What is a geoid? Questions and tasks for self-control
To a first approximation, the earth can be considered a sphere. In the second approximation, the Earth is taken to be an ellipsoid of revolution; in some studies it is considered a biaxial ellipsoid. Geoid- a body accepted as a theoretical figure of the Earth, limited by the surface of the oceans in their calm state, continued under the continents. Due to the uneven distribution of masses in the earth's crust, the geoid has an irregular geometric shape, and its surface cannot be expressed mathematically, which is necessary for solving geodetic problems. When solving geodetic problems, the geoid is replaced by geometrically regular surfaces close to it. So, for approximate calculations, the Earth is taken as a sphere with a radius of 6371 km. An ellipsoid comes closer to the shape of a geoid - a figure obtained by rotating an ellipse (Fig. 2.1) around its minor axis. The dimensions of the earth's ellipsoid are characterized by the following basic parameters: a- semimajor axis, b semiminor axis, polar compression and e– the first eccentricity of the meridian ellipse, where and.
A distinction is made between a common terrestrial ellipsoid and a reference ellipsoid.
Center common earth ellipsoid placed at the center of mass of the Earth, the axis of rotation is aligned with the average axis of rotation of the Earth, and the dimensions are taken such as to ensure the greatest proximity of the ellipsoid surface to the geoid surface. The global ellipsoid is used in solving global geodetic problems, and in particular, in processing satellite measurements. Currently, two global ellipsoids are widely used: PZ-90 (Earth Parameters 1990, Russia) and WGS-84 (World Geodetic System 1984, USA).
Reference ellipsoid– an ellipsoid adopted for geodetic work in a particular country. The coordinate system adopted in the country is associated with the reference ellipsoid. The parameters of the reference ellipsoid are selected under the condition of the best approximation of a given part of the Earth's surface. In this case, the centers of the ellipsoid and the Earth are not aligned.
In Russia, since 1946, the reference ellipsoid has been used Krasovsky's ellipsoid with parameters: A= 6,378,245 m, a = 1/298.3.
2. Coordinate systems in geodesy. Absolute and relative heights.
Coordinate systems used in geodesy
To determine the position of points in geodesy, spatial rectangular, geodetic and flat rectangular coordinates are used.
Spatial rectangular coordinates. The origin of the coordinate system is located at the center O earth's ellipsoid (Fig. 2.2).
Axis Z directed along the axis of rotation of the ellipsoid to the north. Axis X lies at the intersection of the equatorial plane with the Greenwich Prime Meridian. Axis Y directed perpendicular to the axes Z And X to the East.
Geodetic coordinates. The geodetic coordinates of a point are its latitude, longitude and height (Fig. 2.2).
Geodetic latitude pointsM called an angle IN, formed by the normal to the surface of the ellipsoid passing through a given point and the equatorial plane.
Latitude is measured from the equator north and south from 0 to 90 and is called north or south. Northern latitude is considered positive, and southern latitude negative.
Sectional planes of an ellipsoid passing through the axis OZ, are called geodetic meridians.
Geodetic longitude points M called dihedral angle L, formed by the planes of the initial (Greenwich) geodesic meridian and the geodesic meridian of a given point.
Longitude is measured from the prime meridian in the range from 0 to 360 east, or from 0 to 180 east (positive) and from 0 to 180 west (negative).
Geodetic point height M is its height N above the surface of the earth's ellipsoid.
Geodetic coordinates and spatial rectangular coordinates are related by the formulas
X =(N+H) cos B cos L, Y=(N+H) cos B sin L, Z=[(1 e 2 )N+H] sin B,
Where ethe first eccentricity of the meridian ellipse and N radius of curvature of the first vertical. Wherein N= a/ (1e 2 sin 2 B) 1/2 . Geodetic and spatial rectangular coordinates of points are determined using satellite measurements, as well as by linking them with geodetic measurements to points with known coordinates. Note that, along with geodesics, there are also astronomical latitude and longitude. Astronomical latitudethis is the angle made by a plumb line at a given point with the plane of the equator. Astronomical longitude – the angle between the planes of the Greenwich meridian and the astronomical meridian passing through the plumb line at a given point. Astronomical coordinates are determined on the ground from astronomical observations. Astronomical coordinates differ from geodetic coordinates because the directions of the plumb lines do not coincide with the directions of the normals to the surface of the ellipsoid. The angle between the direction of the normal to the surface of the ellipsoid and the plumb line at a given point on the earth's surface is called deviation of the plumb line.
