra has a circular cross-section. It's wider than the Moon at the distance of the Moon's orbit though. But during the lunar eclipse of November 18/19, part of the Moon remained just outside the umbral shadow. The successive pictures in this composite of 5 images from that almost total lunar eclipse were taken over a period of about 1.5 hours. The series is aligned to trace part of the cross-section's circular arc, with the central image at maximum eclipse. It shows a bright, thin sliver of the lunar disk still beyond the shadow's curved edge. Of course, even within the shadow the Moon's surface is not completely dark, reflecting the reddish hues of filtered sunlight scattered into the shadow by Earth's atmosphere.

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[VictorBorun]

micro-exam in geometry

Does the shadow's edge we see presents in fact the roundness of Earth's edge?
After all the Shadow play we use here to guess the shape of Earth has a peculiar screen: Moon is no flat disk, it's a ball

[JohnD]

That composite gives an excellent mental image of the Earth's conic shadow!

[VictorBorun]

micro-exam in image processing.

The true shape of Earth revealed at last! The cat let out of the bag!

(I took it from here)

What is wrong with this edge detection?

[Ann]

micro-exam in geometry

Does the shadow's edge we see presents in fact the roundness of Earth's edge?
After all the Shadow play we use here to guess the shape of Earth has a peculiar screen: Moon is no flat disk, it's a ball

Yes indeed, we see the roundness of the Earth as it casts its shadow on the face of the Moon. If the Earth had not been round, the shape of its shadow would have been quite different!

Shape of the Earth's shadow on the Moon.
Image: Jean-Francois Gout

Shape of the outer disk of an almost edge-on of spiral galaxy in front of an
elliptical galaxy. NASA, ESA, the Hubble Heritage ESA/Hubble Collaboration, and W. Keel

If you want to see what AM 1316-241 looks like without my ungainly doodling on it, it is here.

Ann

[Ann]

micro-exam in image processing.

The true shape of Earth revealed at last! The cat let out of the bag!

Click to view full size image

(I took it from here)

---

Goodness me, the Earth is an American football! Who'd a thunk it?

(And can you imagine the size of the cosmic footballers using our Earth in their games??)

Ann

[VictorBorun]

micro-exam in geometry

Does the shadow's edge we see presents in fact the roundness of Earth's edge?
After all the Shadow play we use here to guess the shape of Earth has a peculiar screen: Moon is no flat disk, it's a ball

Yes indeed, we see the roundness of the Earth as it casts its shadow on the face of the Moon. If the Earth had not been round, the shape of its shadow would have been quite different!

Shape of Earths shadow on the Moon.png

Shape of the Earth's shadow on the Moon.
Image: Jean-Francois Gout

Shape of spiral galaxy in front of elliptical galaxy.png

Shape of the outer disk of an almost edge-on of spiral galaxy in front of an
elliptical galaxy. NASA, ESA, the Hubble Heritage ESA/Hubble Collaboration, and W. Keel

If you want to see what AM 1316-241 looks like without my ungainly doodling on it, it is here.

Ann

As an examiner in geometry I am not yet satisfied. A rounded edge of a shadow on a ball can in fact be casted by a linear object, in general.

[JohnD]

I submit, M'Luds (and M'Ladies), that the shadow, and hence the Earth, is RUGBY ball shaped, not the shape of an American football!
The diference is in the pointy ends, an NFL ball is more sharply pointed, and the shadow is blunt.
See: https://www.exploratorium.edu/sports/as ... _july.html

This means of course, that RUBGY RULES! Big Smiley!
JOhn

[orin stepanek]

The almost full eclypse!

Football's come a long way baby!

[VictorBorun]

micro-exam in geometry

Does the shadow's edge we see presents in fact the roundness of Earth's edge?
After all the Shadow play we use here to guess the shape of Earth has a peculiar screen: Moon is no flat disk, it's a ball

Yes indeed, we see the roundness of the Earth as it casts its shadow on the face of the Moon. If the Earth had not been round, the shape of its shadow would have been quite different!

