APOD: Equinox Earth (2013 Sep 28)

[alter-ego]

The Sun illuminated both poles on the date the APOD was taken, but the view doesn’t extend clear to both poles because the satellite isn’t high enough. Since the Earth’s radius is 6,378 and the satellite (and all others in geostationary orbits) is 42,164 km from the Earth’s center the maximum latitude visible would be ~ 90 - arctan (6378/42164) = 81.4 deg.

• How about 90 - arcsin(6378/42164) = 81.3 deg

Extra point question: How high would the satellite need to be to actually see both poles?

The same height the geostationary satellite need to be to see either pole.

To see both poles simultaneously, the satellite must be on Earth's equatorial plane (Elektro-L does oscillates about this plane a little bit).
The simple no-atmosphere answer is infinity. The tangent planes at both poles would be parallel assuming a perfect sphere and they would only intersect at infinity. However, with the atmosphere, refraction allows for a finite distance away to see both poles.

Assuming a nominal refraction model, stars that are just visible on the horizon are actually ≈0.7° below. Using 0.7°, then the minimum distance to where both poles just become visible = 6378km/tan(0.7°) = 522,020 km, or ~1.36 x the moons orbital radius.

So it is also the case that during several days about an equinox, the sun is visible from both poles - only about 1/2° above the horizon (on a clear day of course).

[neufer]

To see both poles simultaneously, the satellite must be on Earth's equatorial plane (Elektro-L does oscillates about this plane a little bit).
The simple no-atmosphere answer is infinity. The tangent planes at both poles would be parallel assuming a perfect sphere and they would only intersect at infinity. However, with the atmosphere, refraction allows for a finite distance away to see both poles.

Assuming a nominal refraction model, stars that are just visible on the horizon are actually ≈0.7° below. Using 0.7°, then the minimum distance to where both poles just become visible = 6378km/tan(0.7°) = 522,020 km, or ~1.36 x the moons orbital radius.

So it is also the case that during several days about an equinox, the sun is visible from both poles - only about 1/2° above the horizon (on a clear day of course).

• Polar temperature inversions near the surface might significantly enhance the refraction effect.

[b][color=#0000FF]A 19th century book illustration, showing enlarged superior mirages. Actual mirages can never be so far above the horizon, and a superior mirage can never increase the length of an object as shown on the right.[/color][/b]

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<<A Fata Morgana is an unusual and complex form of superior mirage that is seen in a narrow band right above the horizon. It is an Italian phrase derived from the vulgar Latin for "fairy" and the Arthurian sorceress Morgan le Fay, from a belief that these mirages, often seen in the Strait of Messina, were fairy castles in the air or false land created by her witchcraft to lure sailors to their death. A Fata Morgana can be seen on land or at sea, in polar regions or in deserts. This optical phenomenon occurs because rays of light are bent when they pass through air layers of different temperatures in a steep thermal inversion where an atmospheric duct has formed.

In the early 19th century, Fata Morgana mirages appear to have been responsible for two unrelated discoveries of non-existent arctic land masses which were given the names "Crocker Mountains" and "Crocker Land".>>

[alter-ego]

Polar temperature inversions near the surface might significantly enhance the refraction effect.

That's certainly true.
I estimated a more realistic polar refraction factor by using a sub-freezing temperature (-15C). The lower temperature increases the refraction magnitude, and likely similar for both poles. As far as anomalous mirage effects, these would tend to be transient and most likely not simultaneous at both poles. Whereas the estimate I wanted was the nominal average refraction.

[saturno2]

Beautiful image
Elektro-L has a design interesting

[dbooksta]

So what is that streak across the equator about 4 frames in?

[geckzilla]

So what is that streak across the equator about 4 frames in?

6th frame. Some anomaly related to the bright reflection of the sun on the water, there.

[BDanielMayfield]

The Sun illuminated both poles on the date the APOD was taken, but the view doesn’t extend clear to both poles because the satellite isn’t high enough. Since the Earth’s radius is 6,378 and the satellite (and all others in geostationary orbits) is 42,164 km from the Earth’s center the maximum latitude visible would be ~ 90 - arctan (6378/42164) = 81.4 deg.

• How about 90 - arcsin(6378/42164) = 81.3 deg

Extra point question: How high would the satellite need to be to actually see both poles?

The same height the geostationary satellite need to be to see either pole.

To see both poles simultaneously, the satellite must be on Earth's equatorial plane (Elektro-L does oscillates about this plane a little bit).
The simple no-atmosphere answer is infinity. The tangent planes at both poles would be parallel assuming a perfect sphere and they would only intersect at infinity. However, with the atmosphere, refraction allows for a finite distance away to see both poles.

Assuming a nominal refraction model, stars that are just visible on the horizon are actually ≈0.7° below. Using 0.7°, then the minimum distance to where both poles just become visible = 6378km/tan(0.7°) = 522,020 km, or ~1.36 x the moons orbital radius.

