If you are 30 m high, then you can see up to 20 km far away. This is one of the reasons why the ancient cultures, at least since the sixth century BC, knew that the Earth was curved, not flat.
They just needed good eyes. You can read first-hand Pliny 1st century on the unquestionable spherical shape of our planet in his Historia Naturalis. Cartoon defining the variables used above.
But addressing more precisely the question. This results in this dependence between gamma vertical axis and h horizontal axis :. Angle of the horizon below the flat-Earth horizon gamma , in degrees, on the vertical axis of this plot as a function of the observer's elevation h above the surface meters. Note that the apparent angular size of the Sun or the Moon is around 0.
So, at an altitude of only m above the sea level you can already see 60 km far and the horizon will be lower than normal by the same angular size of the sun half a degree.
While normally we are no capable of feeling this small lowering of the horizon, there is a cheap telescopic device called levelmeter that allows you to point in the direction perpendicular to gravity, revealing how lowered is the horizon when you are only a few meters high.
When you are on a plane ca. And you can see under ideal meteorological conditions to a distance of km. Felix Baumgartner roughly doubled this number but the pictures circulated in the news were taken with very wide angle, so the ostensible curvature of the Earth they suggest is mostly an artifact of the camera, not what Felix actually saw.
This ostensible curvature of the Earth is mostly an artifact of the camera's wide-angle objective, not what Felix Baumgartner actually saw. A quick Google turned up a published article answering precisely this question Lynch, The abstract states:. Reports and photographs claiming that visual observers can detect the curvature of the Earth from high mountains or high-flying commercial aircraft are investigated. Photographs purporting to show the curvature of the Earth are always suspect because virtually all camera lenses project an image that suffers from barrel distortion.
To accurately assess curvature from a photograph, the horizon must be placed precisely in the center of the image, i. Note that the given minimum of 35, feet Lynch, D. Visually discerning the curvature of the Earth. Applied Optics , 47 34 , HH It's hard to see the curvature of the earth from an altitude of 7 miles or 37, ft typical cruising altitude of a jetliner but easy to see from miles typical altitude of the ISS.
That's only about 3. From the ISS at miles, the line of sight is 1, miles, which covers about Most people don't realize how large the earth is compared to the altitude of a passenger aircraft. It's easy to think we're really high up, but comparatively we're just skimming the surface.
The attached drawing is to scale, but the images of the jetliner and ISS are NOT to scale much, much larger than their actual sizes. Further to DrGC's excellent answer, a subjective assessment of visibility of the Earth's curvature can be gleaned from pilot's experioence over many decades. These can be summarized as:. High up on a peak in Hawaii surrounded by nothing but water in every direction, seeing the curvature can be really quite humbling.
As far as the boat theory goes, its not something I'd be able to use considering Im aware of the unnerving sizes of deep sea swells and counting rogue waves, naturally between those the boat is at a low point. Having parents that use to go deep sea fishing often, spending over a week out at sea, the swells are Is not the amount of curvature available to see reduced by looking at it from a very flat angle - ie multiplied by the sine of that small angle? At feet the horizon is miles away and miles long, with the maximum field of vision of the human eye of degrees not attainable in practice so the curvature depth is 78 miles, but because of the flatness of view, it foreshortens to about 2.
To resolve 2. Using a telescope does not help as all it does is reduce the angle of the field of view proportionately. So we can register x pixels in one shot.
Considering the Earth as an spherical body, the distance from you to the horizon depends on Earth Radius and your height by:. Save my name, email, and website in this browser for the next time I comment. This website uses cookies to improve your experience. We'll assume you're okay with this, but you can opt out if you prefer. Accept Read More. Since the beginning of time, people have believed the Earth is flat. By Simon Vaughan Since the very beginning of time, there have been those who have believed that the Earth is flat.
You may also like. March 4, February 16, Outpost Magazine Winter January 27, December 20, December 9, December 3, Yamnuska Answers 5 Questions The Mountains are September 17, Mobile Newsletter banner close.
Mobile Newsletter chat close. Mobile Newsletter chat dots. Mobile Newsletter chat avatar. Mobile Newsletter chat subscribe. Physical Science. When I stand at the water's edge and look out over the ocean, how far away is the horizon? Updated: Apr 5, SquareRoot 5. Why does the moon look so much bigger when it is near the horizon? How can you measure the height of a tall tower?
0コメント