Shape of Earths shadow on the Moon.png

Shape of the Earth's shadow on the Moon.
Image: Jean-Francois Gout

Shape of spiral galaxy in front of elliptical galaxy.png

Shape of the outer disk of an almost edge-on of spiral galaxy in front of an
elliptical galaxy. NASA, ESA, the Hubble Heritage ESA/Hubble Collaboration, and W. Keel

If you want to see what AM 1316-241 looks like without my ungainly doodling on it, it is here.

Ann

To my eye AM 1316-241 looks like pretty planar grand design disk galaxy, asking for an attempt to compensate for our sideway glance

[rj rl]

Yes indeed, we see the roundness of the Earth as it casts its shadow on the face of the Moon. If the Earth had not been round, the shape of its shadow would have been quite different!

Shape of Earths shadow on the Moon.png

Shape of the Earth's shadow on the Moon.
Image: Jean-Francois Gout

Shape of spiral galaxy in front of elliptical galaxy.png

Shape of the outer disk of an almost edge-on of spiral galaxy in front of an
elliptical galaxy. NASA, ESA, the Hubble Heritage ESA/Hubble Collaboration, and W. Keel

If you want to see what AM 1316-241 looks like without my ungainly doodling on it, it is here.

Ann

As an examiner in geometry I am not yet satisfied. A rounded edge of a shadow on a ball can in fact be casted by a linear object, in general.

yes, but to see it as rounded we'd have to be far enough away from the plane containing the light source and the line (edge of the linear object), casting the shadow. Earth is pretty far from the Moon (at infinite distance the Moon would act as a totally flat screen) and obviously lies very near the said plane, I'd say the shadow we see on the Moon represents the Earth's shape pretty accurately

[VictorBorun]

yes, but to see it as rounded we'd have to be far enough away from the plane containing the light source and the line (edge of the linear object), casting the shadow. Earth is pretty far from the Moon (at infinite distance the Moon would act as a totally flat screen) and obviously lies very near the said plane, I'd say the shadow we see on the Moon represents the Earth's shape pretty accurately

test result positive!
Care to take on the other exam, above? viewtopic.php?f=9&t=42056&p=318548#p318542

[rj rl]

yes, but to see it as rounded we'd have to be far enough away from the plane containing the light source and the line (edge of the linear object), casting the shadow. Earth is pretty far from the Moon (at infinite distance the Moon would act as a totally flat screen) and obviously lies very near the said plane, I'd say the shadow we see on the Moon represents the Earth's shape pretty accurately

test result positive!
Care to take on the other exam, above? viewtopic.php?f=9&t=42056&p=318548#p318542

what's the question, what are we looking at? Not sure I follow

[Fred the Cat]

Star Transit (2).jpg (37.03 KiB) Viewed 7972 times

Ok. I'll ask. Why is there a star transitting the moon?

[VictorBorun]

yes, but to see it as rounded we'd have to be far enough away from the plane containing the light source and the line (edge of the linear object), casting the shadow. Earth is pretty far from the Moon (at infinite distance the Moon would act as a totally flat screen) and obviously lies very near the said plane, I'd say the shadow we see on the Moon represents the Earth's shape pretty accurately

test result positive!
Care to take on the other exam, above? viewtopic.php?f=9&t=42056&p=318548#p318542

what's the question, what are we looking at? Not sure I follow

My bad.
Fitting a curve to the composite 5 moons' edge of Earth shadow we get an ellipsis rather than a circle.
What went wrong?

[johnnydeep]

I have no idea what most of you are talking about today. Must be the Thanksgiving brain fog. Not mine of course

[VictorBorun]

I have no idea what most of you are talking about today. Must be the Thanksgiving brain fog. Not mine of course

It's a quick test in image processing. If we take the posted image as an edge-detecting material,
we can't fit a circle to the supposed Earth's shadow across the 5 Moons:

What's wrong with this technique?
Or is Earth's shadow that far from being round?