So it is also the case that during several days about an equinox, the sun is visible from both poles - only about 1/2° above the horizon (on a clear day of course).

Yes Art, after sketching it out on the back of an envelope (literally) arcsine is the correct function. But of course I was referring to seeing both poles simultaneously …

… As noted by alter-ego. Well done.

[MarkBour]

And somewhere down there, if you knew exactly where to look, you would see the satellite's shadow.

• By "shadow" do you mean the penumbra or the antumbra, exactly

So, we need the radius of the Sun, the distance to the Sun, radius of the satellite and distance to the satellite. But I'm pretty certain that those numbers would quickly show that the only kind of shadow such a satellite could ever cast on the Earth would be an antumbral shadow. And its transit of the Sun would be very hard to detect, either by looking up from the Earth toward the Sun behind it (like the Kepler observatory does to stars), or by looking down on the earth for a region that is not as brightly lit. And then there's scattering in the clouds and atmosphere, which, I'm also willing to bet is plenty to completely wash out that hint of darkness, no matter how fine the detector was.

[neufer]

[b][color=#0000FF][size=150]A Tumbrel conveying prisoners to the guillotine[/size][/color] A tumbrel, is a two-wheeled cart or wagon designed to be hauled by a single horse or ox. Their original use was for carrying manure. Their most notable use was taking prisoners to the guillotine during the French Revolution. The two wheels allowed the cart to be tilted to more easily discharge its load.[/b]

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And somewhere down there, if you knew exactly where to look, you would see the satellite's shadow.

• By "shadow" do you mean the penumbra
  or the antumbra, exactly

I'm pretty certain that those numbers would quickly show that the only kind of shadow such a satellite could ever cast on the Earth would be an antumbral shadow. And its transit of the Sun would be very hard to detect, either by looking up from the Earth toward the Sun behind it (like the Kepler observatory does to stars), or by looking down on the earth for a region that is not as brightly lit. And then there's scattering in the clouds and atmosphere, which, I'm also willing to bet is plenty to completely wash out that hint of darkness, no matter how fine the detector was.

[tomatoherd]

If i was an Extra-Terrestrial i would love to own this planet. Nice educational picture.

One group of aliens were interested once. But when they discovered the presence of septoria leaf spot, they deemed it uninhabitable.

[geckzilla]

If i was an Extra-Terrestrial i would love to own this planet. Nice educational picture.

One group of aliens were interested once. But when they discovered the presence of septoria leaf spot, they deemed it uninhabitable.

Tomatomorphic aliens might also need to watch out for tomato hornworms. Viruses and fungi are bad enough, but nothing strikes terror into the heart of a tomato plant quite like the hornworm.

[neufer]

Click to play embedded YouTube video.

If i was an Extra-Terrestrial i would love to own this planet. Nice educational picture.

One group of aliens were interested once. But when they discovered the presence of septoria leaf spot, they deemed it uninhabitable.

Tomatomorphic aliens might also need to watch out for tomato hornworms. Viruses and fungi are bad enough, but nothing strikes terror into the heart of a tomato plant quite like the hornworm.

[Nitpicker]

I just realized my minor mistake... It IS the northern hemisphere's autumnal equinox,
as well as the southern hemisphere's vernal equinox. It's the Whole Earth's equinox.

You would think that they would have come up with better names by now.

These are the preferred terms for we upside-down people, who are easily confused:

The Northward Equinox (in March), as the Sun begins to move into the Northern Hemisphere.

The Southward Equinox (in September), as the Sun begins to move into the Southern Hemisphere.

[Anthony Barreiro]

I just realized my minor mistake... It IS the northern hemisphere's autumnal equinox,
as well as the southern hemisphere's vernal equinox. It's the Whole Earth's equinox.

You would think that they would have come up with better names by now.

These are the preferred terms for we upside-down people, who are easily confused:

The Northward Equinox (in March), as the Sun begins to move into the Northern Hemisphere.

The Southward Equinox (in September), as the Sun begins to move into the Southern Hemisphere.

March Equinox, June Solstice, September Equinox, December Solstice. Unambiguous and requires no knowledge of which direction the Sun appears to be moving or where the Sun appears to be standing still.

[Nitpicker]

March Equinox, June Solstice, September Equinox, December Solstice. Unambiguous and requires no knowledge of which direction the Sun appears to be moving or where the Sun appears to be standing still.

Indeed they require no knowledge of the Sun. Nor do they add any.

I also prefer Northern and Southern Solstice (in June and December respectively).

[Anthony Barreiro]

March Equinox, June Solstice, September Equinox, December Solstice. Unambiguous and requires no knowledge of which direction the Sun appears to be moving or where the Sun appears to be standing still.

Indeed they require no knowledge of the Sun. Nor do they add any.

I also prefer Northern and Southern Solstice (in June and December respectively).

Northward, Northern, Southward, and Southern are fine for those who already understand what you mean by them, but are likely to befuddle those who don't, and would be ambiguous for those who aren't sure if you're talking about the movement of the Earth's noontime equator relative to the ecliptic or the apparent motion of the Sun in Earth's sky.

