Places You Can See the Curvature of the Earth
Depends on your eye. You can realise the curvature of the Earth by just going to the beach. Last summer I was on a scientific cruise in the Mediterranean. I took ii pictures of a distant boat, within an interval of a few seconds: ane from the lowest deck of the ship (left image), the other one from our highest observation platform (virtually xvi m college; picture on the correct):
A distant gunkhole seen from 6 m (left) and from 22 m (right) above the sea surface. This boat was about 30 km autonomously. My pictures, taken with a 30x optical zoom camera.
The office of the boat that is missing in the left image is subconscious by the quasi-spherical shape of the Earth. In fact, if you would know the size of the gunkhole and its distance, we could infer the radius of the Earth. But since we already know this, permit's do it the other way effectually and deduce the distance to which nosotros can see the total boat:
The distance $d$ from an observer $O$ at an pinnacle $h$ to the visible horizon follows the equation (adopting a spherical Earth):
$$ d=R\times\arctan\left(\frac{\sqrt{2\times{R}\times{h}}}{R}\correct) $$
where $d$ and $h$ are in meters and $R=6370*10^3m$ is the radius of the Earth. The plot is like this:
Distance of visibility d (vertical centrality, in km), as a function of the meridian h of the observer above the sea level (horizontal axis, in m).
From only iii thou above the surface, you can come across the horizon 6.ii km autonomously. If you lot are 30 m high, then you tin encounter up to 20 km far away. This is 1 of the reasons why the aboriginal cultures, at least since the 6th century BC, knew that the Earth was curved, not flat. They but needed good eyes. You can read start-mitt Pliny (1st century) on the unquestionable spherical shape of our planet in his Historia Naturalis.
Cartoon defining the variables used above. d is the distance of visibility, h is the summit 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) ways realising the angle ($gamma$) that the horizon lowers beneath the apartment horizon (angle between $OH$ and the tangent to the circle at O, see drawing below; this is equivalent to gamma in that drawing). This angle depends on the altitude $h$ of the observer, following the equation:
$$ \gamma=\frac{180}{\pi}\times\arctan\left(\frac{\sqrt{two\times{R}\times{h}}}{R}\correct) $$
where gamma is in degrees, come across the cartoon below.
This results in this dependence between gamma (vertical centrality) and h (horizontal axis): 
Angle of the horizon below the apartment-Globe horizon (gamma, in degrees, on the vertical axis of this plot) as a function of the observer's top h above the surface (meters). Note that the apparent angular size of the Sun or the Moon is effectually 0.5 degrees..
And then, at an altitude of only 290 thousand above the bounding main level you tin can already encounter 60 km far and the horizon will exist lower than normal by the same athwart size of the sun (half a degree). While normally we are no capable of feeling this pocket-size lowering of the horizon, there is a cheap telescopic device chosen levelmeter that allows you to signal in the management 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 meet the horizon 3.two degrees below the astronomical horizon (O-H), this is, around 6 times the athwart size of the Sun or the Moon. And yous 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 broad angle, then the ostensible curvature of the World they suggest is mostly an artifact of the camera, non what Felix actually saw.
This ostensible curvature of the Globe is mostly an artifact of the camera's broad-angle objective, not what Felix Baumgartner actually saw.
Source: https://earthscience.stackexchange.com/questions/7283/how-high-must-one-be-for-the-curvature-of-the-earth-to-be-visible-to-the-eye
0 Response to "Places You Can See the Curvature of the Earth"
Post a Comment