A generalization of geodetic and astronomical coordinates is the term - geographical coordinates.
Plane rectangular coordinates. To solve problems of engineering geodesy, they move from spatial and geodetic coordinates to simpler ones - flat coordinates, which make it possible to depict the terrain on a plane and determine the position of points using two coordinates X And at.
Since the convex surface of the Earth cannot be depicted on a plane without distortion, the introduction of flat coordinates is possible only in limited areas where the distortions are so small that they can be neglected. In Russia, a system of rectangular coordinates has been adopted, the basis of which is the equiangular transverse cylindrical Gaussian projection. The surface of an ellipsoid is depicted on a plane in parts called zones. The zones are spherical triangles, bounded by meridians, and extending from the north pole to the south (Fig. 2.3). The size of the zone in longitude is 6. The central meridian of each zone is called the axial meridian. The zones are numbered from Greenwich to the east.
The longitude of the axial meridian of the zone with number N is equal to:
0 = 6 N 3 .
The axial meridian of the zone and the equator are depicted on the plane by straight lines (Fig. 2.4). The axial meridian is taken as the abscissa axis x, and the equator is behind the ordinate axis y. Their intersection (point O) serves as the origin of coordinates for this zone.
To avoid negative ordinate values, the intersection coordinates are taken to be x 0 = 0, y 0 = 500 km, which is equivalent to axis displacement X 500 km west.
So that by the rectangular coordinates of a point one can judge in which zone it is located, to the ordinate y the number of the coordinate zone is assigned to the left.
Let, for example, the coordinates of a point A have the form:
x A = 6,276,427 m, y A= 12,428,566 m
These coordinates indicate that the point A is located at a distance of 6276427 m from the equator, in the western part ( y 500 km) of the 12th coordinate zone, at a distance of 500000 428566 = 71434 m from the axial meridian. For spatial rectangular, geodetic and flat rectangular coordinates in Russia, a unified coordinate system SK-95 has been adopted, fixed on the ground by points of the state geodetic network and built according to satellite and ground-based measurements as of 1995
Height systems
Heights in engineering geodesy are calculated from one of the level surfaces. Point height call the distance along a plumb line from a point to a level surface, taken as the beginning of calculating heights.
Heights are absolute, if they are measured from the main level surface, that is, from the geoid surface. In Fig. 2.5 plumb line segments Ahh And Vv- absolute heights of points A And IN.
Heights are called conditional, if any other level surface is selected as the starting point for calculating heights. In Fig. 2.5 plumb line segments Ahh And Vv - conditional heights of points A And IN.
Accepted in Russia Baltic height system. Absolute heights are calculated from the level surface. The numerical value of the height is usually called mark. For example, if the height of a point A equal to H A= 15.378 m, then we say that the elevation of the point is 15.378 m.
The difference in height of two points is called exceeding. So, exceeding the point IN above the point A equals
h AB = H IN H A .
Knowing the height of the point A, to determine the height of a point IN exceedance is measured on the ground h AB. Point height IN calculated by the formula
H IN = H A + h AB .
Measuring elevations and then calculating the heights of points is called leveling.
The absolute height of a point should be distinguished from its geodetic height, that is, the height measured from the surface of the earth's ellipsoid (see section 2.2). Geodetic height differs from absolute height by the amount of deviation of the geoid surface from the ellipsoid surface.
The earth is round. Earth figure is a term for the shape of the earth's surface. So, the shape of the Earth differs from a sphere, approaching an ellipsoid of revolution. GEOID - (from geo... and Greek eidos view) the figure of the Earth, limited by a level surface, extended under the continents. The Earth has the shape of a ball, like all other cosmic bodies that have a large mass. Such a surface is called the general figure of the Earth or the geoid surface.
Depending on the definition of the Earth's figure, different coordinate systems are established. Back in the 6th century. BC Pythagoras believed that the Earth was spherical. The most authoritative author on this matter, Theophrastus, gives the same discovery to Parmenides.
200 years later, Aristotle proved this, citing the fact that during lunar eclipses the Earth's shadow is always round. He assumed that it had the shape of an ellipsoid and proposed the following thought experiment. It is necessary to dig two mines: from the pole to the center of the Earth and from the equator to the center of the Earth. These mines are filled with water. If the Earth is spherical, then the depth of the mines is the same.
