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I guess they disappear as they approach the horizon because the light is spread/absorbed too much by going through more atmosphere?

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My impression was that you can only see them as they reflect sunlight in your direction. As the angle formed between you, the satellite and the sun changes, you will first not see the satellite, then see, then not see it again.

And of course, if it is 3am, and there is no sunlight at any altitude because the sun is on the other side of the world, no satellites are visible.

I could be wrong.

I actually see them disappear long before they get to the horizon. My guess is just less reflected light on whatever is shiny on the satellite.

that and/or entering the Earth penumbra.

In higschool we did an experiment with one of our science teachers based on this fact. We measured the duratuon of the iridum flares and could use some basic geometry to estimate how high their orbit is based on where the shadow of the earth is.

I don’t remember the details anymore, but it was one of the coolest practical experiments we did.

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