[rj rl]

What's wrong - the fitting, probably A circle fits pretty decently actually.

[alter-ego]

I have no idea what most of you are talking about today. Must be the Thanksgiving brain fog. Not mine of course

It's a quick test in image processing. If we take the posted image as an edge-detecting material,
we can't fit a circle to the supposed Earth's shadow across the 5 Moons:
Gout_EclipseCollage 3.png
What's wrong with this technique?
Or is Earth's shadow that far from being round?

A couple reasons are contributing to your analysis uncertainty.
First the umbral edge is fuzzy - not perfectly sharp, and imaging the fuzzy edge against the various lunar contrasting shades, some saturated, will be uncertain. In this case, visually fitting a circle is most useful. To answer your question, the Earth's umbral shadow is a good circle.
Second, this particular composite is technically not accurate. The best-fit circle I see is about 15% smaller than the average shadow. In fact, the range of shadow-to-moon diameter ratio ≈ 2.58 → 2.73. In today's image this ratio ≈ 2.2 which is significantly less than the minimum. In composite below, I used two APOD images to help define the best fit circle. The dashed red line shows the umbra with a ratio of 2.2. The solid red line shows where the umbra would be with a ratio of 2.6. Looks to me that the significantly smaller umbra diameter is likely driven by lunar image spacings that are too small.
 

 
The second image shows a set of lunar images taken during a partial eclipse in 2017. Here, a reasonable circle fitting the umbra shows a ratio ≈ 2.65, which is right in the expected range. Note: The link for this composite does not mention the shadow size or diameter ratio. It only supports the Earth's shadow as a circle. I did the fit and obtained my own estimate for the umbra size / diameter ratio.
 

 
So really, I'd say the umbra size / shape details we can determine is limited in today's image.

[VictorBorun]

I have no idea what most of you are talking about today. Must be the Thanksgiving brain fog. Not mine of course

It's a quick test in image processing. If we take the posted image as an edge-detecting material,
we can't fit a circle to the supposed Earth's shadow across the 5 Moons:
Gout_EclipseCollage 3.png
What's wrong with this technique?
Or is Earth's shadow that far from being round?

A couple reasons are contributing to your analysis uncertainty.
First the umbral edge is fuzzy - not perfectly sharp, and imaging the fuzzy edge against the various lunar contrasting shades, some saturated, will be uncertain. In this case, visually fitting a circle is most useful. To answer your question, the Earth's umbral shadow is a good circle.
Second, this particular composite is technically not accurate. The best-fit circle I see is about 15% smaller than the average shadow. In fact, the range of shadow-to-moon diameter ratio ≈ 2.58 → 2.73. In today's image this ratio ≈ 2.2 which is significantly less than the minimum. In composite below, I used two APOD images to help define the best fit circle. The dashed red line shows the umbra with a ratio of 2.2. The solid red line shows where the umbra would be with a ratio of 2.6. Looks to me that the significantly smaller umbra diameter is likely driven by lunar image spacings that are too small.
 
Earth's Shadow - APOD.jpg
 
The second image shows a set of lunar images taken during a partial eclipse in 2017. Here, a reasonable circle fitting the umbra shows a ratio ≈ 2.65, which is right in the expected range. Note: The link for this composite does not mention the shadow size or diameter ratio. It only supports the Earth's shadow as a circle. I did the fit and obtained my own estimate for the umbra size / diameter ratio.
 
Eath's Shadow - 2017.jpg
 
So really, I'd say the umbra size / shape details we can determine is limited in today's image.

