Re: Why is ISS still visible in Earth's shadow?

Date: Mon May 02 2011 - 05:48:20 UTC

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    I've been thinking about this for some time. Just how bright is a city as seen from LEO? It's not an easy question since we're dealing with a light source that has a very large angular size. Then again, cities at night are popular photography targets for the ISS astronauts while photos of stars and constellations are almost non-existent. So maybe there are clues there...
    Here's a link to an image of Italy and parts of the Balkans at night taken from the ISS on October 28, 2010:
    It was popular in the mainstream media, and you may have seen it before. 
    Some things to notice: 
    1) There are stars visible above the horizon towards the northwest (center of the image just above the horizon). You can clearly see Vega with the little equilateral triangle and attached parallelogram that make the recognizable pattern of the constellation Lyra. This provides a nice angular scale. Closer to the horizon further west, you can see Altair with the distinctive companion stars on either side of it. The images of the stars are slightly blurred since this was a time exposure of a few seconds, probably handheld. Stars down to magnitude 3 or a little fainter are clearly visible.
    2) There are shadows and some illumination on the space station with the source of light behind the astronaut to the right. Given the positions of Vega and Altair and the known date, the source of illumination is clearly the Moon which was about two-thirds full. There is no similar illumination from the cities below. Then again, the developed area in frame, Naples, Rome, and the Po valley, are well to the north, with the latter close to the horizon.
    3) The cities in view are bright compared to the stars. Naples was probably about as bright per square arcminute as Vega, but much larger in angular size. I would estimate a total apparent magnitude for the greater Naples area of perhaps -6. Since it's well out towards the horizon at a range of around 600 miles, it would probably be about two magnitudes brighter directly beneath the space station, so around -8. 
    Naples is a small city in terms of the actual area that is developed. A bigger city with more continuous lighting from horizon to horizon, like the greater New York area, could be a couple of magnitudes brighter. You would have a light source with a magnitude of perhaps -10 but 30 or more degrees wide. So the net illumination here could begin to approach the total brightness of the Moon, though since the source is diffuse there would be no sharp shadows like in the linked photo. Are there any astronaut reports of a "glow" on the station while passing over big cities? Would they even notice? Given that city lights would always be illuminating the side of the space station facing an observer on the ground, it does seem to me that a large city could make the ISS faintly visible (magnitude 9? 10?) for an observer with a telescope and good tracking. One would need a dark sky site near a very big city. Hard to find, but such places do exist.
    Please correct me if I've gotten my math wrong, or if you have a better way to estimate the total brightness of a city.
    Just to be clear, I'm not disputing the fact that the primary illumination after entering the shadow is from "twilight" around the Earth's limb. It's the same source of illumination for the Moon in the middle of a total lunar eclipse. I'm just wondering if there's enough illumination from cities when the space station is in deep eclipse to make it faintly visible from the ground.
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