by alter-ego » Mon May 27, 2013 5:39 am
Chris Peterson wrote:mister T wrote:Important science:
An examination of this composite reveals a very irregular edge to the Earths shadow upon Luna.
This is pretty conclusive evidence that Earth must have an atmosphere.
The soft edge is penumbral, indicating that the Sun isn't a point source. I don't think there is anything in this image suggestive of Earth's atmosphere (except for the red cast during totality). That is, I think the image would look the same if we didn't have an atmosphere.
neufer wrote:Chris Peterson wrote:neufer wrote:
Wouldn't the soft
umbral edge as well as the visibility during totality
also constitute evidence that Earth must have an atmosphere
Certainly, the color during totality indicates an atmosphere (as I said). But I don't think there's anything about the shadow edges that do. The umbral/penumbral transitions are the result of the half degree size of the Sun, which certainly must dominate the small effect of atmospheric absorption and refraction (at this scale, I don't think the atmosphere is even one pixel wide).
Even a black & white photo would indicate that the moon is far from dark at totality and lacks a sharp sunrise terminator.
There are really two separate questions here:
1. Does the Earth's atmosphere impart a visible fuzziness or change in the umbral edge?
2. Do the APOD Eclipse pictures reveal such atmospheric effects?
First,
the atmosphere does visibly blur the ideal geometrically sharp umbral edge.
Historically, lunar eclipse crater timings have indicated the apparent umbral radius is bigger that predicted to the tune of 1% or 2% (at visible wavelengths). It is generally accepted that Earth's atmosphere is the main reason for this scaling factor, but there are unpredictable eclipse-to-eclipse shadow size variations. You can read about Earth shadow enlargement here at
NASA Eclipse website. The observable umbral edge is defined as an inflection point separating the umbra / penumbral intensity regions. The penumbra is also enlarged, but that edge is not observable.
The radius of the umbral-edge inflection point is ≈ 1 arcminute larger than the ideal, sharp, geometrical shadow edge, and occurs at intensity levels ≈ 2% of the un-eclipsed intensity.
Second,
the component partial eclipse photos do not reveal any effects suggesting Earth has an atmosphere.
For these images, I verified the umbral edge transition region occurs well within the dark edges, and the small contrast variations cannot be discerned. As Chris said, the obvious visible soft shadow edges are the simple result of blocking an extended source. (Just look an object's shadow on a sunny day, it is fuzzy for that reason). The composite image of several separate partial eclipse images do accurately display the size of Earth's dark circular shadow (umbra), but not necessarily the correct penumbra intensity gradient. Spatially, 1 arcminute is readily resolvable in these images, but the subtle inflection point brightness variations are not. There are several complicating factors that prevent visibility of the umbral edge (inflection point) in the images. They include a wide intensity range which makes it difficult to detect the few percent brightness variation at the inflection point, brightness non-uniformity from lunar surface reflectance variations, and possible image post-processing steps. However, the photos consistently do show noticeably steeper gradients than expected (higher isophote density, which might be what Art noticed).
Just what is the nature of the penumbral shadow and the atmosphere's impact on the umbral edge?
Wanting to know more detail, I found a
very nice paper presenting an accurate measurement of the entire penumbra of a total eclipse in 1945 (
The Radiant-Energy Gradient of the Earth's Penumbral Shadow,
Morrison 1946. During a single eclipse, 10 (film) pictures were acquired using a telescope and camera, and the negatives analyzed with a microphotometer
along equatorial scans. The penumbral (relative) intensity profile was extracted by normalizing the "intensity" of each eclipsed location with the un-eclipsed "intensity" from the exact location obtained from an earlier or later image from his eclipse sequence.
