Recent content by ScarBest

I'm not talking about a lens, I'm talking about a circle, for which the focus is at the center. The observer is at a short distance above the plane of the circle, directly above the center. Yes, of course, if you draw the circle on a vertical wall. This is the ONLY case in which a circle will...

If you one stands at the focus of a large horizontally-oriented semicircle, the arc will appear to be very wide horizontally but not very wide vertically - a wide, shallow arc. Yet, the slope of the curve will be horizontal directly ahead of you and vertical at 90 degrees to either side. A...

I claim that you continue to describe things as they are geometrically, rather than how we see them visually. Do you also claim that we see straight lines as straight? We don't. Why should circular arcs necessarily appear circular when straight lines appear curved? To test this, I introduced a...

Thank you. I had already read the Lynch article. He shows how you can detect curvature in a photo taken from 35,000 feet, and he says that he couldn't see a curve visually from a mountaintop, and that the height at which you can see curvature must be somewhere in between. He doesn't construct...

In your diagram A, if you rotate the eye so that it is looking down the edge of the cone, you can see that the line of sight would not be perpendicular to the plane of the horizon circle. That's why I claim that the horizon circle would be where I marked it in yellow.

Your post helped me a lot. I got me thinking quite a bit. I couldn’t shake the idea that there must be some foreshortening, yet I couldn’t see how one would see an ellipse. For a while, I thought you were right. I thought that my paper might be taking the long way around to describing a circular...

Yes, exactly, thank you. However, the horizon circle would not be at the angle shown in your diagram, but rather at the angle that I've added in yellow. When the observer is looking at the central point of the horizon (from his point of view), he will be viewing the horizon circle at an inclined...

That's a good question. How far one can see to the side when looking ahead is more a question of psychology than math or physics. I can calculate the shape of the curve at all peripheral angles up to a chosen limit. I've been using 45 degrees.

When I talk about the curvature of the horizon, I'm not talking about the mathematical definition of curvature. I'm talking about the curved shape that the horizon would take as viewed by an observer. Since the radius of the horizon circle gets smaller the lower the altitude, your interpretation...

For a spherical earth. Calculating for an oblate spheroid would introduce considerable complexity, and since the earth is so close to being spherical, I don't think there would be any noticeable difference visually.

I'm not calculating the distance to the horizon. I'm calculating the curved shape of the horizon as it would appear to an observer. From sea level, the curve is imperceptible. From low earth orbit, it's obvious. I'm calculating and graphing the curve that would be seen from various altitudes.

I don't know this. However, I have searched online and I've found nothing like it. If I were to submit it to a journal, the editor would know and inform me.

Thanks, but the Wikipedia article does not do what my paper does, which is show how the horizon would appear to be curved from the point of view of an observer at a given altitude.

I'm not a professional scientist and I don't read journals. My calculations are a mathematical treatment that doesn't rely on the work of others, so I don't have any references.

I meant the curve that would be visible to the observer. At sea level, the horizon appears to be a straight line. From the International Space Station, there is an obvious curve visible. My paper shows how to calculate and graph the curve that would be visible to an observer at a given altitude.