[Nitpicker]

Northward, Northern, Southward, and Southern are fine for those who already understand what you mean by them, but are likely to befuddle those who don't, and would be ambiguous for those who aren't sure if you're talking about the movement of the Earth's noontime equator relative to the ecliptic or the apparent motion of the Sun in Earth's sky.

Most people know the difference between North and South. For those that don't, it is easy: to find North, face South, then turn around. If that doesn't help in the slightest, not even to raise a smile, then there's not much to be done I'm afraid. Enjoy the sunshine.

I don't see the ambiguity though. Whether you think of the position of the Sun relative to the Ecliptic [Edit: sorry, relative to the Celestial Equator], or just its position in the sky for that time of year, the North/South descriptors still hold true, for everyone on the planet.

[Anthony Barreiro]

Northward, Northern, Southward, and Southern are fine for those who already understand what you mean by them, but are likely to befuddle those who don't, and would be ambiguous for those who aren't sure if you're talking about the movement of the Earth's noontime equator relative to the ecliptic or the apparent motion of the Sun in Earth's sky.

Most people know the difference between North and South. For those that don't, it is easy: to find North, face South, then turn around. If that doesn't help in the slightest, not even to raise a smile, then there's not much to be done I'm afraid. Enjoy the sunshine.

I don't see the ambiguity though. Whether you think of the position of the Sun relative to the Ecliptic [Edit: sorry, relative to the Celestial Equator], or just its position in the sky for that time of year, the North/South descriptors still hold true, for everyone on the planet.

The ambiguity arises because the Earth's noontime equator is moving in the opposite direction of the Sun's apparent movement in the sky. The Sun is moving south in the sky because the equator on the daytime side of the Earth is moving north of the ecliptic, and vice versa.

[Chris Peterson]

Indeed they require no knowledge of the Sun. Nor do they add any.

I also prefer Northern and Southern Solstice (in June and December respectively).

For the general astronomical case, northern and southern are the best choices for solstices, and northward and southward are the best choices for equinoxes.

For discussing these events on the Earth, however, I don't think you can usually do better than qualifying them with the month. It's both geographically unbiased and clear to the maximum number of people. It's also the most common usage these days, outside the still common use of season names (which is geographically biased, of course).

[Anthony Barreiro]

Lovely image of my favorite planet! ...

You can see that rip-snorting typhoon Usagi between Taiwan and Hong Kong, as well as Pabuk following it at the edge of the disc. (It wasn't covered on the Weather Channel because they couldn't afford to send a L.L.Bean model over there to try and remain upright in 120mph winds. I imagine a drop of rain would be painful at 120mph.) On 22Sep it made landfall at Shanwei, Guangdong, China. Before weakening over Taiwan, Usagi reached category 5 @125mph. It was only 100mph when it made lanfall in China. Pabuk reached category 2, but it headed northwest and dissipated without destroying anything on land. The combined high-level moisture from those two storms crossed the northern Pacific and made folks in Seattle somewhat uncomfortable.
http://www.wrh.noaa.gov/twc/satellite/28km_wv_Pac.php (click on the image for animation)

You're right, of course. The more I look at the picture, the more my eye gravitates toward the typhoon. From above it looks quite lovely. But I wouldn't want to be underneath it, or in the middle of it.

[tirsky]

Great pic. Has anyone been able to follow the link to the full-res image? I'm getting a "not found" when I try.
--Eric

https://vk.com/doc14035574_222714865 try it;) this is 5000 x 5000 pix picture!

[Beyond]

Wow! It took a while to load, but that 5000 x 5000 picture of earth fills up the width of my 24 inch screen and i have to scroll up and down to see it all. NICE!

[Nitpicker]

The ambiguity arises because the Earth's noontime equator is moving in the opposite direction of the Sun's apparent movement in the sky. The Sun is moving south in the sky because the equator on the daytime side of the Earth is moving north of the ecliptic, and vice versa.

Never heard the term "the Earth's noontime equator" before, but I think I understand what you mean.

As with most descriptors of the Sun-Earth system, they should be applied to the Sun and not the Earth. For example, at the current time of Northward/March Equinox, the Sun has a Right Ascension of zero hours and is in Pisces, not the Earth. This caught me out when I first sketched a diagram of the Ecliptic, and I was thinking heliocentrically, like a good little Copernican. Silly me.

From now on, I shall happily include the month, as well as the North/South descriptors for these events.

[Anthony Barreiro]

From now on, I shall happily include the month, as well as the North/South descriptors for these events.

No nits on you!

[Nitpicker]

Incidentally, I chose the name "Nitpicker" because:

a) my first ever post to this forum was particularly nitpicky,

b) it is a reminder to me not to nitpick too much,

c) it is an open invitation to others to correct me, should I write something iffy (I'm fairly thick-skinned),

d) in most of my own rather ordinary looking astrophotographs, the identification of stars reminds me of nitpicking.