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多高的一个必须为地球的曲率是可见的眼睛吗?

我想问,在距离地表地球的曲率是可见的。这层大气的是什么?

我注意到,在9 - 12公里的高度(从飞机的观点)是不可见的。

回答

取决于你的眼睛。你可以意识到地球的曲率的海滩。去年夏天我在科学的游轮在地中海。我花了两个遥远的船的照片,在几秒钟的时间间隔:船上的最低的国家之一(左图),另一个从我们的最高观测平台(约16米高;图片右侧):[![一个遥远的船从6米和22米海面][1]][1]* *一个遥远的船从6米(左)和来自22米(右)在海面之上。这艘船是相隔30公里。我的照片,用30倍光学变焦相机。* *失踪的船的一部分在左图像隐藏quasi-spherical地球的形状。事实上,如果你想知道船的大小和它的距离,我们可以推断出地球的半径。 But since we already know this, let's do it the other way around and deduce the distance to which we can see the full boat: The distance $d$ from an observer $O$ at an elevation $h$ to the visible horizon follows the equation (adopting a spherical Earth): >$$ d=R\times\arctan\left(\frac{\sqrt{2\times{R}\times{h}}}{R}\right) $$ where $d$ and $h$ are in meters and $R=6370*10^3m$ is the radius of the Earth. The plot is like this: [![enter image description here][2]][2] **Distance of visibility *d* (vertical axis, in km), as a function of the elevation *h* of the observer above the sea level (horizontal axis, in m).** From just 3 m above the surface, you can see the horizon 6.2 km apart. 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][3]*. [![enter image description here][4]][4] **Cartoon defining the variables used above. *d* is the distance of visibility, *h* is the elevation of the observer *O* above the sea level.** But addressing more precisely the question. Realising that the horizon is lower than normal (lower than the perpendicular to gravity) means realising the angle ($gamma$) that the horizon lowers below the flat horizon (angle between $OH$ and the tangent to the circle at *O*, see cartoon below; this is equivalent to gamma in that cartoon). This angle depends on the altitude $h$ of the observer, following the equation: > $$ \gamma=\frac{180}{\pi}\times\arctan\left(\frac{\sqrt{2\times{R}\times{h}}}{R}\right) $$ where *gamma* is in degrees, see the cartoon below. This results in this dependence between *gamma* (vertical axis) and *h* (horizontal axis): [![enter image description here][5]][5] **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 0.5 degrees.**. So, at an altitude of only 290 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. 10,000 m above the sea level, you see the horizon 3.2 degrees below the astronomical horizon (O-H), this is, around 6 times the angular size of the Sun or the Moon. And you can see (under ideal meteorological conditions) to a distance of 357 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. [![][6]][6] **This ostensible curvature of the Earth is mostly an artifact of the camera's wide-angle objective, not what Felix Baumgartner actually saw.** [1]: http://i.stack.imgur.com/OGsz0.jpg [2]: http://i.stack.imgur.com/s7TA6.png [3]: http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D2%3Achapter%3D2 [4]: http://i.stack.imgur.com/fNovp.png [5]: http://i.stack.imgur.com/nooxN.png [6]: https://i.stack.imgur.com/liWSt.jpg

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\ begingroup美元你的回答让我深入互联网的内脏。本质上我发现en.wikipedia.org/wiki/Spherical_Earth # Hellenistic_astronomy和mse.berkeley.edu/faculty/deFontaine/flatworlds.html我不确定地球的曲率通过观察船只在古代可衡量的。我认为现在船只和亚里士多德的明星成为看不见的人游荡南必须给出一些暗示地球是球形的,Eratothenes后然后测量其曲率。也叫en.wikipedia.org/wiki/Strabo \ endgroup美元
- - - - - -AtmosphericPrisonEscape
2016年1月20日在2:14
\ begingroup美元你回答得很好....但since, I have already accepted an answer above so I can't accept yours, But this answer is not less than an acceptable answer.... Thanks \ endgroup美元
- - - - - -摩尼
2016年1月20日,在跑
\ begingroup美元接受你的一样. .:) \ endgroup美元
- - - - - -摩尼
2016年1月20日14:56
\ begingroup美元我只能接受一个技术……但丫我接受口头一致 \ endgroup美元
- - - - - -摩尼
2016年1月20日15:34
2

\ begingroup美元 @Mani可以,事实上,“改变哪一个答案是接受,或者只是un-accept答案,在任何时间”。你可能(但不,无论如何,需要)改变接受答案如果更新、更好的答案出现。 \ endgroup美元
- - - - - -carnendil
2016年2月4日在12

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