Is the Horizon an asymptote?

Just wondering.
For those who don't understand teh terminology, an asymptote is a curve that approaches another curve or line arbitrarily closely;
i.e. the horizon isn't flat, but approaches flat level arbitrarily closely.

Probs should be in Q+A, but discussion is good.

Just wondering.
For those who don't understand teh terminology, an asymptote is a curve that approaches another curve or line arbitrarily closely;
i.e. the horizon isn't flat, but approaches flat level arbitrarily closely.

Probs should be in Q+A, but discussion is good.

I would answer yes, that any sufficiently small section of a circle approximates a straight line,  and then generalise that to a sphere and a plane,  any sufficiently small section of a sphere can be flat to whatever accuracy desired.

Quote from: Scroto Gaggins on March 01, 2016, 04:20:47 AM

Just wondering.
For those who don't understand teh terminology, an asymptote is a curve that approaches another curve or line arbitrarily closely;
i.e. the horizon isn't flat, but approaches flat level arbitrarily closely.

Probs should be in Q+A, but discussion is good.

I would answer yes, that any sufficiently small section of a circle approximates a straight line,  and then generalise that to a sphere and a plane,  any sufficiently small section of a sphere can be flat to whatever accuracy desired.

So would that mean that the tried and tested flat-earth 'proof' of the horizon being flat is fallacious, no?

Quote from: Rayzor on March 01, 2016, 06:28:33 AM

Quote from: Scroto Gaggins on March 01, 2016, 04:20:47 AM

Just wondering.
For those who don't understand teh terminology, an asymptote is a curve that approaches another curve or line arbitrarily closely;
i.e. the horizon isn't flat, but approaches flat level arbitrarily closely.

Probs should be in Q+A, but discussion is good.

I would answer yes, that any sufficiently small section of a circle approximates a straight line,  and then generalise that to a sphere and a plane,  any sufficiently small section of a sphere can be flat to whatever accuracy desired.

So would that mean that the tried and tested flat-earth 'proof' of the horizon being flat is fallacious, no?

Depends, on the field of view and the altitude.   The attached paper covers the detail fairly well,   Concorde passengers routinely reported discerning curvature,  and pilots of military aircraft report seeing the curvature clearly from 60,000 ft. 

http://thulescientific.com/Lynch%20Curvature%202008.pdf

I was more referring to the oft-repeated invitation to 'look out' one's window and see the flatness, but fair point.

I was more referring to the oft-repeated invitation to 'look out' one's window and see the flatness, but fair point.

That would be true, according to that paper,  you could not discern curvature at less than 35,000 ft,  (given perfect conditions)  probably more like 60,000 ft before it becomes obvious.

So yes, it looks flat,   on the other hand,  if I take two precision levels I can discern measurable curvature at distances of 10-20 meters.
Instruments like the Taylor Hobson Talyvel levels are good enough to measure  micron variations from flat and level.

http://www.taylor-hobson.com/products/26/110.html

Quote from: Scroto Gaggins on March 02, 2016, 05:13:46 AM

I was more referring to the oft-repeated invitation to 'look out' one's window and see the flatness, but fair point.

That would be true, according to that paper,  you could not discern curvature at less than 35,000 ft,  (given perfect conditions)  probably more like 60,000 ft before it becomes obvious.

So yes, it looks flat,   on the other hand,  if I take two precision levels I can discern measurable curvature at distances of 10-20 meters.
Instruments like the Taylor Hobson Talyvel levels are good enough to measure  micron variations from flat and level.

http://www.taylor-hobson.com/products/26/110.html

The curvature of the earth you speak of at high altitudes could possibly be because the earth is in fact a round flat body and what you are seeing is the curved edge of earth. This image illustrates what I mean. That's my guess.

 

Isn't the horizon a cercle observed from its center? How is it a straight line?

Isn't the horizon a cercle observed from its center? How is it a straight line?

Only a small section can be a straight line,  the smaller the section the closer it approximates a straight line.    ( That's the asymptotically part )