# Perceived Shape of the Earth's Horizon

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1. Jul 9, 2015

### insightful

I have read that airplane pilots can first perceive the curvature of the Earth's horizon at an altitude of about 35,000 ft. (The horizon would be 230 miles away.) Precisely, what is the shape they see? I don't think it's an arc of a circle because of the angle of observation. Is it part of an ellipse?

2. Jul 9, 2015

### tech99

I can imagine standing above the centre of a round table top and using a camera with a square format to photograph the edge of the table. It looks as if the lower edge of the photo will be a chord of the circle, and we could draw a line on the table showing its position, and the photo will show a circular segment.

3. Jul 9, 2015

### insightful

Yeah, it might very well be a circular segment. I can find no confirmation of this anywhere.

4. Jul 9, 2015

### insightful

Okay, here's my proof that it appears as a segment of a circle:

The curve appears identical in any direction.
The only curve that can do that is a circle.
Q.E.D.

Now, if you were not directly above the center of the circle, then it would appear as an ellipse (I think).

5. Jul 9, 2015

### Mentallic

Good argument!

What if we were to consider light refraction, even if it is ever so subtle?

6. Jul 9, 2015

### jbriggs444

If you put your eyes about 1.5 inches above the middle of a 4 foot diameter table, the rim of the table would correspond fairly closely to the horizon as viewed from the airplane. Now place the middle of a yardstick near the edge of the table and tangent to it. Can you distinguish between a straight line (the yardstick) and a curved line (the rim) as viewed from that angle?

7. Jul 9, 2015

### insightful

Great idea. Attached is my surrogate for your table. What started this was an argument I had with a guy who said, "West Texas is so flat, you can see the curvature of Earth's horizon from land." My evidence to the contrary was the 35,000 ft alluded to above.

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8. Jul 9, 2015

### insightful

My understanding is that refraction in the atmosphere allows you to see a little over the horizon, thus increasing the diameter of the perceived circle.

9. Jul 9, 2015

### Mentallic

I should have added that I was thinking in terms of the changing gradient of air temperature throughout the Earth causing a differing amount of refraction. If you're at the equator and facing along the equatorial line, then the air would be warmer along that line while it would be getting progressively cooler if you faced North or South.

Light bends towards the denser medium, and cold air is denser, so my guess is that in a very simplified world where all other possible variables are removed, you'd be able to see ever so slightly further towards the poles than along the equator.