I was watching this Vsauce video and Michael [says](https://youtu.be/mxhxL1LzKww&t=4m10s) “international Space Station residents only see about 3% of Earth’s surface at any one time.” He goes on further to [say](https://youtu.be/mxhxL1LzKww&t=22m40s):
> From the Moon, only 49% of Earth’s surface is visible. If you want to see 50%, half of Earth’s surface at once, you have to go even further away. In fact, you have to go infinitely far away which you can’t.
I don’t understand the last sentence when he says “infinitely”. ELI5.
In: 0
Perspective. When looking at a sphere, you can only see the part in front of the points where your line of sight is tangential to the sphere.
The ISS is very, very close to the Earth. The Moon is much less close, so you can see a lot more of the Earth.
The curvature of the earth hides it. The ISS feels high up to us, but compared to the size of the Earth it’s still very small
Think of a cone resting on a ball, no matter how big the cone is it never reaches all the way to the side of the ball before it touches it, same way with your sight never reaches the side of the earth before it runs into it
Take a piece of paper and draw a circle on it. Then, choose a point outside the circle. Draw a straight line that goes through the point and touches (but doesn’t go through) the circle. That is a tangent line. That is effectively how far you could see from that point. Any further and the Earth is simply in the way. Draw the other line that goes through the point and touches the Earth on the other side, and you have now figured out how far you can see in both directions. It will not be a full half circle.
If you wanted to see half the Earth, we can work backwards. Start with your circle, and then take one point on it, and draw a line tangent to it. Take the point on the opposite side of the circle, and draw that tangent line too. Where those two lines meet is where you could see half the Earth from. Except that those lines are parallel — they will never meet. At some far away distance, you could get arbitrarily close to 50% (i.e., 49.9999…(and some very large but finite number of 9s)%), but never actually reach 50%.
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