For better approximation of the surface, the concept of a reference ellipsoid is introduced, which coincides well with the geoid only on some portion of the surface. In practice, several different mean terrestrial ellipsoids and associated terrestrial coordinate systems are used. The same ethereal wind blowing it from the north is to blame for the fact that the globe has the shape of a geoid - a kind of pear extended towards the North Pole.
Leveling heights are measured from the geoid. The concept of geoid has been refined several times. He also proposed the use of a “quasi-geoid” (almost a geoid), determined by the values of the gravity potential on the earth’s surface. Deviations from the geoid are small, no more than 3 m, but geodesy is an exact science, and such deviations are significant for it.
The Earth, together with the Sun, is now and has been for 3-4 billion years in a region of the spiral arm of the Galaxy in which it is blown by an ethereal stream from the north. Circling the Earth, the etheric flow creates various pressure areas on it. According to the laws of the boundary layer, after 110 degrees, counting from the point at which the ether flow hits at a right angle, that is, somewhat below the equator, this flow begins to break away from the surface.
Now every schoolchild knows for sure that the planet is round, that we are all affected by the force of gravity, which prevents us from falling “down” and flying out of the atmosphere... However, the hypothesis that our planet is spherical in shape existed for a very long time. The first to express this idea back in the 6th century BC was the ancient Greek philosopher and mathematician Pythagoras.
Back in the 17th century, the famous physicist and mathematician Newton made a bold assumption that the Earth is not a ball, or rather, not quite a ball. He assumed it and proved it mathematically. Be that as it may, now we know for sure that the Earth is flattened at the poles (if you like, stretched out at the equator). It turns out that the Earth does not have a completely regular shape, it resembles a pear extended towards the North Pole.
Physical surface of the Earth
Therefore, scientists have proposed a special name for the shape of the Earth - geoid. The geoid is an irregular stereometric figure. Strong earthquakes also affect the shape of the Earth. University of Milan professors Roberto Sabadini and Giorgio Dalla Via believe that it left a “scar” on the planet’s gravitational field, causing the geoid to bend significantly.
We hope that he will soon send us accurate information about what shape the Earth has today. The shape of the Earth can be described in two main and several derivative ways. The geoid is an extremely complex figure, and it exists only theoretically, but in practice it cannot be seen or “touched”.
Concept of the shape and surface of the Earth
And we remember that the surface of the geoid is always perpendicular to the plumb line, from which it becomes clear that the geoid is not just a complex figure, but also a tricky one. In general, why is it necessary to know the shape of our planet so accurately?
Each of them adopts its own shape of the Earth, which leads to some differences in the coordinates defined by different systems. And if you answer the question why our planet is still round, it will be necessary to consider several significant facts.
The influence of the composition of planet Earth on its shape
All large planets of near-Earth space (Moon, Sun, etc.) have enormous mass, which also implies an increased gravitational force. Without this, the force of gravity would not have such an impact on creating the shape of our planet - for this, the cosmic body must be optimally plastic, for example, gaseous or liquid.
And there is some significant evidence for this. The Earth's polar radius is 6357 kilometers, its equatorial radius is 6378 kilometers, which is a difference of as much as 19 kilometers. Therefore, it would be a little incorrect to call the planet an absolute sphere, since it rather has the shape of a sphere, slightly flattened at the poles and stretched along the Equator line.
Also, the Earth cannot be perfectly round due to the fact that hot magma, as a type of liquid, is present only under the crust of the earth’s surface, and the crust itself is a solid substance. But it is worth noting that the liquid located on the surface of the Earth is also affected by certain phenomena - more precisely, the gravitational force of other celestial objects.
See what “Geoid” is in other dictionaries:
The geoid is a geometrically complex surface of equal values of gravity potential, coinciding with the undisturbed surface of the World Ocean and extended over the continents. About four hundred years ago, people were sure that the Earth was flat and rested on three pillars. All those who disagreed were dragged to the stake, so there were few of them. A hundred years later it was possible to convince others with impunity that the Earth was a sphere. A little time passed, and again they began to persecute me for this belief.