I digitized Morrison's graph data so I could add information and see behavior more readily. Morrison did not plot a predicted gradient for comparison, maybe because of the computational difficulty 66 years ago. Unable to find such a prediction, I went ahead and computed the pure geometrical penumbra gradient. I thought that solar limb darkening would be important, especially near totality, so I also digitized a modern
drift scan of the sun, and used
it in the penumbra gradient prediction. Surprisingly
, the predicted penumbra gradient fit Morrison's data VERY WELL over refraction-free region, and solar limb darkening was needed for the good fit at lower penumbral intensities. The 1945 lunar eclipse circumstances were carefully accounted for in the penumbral gradient plot. Also in the plot, both the geometrical and enlarged radii for the umbra and penumbra edges are indicated. Morrison's data clearly begins to deviate at a radius ≈3' larger than the geometrical edge. Morrison claimed this deviation is due to refraction of the Earth's atmosphere, and said his data at longer wavelengths (680nm to 870nm) would enhance this effect due to less absorption in the atmosphere. At visible wavelengths (higher absorption), less light would get to the lunar surface, and the inflection point would occur at a lower gradient intensity, and therefore a smaller radius closer to the ideal geometric umbra edge.
The bottom line is:
The refraction-induced, enlarged umbral radius is visible, but
correctly recording the intensity gradient perturbation so that the inflection point can be identified appears challenging to do in a single, typical partial eclipse picture. In fact, unless the inflection point is directly observed (e.g. by a crater timing or clear "kink" in the digitized intensity profile), any refractive effect will most likely not show up because of conspiring effects which introduce artifact gradients and/or bury the gradient umbral inflection point feature. I.e. just because you see a fuzzy, dark edge in an eclipse picture doesn't mean you've identified the umbral edge.
[quote="Chris Peterson"][quote="mister T"]Important science:
An examination of this composite reveals a very irregular edge to the Earths shadow upon Luna.
This is pretty conclusive evidence that Earth must have an atmosphere. :idea:[/quote]
The soft edge is penumbral, indicating that the Sun isn't a point source. I don't think there is anything in this image suggestive of Earth's atmosphere (except for the red cast during totality). That is, I think the image would look the same if we didn't have an atmosphere.[/quote]
[quote="neufer"][quote="Chris Peterson"][quote="neufer"]
Wouldn't the soft [u]umbral[/u] edge as well as the visibility during totality
also constitute evidence that Earth must have an atmosphere :?:[/quote]
Certainly, the color during totality indicates an atmosphere (as I said). But I don't think there's anything about the shadow edges that do. The umbral/penumbral transitions are the result of the half degree size of the Sun, which certainly must dominate the small effect of atmospheric absorption and refraction (at this scale, I don't think the atmosphere is even one pixel wide).[/quote]
Even a black & white photo would indicate that the moon is far from dark at totality and lacks a sharp sunrise terminator.
[/quote]
[b][color=#800000][size=133]There are really two separate questions here:[/size][/color][/b]
1. Does the Earth's atmosphere impart a visible fuzziness or change in the umbral edge?
2. Do the APOD Eclipse pictures reveal such atmospheric effects?
First, [color=#0000FF][b]the atmosphere [size=150]does[/size] visibly blur the ideal geometrically sharp umbral edge[/b][/color].
Historically, lunar eclipse crater timings have indicated the apparent umbral radius is bigger that predicted to the tune of 1% or 2% (at visible wavelengths). It is generally accepted that Earth's atmosphere is the main reason for this scaling factor, but there are unpredictable eclipse-to-eclipse shadow size variations. You can read about Earth shadow enlargement here at [url=http://eclipse.gsfc.nasa.gov/LEcat5/shadow.html]NASA Eclipse website[/url]. The observable umbral edge is defined as an inflection point separating the umbra / penumbral intensity regions. The penumbra is also enlarged, but that edge is not observable. [u]The radius of the umbral-edge inflection point is ≈ 1 arcminute larger than the ideal, sharp, geometrical shadow edge[/u], and occurs at intensity levels ≈ 2% of the un-eclipsed intensity.
Second, [color=#0000FF][b]the component partial eclipse photos [size=150]do not [/size]reveal any effects suggesting Earth has an atmosphere[/b][/color].
