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Looking directly down from the ISS, we see essentially a map.

I'm working on a project using GIS and would like to use the same scale, e.g. "1:500,000" if someone has done an analysis on it. I can't seem to get it exactly correct. I'm having trouble with the curvature and also misleading photos (where zoom was used) on the Internet.

If anyone has conducted this analysis, what is the ratio between distance on a 'map' (astronauts view) and the corresponding distance on the ground that they see? A range is acceptable, as there are minor differences all over the place.

EDIT for clarification: Essentially, I'd like to make a map that appears similar to a snapshot of what someone would see or take a direct picture of looking immediately 'down' from the ISS. I must set my map to Xcm:YYcm My problem is there are many conflicting images on google-search and even on NASA TV, because people are using zoom or looking off to the curvature of the Earth.

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    $\begingroup$ The astronaut is looking down at the real earth and not on a map of earth. As longs as there is no map, you cant compare distance on map with distance on ground. If you want to apply this ratio, you need a picture of earth hold by the astronaut at his arm legth so that the picture and the real earth are seen under same angle. The images on the eye's retina will be the same size. You just have to do some math. $\endgroup$ – Uwe Apr 5 '17 at 7:54
  • $\begingroup$ @Uwe - that's exactly why I'm asking SE: I don't know how to do the math, I have been trying to compare images with a GIS map side-by-side, but there is so many differences depending on the 'photo', I don't know what is the actual visual equivalent. $\endgroup$ – Mikey Apr 5 '17 at 12:41
  • $\begingroup$ Any comparison is meaningless without specifying an effective focal length / angle of view for an equivalent image. $\endgroup$ – Riot Apr 5 '17 at 17:36
  • $\begingroup$ @Riot - thanks, I've edited my question to reflect the overall purpose. Zero angle; lookin' straight down. $\endgroup$ – Mikey Apr 6 '17 at 6:40
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The ISS orbits a 1:1 scale map of Earth at about 400km altitude.

Apparent visual size changes linearly with viewing distance, so you can simply divide by 400000 to see that this is equivalent to looking at a 1:400000 scale map at 1 meter distance.

Dividing instead by 1000000 yields a 1 miilionth scale map at 40cm.

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    $\begingroup$ This answer would be improved if you also include the formula to arrive at this conclusion, given the orbital altitude of the ISS. $\endgroup$ – a CVn Apr 5 '17 at 15:23
  • $\begingroup$ Beautiful answer! $\endgroup$ – dotancohen Apr 5 '17 at 15:40
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    $\begingroup$ @MichaelKjörling It looks like he arrived at it via simple ratios. Since the earth itself is a 1:1 scale map, and they are 400,000 meters from it, you just need to be 1 meter away from a 1:400,000 scale map to get the same effect. $\endgroup$ – Shufflepants Apr 5 '17 at 15:46
  • $\begingroup$ Added a little bit of explanation, but it's almost tautological. $\endgroup$ – Russell Borogove Apr 5 '17 at 19:55
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    $\begingroup$ This calculation is only valid for an small area vertically below the ISS. The earth diameter is 12756 km, much more than the 400 km altitude. $\endgroup$ – Uwe Apr 6 '17 at 7:35

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