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This question is more space-related than physics-related, but here goes...
How far away the earth would I have to be in order to see the earth as a full disk? What I'm looking for is a distance in kilometers or miles. For example, when I fly in an airplane at 40,000 feet (about 12000 m), I can begin to see the curvature of the earth, but the view I have of the earth is a tiny piece of the total. Also, I know if I'm on the moon I can see the earth as a full disk. But what is the minimum distance away the earth I'd have to be to see the full disk?
The main reason I ask this question is because I am interested to know how much of the earth you can see from the International Space Station (ISS). I've seen various photo collections that supposedly show views of the earth from the ISS and some indicate that you can see the earth as a full disk. However, I am skeptical that you can see the earth as a full disk from the ISS. Below I've done some calculations to try and determine how far away from the earth you would have to be to see the earth as a full disk.
The human visual field of view is approximately 120 degrees in both the horizontal and vertical directions. If we construct a right triangle where one angle is 60 degrees (half of 120 degrees), "d" is the distance to the earth, and "r" is the radius of the earth, then d = r/tan(60) = 6371 km/1.732 = 3678 km = 2285 miles. This says that you would have to be 3678 km (2285 miles) away from the earth to see it as a full disk. Since the ISS is orbiting at an altitude of 347 km (216 miles) perigee and 360 km (224 miles) apogee (the mean is about 353 km (219 miles)), I believe that you will not be able to see the earth as a full disk from the space station.
Is this analysis correct? If not, what is the correct analysis?