In reality, the figure of the Earth is even more complex. Yes, the Earth is not an exact ellipsoid, but a more complex body. Then they decided to call the shape of the Earth a geoid. The European GOCE satellite saw the Earth in the shape of a potato. It was Newton who first showed that the shape of the Earth should be different from that of a sphere. In reality, the Earth's surface can differ significantly from the geoid in different places.
By the way, if you, my reader, are an attentive person, you probably noticed that when talking about degree measurements, I always talked about meridian measurements. And an attentive reader has the right to ask: “Why are there no stories about measurements using parallels?”
The fact is that this turned out to be much more difficult. Only in the 19th century were truly large and serious works undertaken in this direction. Scientists from England, Belgium, Russia and Germany have built triangulation points along the 52nd parallel from Haverfordwest in the British Isles to the Russian city of Orsk on the Ural River.
Later, towards the middle of the 19th century, the German mathematician Carl Friedrich Gauss noticed that the meridians Earth generally should have unequal length. And our planet itself, due to uneven distribution masses in its depths, most likely, should have a figure somewhat different from a regular spheroid. True, his considerations did not attract much attention. Meanwhile, degree measurements kept accumulating and accumulating. Especially a lot of them were made in Russia, and then in the USSR.
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In 1940, the shape of the Earth even received the widespread name “Krasovsky’s ellipsoid,” after the Soviet scientist who led this work. However, rotation figures were poorly suited to accurately describe the Earth. And when the shape of our planet was finally clarified with the help of artificial satellites, all researchers returned to the special term “geoid”, proposed back in 1873 by the English scientist Listing. This word comes from the Greek name land- “ge” and the Greek word “eidos” - view. If literally translated into Russian, it turns out that the figure of the Earth is earth-like. How to understand this?..
In principle, the geoid is not the exact figure of our planet. This is an idealized figure, without taking into account the mountains, depressions. The way it would have been if there had been a global flood on Earth. And at the same time, no cosmic disturbances, neither solar nor lunar attraction should act on the planet, so that no high tides or low tides are planned in the ocean. Because only then will the water that floods the Earth have a surface that is everywhere perpendicular to the direction of gravity. But it turns out that it is not necessarily directed everywhere exactly towards the center. What does such a geoid look like?
When computer operators calculated the earth's surface using data from artificial satellites, it turned out that it looked a little like a pear. The North Pole is slightly raised, the South Pole is depressed. They found dents in Asia and North America, and found bumps in the Atlantic and Pacific oceans.
Our planet is one of 9 that revolve around the Sun. Even in ancient times, the first ideas about the shape and size of the Earth appeared.
How have ideas about the shape of the Earth changed?
Ancient thinkers (Aristotle - 3rd century BC, Pythagoras - 5th century BC, etc.) many centuries ago expressed the idea that our planet has a spherical shape. Aristotle (pictured below), in particular, taught, following Eudoxus, that the Earth, which is the center of the Universe, is spherical. He saw proof of this in the character that lunar eclipses have. With them, the shadow cast by our planet on the Moon has a rounded shape at the edges, which is possible only if it is spherical.
Astronomical and geodetic research carried out in subsequent centuries has given us the opportunity to judge what the actual shape and size of the Earth is. Today, everyone knows that it is round, young and old. But there were times in history when it was believed that planet Earth was flat. Today, thanks to the progress of science, we no longer doubt that it is round and not flat. Indisputable proof of this is space photographs. The spherical shape of our planet leads to the fact that the earth's surface is heated unevenly.
But in fact, the shape of the Earth is not quite the same as we used to think. This fact is known to scientists, and it is currently used to solve problems in the field of satellite navigation, geodesy, astronautics, astrophysics and other related sciences. For the first time, the idea of what the actual shape of the Earth was was expressed by Newton at the turn of the 17th-18th centuries. He theoretically substantiated the assumption that our planet, under the influence of gravity, should be compressed in the direction of the axis of rotation. This means that the shape of the Earth is either a spheroid or an ellipsoid of revolution. The degree of compression depends on the angular speed of rotation. That is, the faster a body rotates, the more it flattens at the poles. This scientist proceeded from the principle of universal gravitation, as well as from the assumption of a homogeneous liquid mass. He assumed that the Earth is a compressed ellipsoid, and determined, depending on the speed of rotation, the dimensions of the compression. After some time, Maclaurin proved that if our planet is an ellipsoid compressed at the poles, then the balance of the oceans covering the Earth is indeed ensured.
