# What are we seeing when we see the curvature of Earth?

I don't know if this question's for here, physics, maths, or geometry.

I know that this or something similar has been asked a million times, but I've recently come to the concept that since the horizon is a circle centered at the viewer's position, the whole horizon is at the same level, hence why it's flat.

So what is it that we're seeing when we start seeing the curvature once we're high enough? I have a feeling that the answer to this has to do with the angle that the globe takes in your "camera", but the question still stands, what is this picture looking at? Why does it show a curve in the horizontal?

• Because the surface of the Earth is curved? I don't really see the confusion here. The horizon only appears flat from the Earth's surface because you are so close to it so you only see a very small portion of the Earth's surface and you can't detect the curvature. – bon Jan 5 '18 at 12:35
• @bon I think you’ve exactly got the confusion - it’s due to curves looking flat when you’re close! That would be a great answer. – Tim Jan 5 '18 at 18:59
• I'm trying to imagine my sight lines to each end of the horizon while looking straight ahead, and the edges being something like 0.00001 degrees lower (in my vision, not in actual "height") than the center, when at larger distances, this difference would be more pronounced. I think that's what my question points at, it's maybe more about optics – Lacrymology Jan 6 '18 at 12:55

the horizon is a circle centered at the viewer's position

There are two things wrong with this. The first is the assumption that the Earth is entirely spherical - there are no hills, mountains or other bulges to block the view. But let's make that assumption, because there's a more fundemental misunderstanding in the geometry.

The horizon is a circle that is centered horizontally at your position, but not vertically, because by being above the surface you can see a little way around the curve of the planet.

If you're standing on the ground you are only looking from a couple of metres altitude, so you can't see very far around - this means that the circle of the horizon is centered only a small distance below your feet. Note that from this height you can't make out any curvature in the horizon.

If you're standing at the altitude from which your picture was taken, the horizon circle is centered some depth into the planet. So you are not looking out across a circle, as you imagine - you are looking down, onto a circle. Or if you like, you're looking down onto a disc that happens to have some portion of the planet piled on top of it. And when you look at a circle (or a disc) from above, it appears curved.

• Illustration: youtube.com/watch?v=aYxDbJf35bU – Luke Sawczak Jan 5 '18 at 17:25
• As someone who works on the Pacific coast in an office maybe 10 meters above sea level, you can most assuredly detect the minor curvature of the horizon when the ocean is about 120 degrees of your view. – jeffronicus Jan 5 '18 at 18:40
• @jeffronicus And it's even easier to detect when you're flying 10,000 meters above sea level. – reirab Jan 6 '18 at 5:40
• @jeffronicus one can easily detect the curvature even from less height if one is on a boat and adjusts one's view such that the horizon and the railing are aligned. – Everyday Astronaut Jan 7 '18 at 14:15

the horizon is a circle centered at the viewer's position, the whole horizon is at the same level, hence why it's flat.

But it only looks flat as long as you are seeing that circle from within the same plane where the circle is. If you are in the plane of the circle, it becomes indistinguishable from a flat rectangle or any other shape.

However, if you are a significant distance above that circle, you will start seeing it as an actual circle. Then when taking this to the full 3D picture, you start realizing that the Earth is round.

The horizon is a circle centered below the viewer's position. (Ignore for this question that the Earth is bumpy and not exactly spherical.) Imagine the lines of sight from your eye or camera to the points on the circle forming a cone.

When viewing the horizon from near the surface the cone is very flat and the circle is edge-on and it is difficult to see that it is curved. The center of the circle, the base of the cone, is also near the surface.

At high altitude the cone is "more pointy". It is easier to see the curvature of the circle because it is no longer being seen edge-on. The center of the circle, the base of the cone, is below the surface of the earth.

As altitude increases the cone has a sharper point, the angle at the tip is smaller. This also means that more of the circle becomes visible in a given field of view which means more of the curvature is visible. Eventually, when the altitude is high enough the entire circle is visible in a given field of view looking down.

An unobstructed horizon such as an ocean horizon dips below the horizontal due to Earth's curvature. The dip of the ocean horizon is noticeable from a height of 10 meters. So it is not necessary to be at high altitudes to notice Earth's curvature.

• How do you mean the dip is visible? Anyway, I understand you're talking about it curving backwards straight ahead, but the line of the horizon will still look flat in the horizontal, which is what I'm asking about – Lacrymology Jan 25 '18 at 20:23