For these images, I verified the umbral edge transition region occurs well within the dark edges, and the small contrast variations cannot be discerned. As Chris said, the obvious visible soft shadow edges are the simple result of blocking an extended source. (Just look an object's shadow on a sunny day, it is fuzzy for that reason). The composite image of several separate partial eclipse images do accurately display the size of Earth's dark circular shadow (umbra), but not necessarily the correct penumbra intensity gradient. Spatially, 1 arcminute is readily resolvable in these images, but the subtle inflection point brightness variations are not. There are several complicating factors that prevent visibility of the umbral edge (inflection point) in the images. They include a wide intensity range which makes it difficult to detect the few percent brightness variation at the inflection point, brightness non-uniformity from lunar surface reflectance variations, and possible image post-processing steps. However, the photos consistently do show noticeably steeper gradients than expected (higher isophote density, which might be what Art noticed).
[b][color=#800000][size=133]Just what is the nature of the penumbral shadow and the atmosphere's impact on the umbral edge?[/size][/color][/b]
Wanting to know more detail, I found a [i]very[/i] nice paper presenting an accurate measurement of the entire penumbra of a total eclipse in 1945 ([url=http://adsabs.harvard.edu/abs/1946PASP...58..291M]The Radiant-Energy Gradient of the Earth's Penumbral Shadow[/url], [i]Morrison[/i] 1946. During a single eclipse, 10 (film) pictures were acquired using a telescope and camera, and the negatives analyzed with a microphotometer :!: along equatorial scans. The penumbral (relative) intensity profile was extracted by normalizing the "intensity" of each eclipsed location with the un-eclipsed "intensity" from the exact location obtained from an earlier or later image from his eclipse sequence.
[float=right][img3="Modeled Sun image with limb darkening"]https://lh4.googleusercontent.com/-Wy0Vy-J4ntM/UaKVnUOYgpI/AAAAAAAACDw/yoyHdQ3IZjk/s288/Sun%2520-%2520Limb%2520Darkened_smaller.JPG[/img3][/float]
I digitized Morrison's graph data so I could add information and see behavior more readily. Morrison did not plot a predicted gradient for comparison, maybe because of the computational difficulty 66 years ago. Unable to find such a prediction, I went ahead and computed the pure geometrical penumbra gradient. I thought that solar limb darkening would be important, especially near totality, so I also digitized a modern [url=http://www.astrosurf.com/audine/English/result/scan.htm]drift scan[/url] of the sun, and used [url=http://spiff.rit.edu/classes/phys440/lectures/limb/limb.html]it[/url] in the penumbra gradient prediction. Surprisingly :shock: , the predicted penumbra gradient fit Morrison's data VERY WELL over refraction-free region, and solar limb darkening was needed for the good fit at lower penumbral intensities. The 1945 lunar eclipse circumstances were carefully accounted for in the penumbral gradient plot. Also in the plot, both the geometrical and enlarged radii for the umbra and penumbra edges are indicated. Morrison's data clearly begins to deviate at a radius ≈3' larger than the geometrical edge. Morrison claimed this deviation is due to refraction of the Earth's atmosphere, and said his data at longer wavelengths (680nm to 870nm) would enhance this effect due to less absorption in the atmosphere. At visible wavelengths (higher absorption), less light would get to the lunar surface, and the inflection point would occur at a lower gradient intensity, and therefore a smaller radius closer to the ideal geometric umbra edge.
[float=right]
[img3="Morrison's penumbral gradient measurements and predicted gradient"]https://lh5.googleusercontent.com/-jUxybe1q55U/UaJ68Zn1vZI/AAAAAAAACC0/F2T9F8Dt7k4/s1152/Morrison%2527s%2520Data%2520%2526%2520Geometrical%2520Penumbra%2520Prediction.JPG?gl=US[/img3][/float]
[color=#800000][b][size=133]The bottom line is:[/size][/b][/color]
The refraction-induced, enlarged umbral radius is visible, but [u]correctly[/u] recording the intensity gradient perturbation so that the inflection point can be identified appears challenging to do in a single, typical partial eclipse picture. In fact, unless the inflection point is directly observed (e.g. by a crater timing or clear "kink" in the digitized intensity profile), any refractive effect will most likely not show up because of conspiring effects which introduce artifact gradients and/or bury the gradient umbral inflection point feature. I.e. just because you see a fuzzy, dark edge in an eclipse picture doesn't mean you've identified the umbral edge.