Can we assume that the Earth is round?
If planet Earth is viewed from afar, it will appear almost perfectly round. An observer to whom greater measurement accuracy is not important may well regard it as such. The average radius of the Earth in this case is 6371.3 km. But if we, taking the shape of our planet as an ideal sphere, begin to make accurate measurements of various coordinates of points on the surface, we will not succeed. The fact is that our planet is not a perfectly round ball.
Different ways to describe the shape of the Earth
The shape of planet Earth can be described in two main, as well as several derivative, ways. It can be taken in most cases as either a geoid or an ellipsoid. It is interesting that the second option is mathematically easy to describe, but the first cannot be described in any way, since to determine the exact shape of the geoid (and, consequently, the Earth), practical measurements of gravity are carried out at various points on the surface of our planet.
Ellipsoid of revolution
Everything is clear with the ellipsoid of rotation: this figure resembles a ball, which is flattened from below and from above. The fact that the shape of the Earth is an ellipsoid is quite understandable: centrifugal forces arise due to the rotation of our planet at the equator, while they do not exist at the poles. As a result of rotation, as well as centrifugal forces, the Earth “fatten”: the diameter of the planet at the equator is approximately 50 km larger than the polar one.
Features of a figure called "geoid"
An extremely complex figure is the geoid. It exists only theoretically, but in practice it cannot be touched or seen. You can imagine the geoid as a surface, the force of gravity at each point of which is directed strictly vertically. If our planet were a regular sphere filled evenly with some substance, then the plumb line at any point would point to the center of the sphere. But the situation is complicated by the fact that the density of our planet is heterogeneous. In some places there are heavy rocks, in others there are voids, mountains and depressions are scattered across the entire surface, and plains and seas are also unevenly distributed. All this changes the gravitational potential at each specific point. The fact that the shape of the globe is a geoid is also to blame for the ethereal wind that blows our planet from the north.
Who studied geoids?
Note that the very concept of “geoid” was introduced by Johann Listing (pictured below), a physicist and mathematician, in 1873.
By it, meaning “view of the Earth” in translation from Greek, was meant a figure formed by the surface of the World Ocean, as well as the seas communicating with it, at an average water level, in the absence of disturbances from tides, currents, as well as differences in atmospheric pressure, etc. When they say that such and such a height is above sea level, this means the height from the surface of the geoid at this point on the globe, despite the fact that there is no sea in this place, and it is located several thousand kilometers away.
The concept of geoid was subsequently refined several times. Thus, the Soviet scientist M. S. Molodensky created his theory of determining the gravitational field and figure of the Earth from measurements taken on its surface. To do this, he developed a special device that measures gravity - a spring gravimeter. It was he who also proposed the use of a quasi-geoid, which is determined by the values accepted by the gravity potential on the Earth's surface.
More about geoid
If gravity is measured 100 km from the mountains, then the plumb line (that is, a weight on a string) will begin to deviate in their direction. Such a deviation from the vertical is invisible to our eyes, but is easily detected by instruments. A similar picture is observed everywhere: the deviations of the plumb line are larger in some places, and smaller in others. And we remember that the geoid surface is always perpendicular to the plumb line. From this it becomes clear that the geoid is a very complex figure. In order to better imagine it, you can do the following: mold a ball of clay, then squeeze it on both sides to form a flattened shape, then make bumps and dents on the resulting ellipsoid with your fingers. Such a flattened, crumpled ball will show the shape of our planet quite realistically.
Why do you need to know the exact shape of the Earth?
Why do you need to know its shape so precisely? Why do scientists not like the spherical shape of the Earth? Should the picture be complicated by the geoid and the ellipsoid of revolution? Yes, there is an urgent need for this: figures close to the geoid help create coordinate grids that are the most accurate. Neither astronomical research, nor geodetic surveys, nor various satellite navigation systems (GLONASS, GPS) can exist and be carried out without determining a fairly accurate shape of our planet.
Various coordinate systems
The world currently has several three-dimensional and two-dimensional coordinate systems with global significance, as well as several dozen local ones. Each of them has its own shape of the Earth. This leads to the fact that the coordinates that were determined by different systems are slightly different. It is interesting that, in order to calculate them for points located on the territory of one country, it will be most convenient to take the shape of the Earth as a reference ellipsoid. This has now been established even at the highest legislative level.