I am satisfied.
By the way, my attempt at making everything right was to try to darken the middle of the 5 Moons to see a uniformly bluish strip between the reddish full-shadowed part and the bright (half-shadowed) part:

[neufer]

Ancient Greek Astronomy and Cosmology

The Sphere of the World

<<By the 5th century B.C., it was widely accepted that the Earth is a sphere. This is a critical point, as there is a widespread misconception that ancient peoples thought the Earth was flat. This was simply not the case. Empedocles and Anaxagoras offered arguments for the spherical nature of the Earth. During a lunar eclipse, when the Earth is between the sun and the moon, they identified the shadow of the Earth on the moon. As the shadow moves across the moon it is clearly round. This would suggest that the Earth is a sphere.>>

Measuring the Size of the Earth

<<Lunar eclipses also allowed for another key understanding about our home here on Earth. In 3rd Century B.C., Aristarchus of Samos reasoned he could figure out the size of the Earth based on information available during a lunar eclipse:

Aristarchus's 3rd century BCE calculations on the relative sizes of, from left, the Sun, Earth and Moon, from a 10th-century CE Greek copy

---

The diagram at the right illustrates a translation of his work. The large circle is the sun, the medium circle is the Earth and the smallest circle is the moon. When the Earth is in-between the sun and the moon it causes a lunar eclipse and measuring the size of the Earth's shadow on the moon provided part of the information he needed to calculate its size.

Eratosthenes estimated Earth's circumference around 240 B.C. He used a different approach, measuring the shadows cast in Alexandria and Syene to calculate their angle relative to the Sun. There is some dispute on the accuracy of his calculations as we don't know exactly how long the units of measure were. The measurement however was relatively close to the actual size of the Earth. The Greeks were applying mathematics to theorize about the nature of their world. They held a range of beliefs about nature and the world but they were, in many cases, working to ground those beliefs in an empirical exploration of what they could reason from evidence.>>

<<On the Sizes and Distances (of the Sun and Moon) (Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], Peri megethon kai apostematon) is widely accepted as the only extant work written by Aristarchus of Samos. This work calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earth's radius.

Code: Select all

Relation 			Aristarchus 	Modern
--------------------------------------------------------------------
Earth's radius in Moon radii 		2.85 	3.50
Earth-Moon distance in Earth radii 	20 	60.32
Sun's radius in Earth radii 		6.7 	109
Earth-Sun distance in Earth radii 	380 	23,500 

The book was presumably preserved by students of Pappus of Alexandria's course in mathematics, although there is no evidence of this. The editio princeps was published by John Wallis in 1688, using several medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488. There is also a 1572 Latin translation and commentary by Frederico Commandino.>>

<<Aristarchus of Samos (Greek: Ἀρίσταρχος ὁ Σάμιος, Aristarkhos ho Samios; c. 310 – c. 230 BC) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the known universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He was influenced by the concept presented by Philolaus of Croton (c. 470 – 385 BC) of a fire at the center of the universe, but Aristarchus identified the "central fire" with the Sun and he put the other planets in their correct order of distance around the Sun.

Like Anaxagoras before him, Aristarchus suspected that the stars were just other bodies like the Sun, albeit farther away from Earth. Often, his astronomical ideas were rejected in favor of the geocentric theories of Aristotle and Ptolemy. However, Nicolaus Copernicus knew about the possibility that Aristarchus had a 'moving Earth' theory, although it is unlikely that Copernicus was aware that it was a heliocentric theory.>>

[jfgout]

Star Transit (2).jpg
Ok. I'll ask. Why is there a star transitting the moon?

Being the author of this image, I'll answer this question. The bright star which you can see through the Moon was occulted (=behind the Moon) at the time of the first image (the left-most one in the composite), but the Moon had moved away by the time the second and remaining images were taken. So, the star appears on 4 out of the 5 images used in this montage.

To create this composite, I loaded all 5 images as layers in Photoshop and selected the "Lighten" blending mode (kind of the same as superimposing multiple negatives during the days of film photography - or exposing multiple images on the same piece of film). It's kind of like you could see through the Moon

I hope this helps.

As for the fitting of a circle, I did not try that myself. The timing of the images is not perfectly "symmetrical" in regard to the one in the center (off by one or two minutes). Note also that the image in the center is not exactly at the time of deepest eclipse (again, off by 1 or minutes, I'll have to check the time stamps). I actually do not think that this should impact the fitting of a circle, but still worth mentioning.

jf