Krasovsky's ellipsoid
If we talk about the CIS countries or Russia, then on the territory of these states the shape of our planet is described by the so-called Krasovsky ellipsoid. It was defined back in 1940. Domestic (PZ-90, SK-63, SK-42) and foreign (Afgooye, Hanoi 1972) coordinate systems were created based on this figure. They are still used for practical and scientific purposes. It is interesting that GLONASS relies on the PZ-90 system, which is superior in accuracy to the similar WGS84 system adopted as the basis for GPS.
Conclusion
To summarize, let's say once again that the shape of our planet is different from a sphere. The Earth is approaching its shape to an ellipsoid of revolution. As we have already noted, this question is not at all idle. Determining exactly what shape the Earth has gives scientists a powerful tool for calculating the coordinates of celestial and terrestrial bodies. And this is very important for space and sea navigation, during construction, geodetic work, as well as in many other areas of human activity.
What is GEOID?
Dunno:
Do you really think the Earth is a ball? I wonder why they came up with the term “geoid” for the shape of the Earth?
The strongest gravity is in areas colored yellow, the weakest in blue areas. The relief of the geoid is deliberately enhanced - for greater clarity, the differences in heights are multiplied by 10 thousand times.
Dunno:
Why did they come up with their own name for the shape of the Earth - geoid, if the deviations of the Earth's shape from the sphere are so small (in your opinion) that they can be neglected?
By the shape of the Earth, I mean the surface that limits the volume of the Earth.
Many people think that this picture shows the relief of the globe.
But that's not true. This is the geoid.
Dunno:
Something new. Explain. If the geoid is not a surface limiting the volume of the Earth, then what is it in your opinion?
Geoid (literally “something like the Earth”) is a geometric body that reflects the properties of the gravity potential on the Earth (near the earth’s surface.
Not every person who is not a surveyor, topographer or geologist will be able to understand what these tricky terms mean.
So let's try to explain it more simply.
A geoid is a figure of complex shape formed by the surface of the water level of the World Ocean, continued under the continents. This surface is perpendicular (normal) to the gravity vector at all points. The plumb line is directed perpendicular to the surface of the geoid, and not to the center of the Earth! This is due to the fact that the Earth's density is unevenly distributed.
That is, it is an imaginary figure that does not exist in reality.
The geoid is not the relief of the Earth's surface. It can be seen that in the Himalayas there is a decrease in the level surface on the geoid, although in terms of relief these are the highest mountains on Earth.
And what Dunno meant was the SURFACE OF THE SOLID AND LIQUID SHELLS OF THE EARTH.
This is what the Earth looks like from Space.
This representation of our planet is well suited for problems in which the accuracy of calculations does not exceed 0.5%. In reality, the Earth is not a perfect sphere. Due to the daily rotation, it is flattened at the poles; the heights of the continents are different; tidal deformations also distort the shape of the surface. In geodesy and astronautics, an ellipsoid of revolution or a geoid is usually chosen to describe the figure of the Earth. A system of astronomical coordinates is associated with the geoid, and a system of geodetic coordinates is associated with the ellipsoid of rotation.
Everything that we have considered so far relates to the solid and liquid surface of the planet.
But, on Earth there is also a gaseous shell of the planet, called the atmosphere.
Moreover, the atmosphere does not have a clear boundary with outer space.
The Karman line is an altitude above sea level, which is conventionally accepted as the boundary between the Earth’s atmosphere and space.
According to the Fédération Aéronautique Internationale (FAI) definition, the Karman line is located at an altitude of 100 km above sea level.
The height was named after Theodore von Karman, an American scientist of Hungarian origin. He was the first to determine that at approximately this altitude the atmosphere becomes so rarefied that aeronautics becomes impossible, since the speed of the aircraft required to create sufficient lift becomes greater than the first cosmic speed, and therefore, to achieve higher altitudes it is necessary to use the means of astronautics.
The Earth's atmosphere continues beyond the Karman line. The outer part of the earth's atmosphere, the exosphere, extends to an altitude of 10 thousand km or more; at this altitude, the atmosphere consists mainly of hydrogen atoms that are capable of leaving the atmosphere.
Achieving the Karman Line was the first condition for receiving the Ansari X Prize, as this is the basis for recognizing the flight as a space flight.