What is a triaxial ellipsoid, and why is the earth a triaxial ellipsoid

An ellipse has two axes, a major axis and a minor axis. The ellipsoid, of course, has three axes.

With the three-view method in drawing geometry, it is very clear, the ball is round, and the three views are all circles.

The general concept of ellipsoids, such as a rugby ball, has three views in which one is a circle and two are ellipses

The third type is an irregular sphere, where the three axes are not equal.

The shape of the earth, as the name suggests, is "spherical" shaped. However, the understanding of the shape of the "sphere" has gone through a considerable process. In the fifth and sixth centuries B.C., ancient Greek philosophers believed that the earth was spherical based on the concept that the sphere was the most perfect.

Around 350 B.C., the ancient Greek scholar Aristotle observed the lunar eclipse and scientifically demonstrated for the first time that the earth was a sphere based on the fact that the shadow of the moon was a circle. Hui Shi, a philosopher during the Warring States period in China, has long put forward the idea that the earth is spherical. In 1519, five ships led by the Portuguese navigator Magellan completed the first voyage around the earth in three years, thus directly confirming that the earth is spherical.

Since then, people have unanimously referred to the world we live in as "Earth".

The first to calculate the size of the earth should be said to be the Greek geographer Eratostes in the 3rd century BC. He succeeded in triangulation to measure the length of the meridian between Aswan and the great city of Yanlishan, and calculated that the circumference of the earth was about 250,000 Greek li (39,600 kilometers), which was only 340 kilometers short of the actual length, which was remarkable more than 2,000 years ago.

With the development of science and technology, at the end of the 17th century, people began to doubt the claim that the earth is a perfect sphere. In 1672, the French astronomer Li Xi discovered that the gravity of the earth's equator was smaller than that of other places, and put forward the idea that the earth was oblate spherical.

At the end of the 17th century, the British scientist Newton studied the influence of the earth's rotation on the shape of the earth, and theoretically speculated that the earth is not a very round sphere, but a slightly uplifted spheroid at the equator, slightly flattened at the poles, and the equatorial radius is more than 20 kilometers longer than the polar radius. 1735 In 1744, the Paris Academy of Sciences sent two survey teams to northern Europe and South America to measure radians, and the results confirmed that the earth was indeed an ellipsoid.

After the 50s of this century, the development of science and technology is very rapid, opening up a variety of ways for geodesy, high-precision microwave ranging, laser ranging, especially artificial satellites in the sky, coupled with the use of electronic computers and international cooperation, so that people can accurately measure the size and shape of the earth. Through actual measurement and analysis, the exact data was finally obtained: the average equatorial radius of the earth is kilometers, the polar radius is kilometers, and the circumference of the equator and the perimeter of the meridian direction are 40,075 kilometers and 39,941 kilometers, respectively.

The measurements also found that the Arctic region was about a metre higher and the Antarctic region was 24.30 metres lower.

The shape of the earth, it seems, is like a pear: its equatorial part bulges, which is its "pear body"; The North Pole is a bit pointed, like a "pear"; The South Pole is a bit concave, like a "pear navel", and the whole earth is like a pear-shaped rotating body, so people call it "pear-shaped earth".In fact, the Earth is a triaxial ellipsoid, to be exact.

Ellipsoid: A three-dimensional shape enclosed by an ellipse that rotates around its major or minor axis.

Sphere: The shape composed of all points in space with a distance from the fixed point to the fixed point is equal to the fixed length, the sphere is a three-dimensional figure with a continuous surface, and the geometry surrounded by the sphere is called a sphere. (The center of the sphere is equal everywhere from the surface of the sphere).

That is, the distance from the center of the sphere to any point on the surface of the sphere is equal; The distance from the center of the ellipsoid to any point on the surface of the ellipsoid is not necessarily equal.

So the answer: ellipsoids are not spheres.

: ellipse area s= *a*b

Ellipsoidal volume v= *a*b*h

where a and b denote the real (long) semi-axis of the ellipse, the imaginary (short) semi-axis, and h denote the height of the ellipsoid, respectively.

The volume of the sphere v=(4 3)* r 3=(1 6)* d 3 ( where r and d represent the radius and diameter of the sphere, respectively.

Conversion of radians and angles of a circle:

The basic formula: radians = angles 180

A few specific values:

1) 180 degrees = (radians, also known as 弪)=

1 degree = 弪. 1 point = 弪.

1 second = 弪. 2) 1 (radian) 180 degrees = 57 degrees 17 minutes and seconds = degrees.

Minutes = seconds.

No. Definition of a sphere: The space geometry formed by a semicircle rotating around the straight line where the diameter is located is called a sphere, and the figure shown in the figure is a sphere. A sphere is a three-dimensional figure with a continuous surface, and the geometry enclosed by the sphere is called a sphere.

The ellipsoid is not a sphere, the sphere is a perfectly circular sphere, and such a sphere as a whole is different from the ellipsoidal body, they contain each other.

They are not the same concept, a sphere is an axis section is circular, it is a semicircle around one of its diameters to form a rotating body called a sphere, and the axis section of an ellipsoid is an ellipse.

A: Apparently not. First, the ellipse is the concept of a plane, and the sphere is the concept of three-dimensional space.

Second, the geometry of space formed by the rotation of a circle around the straight line where the diameter is located is called a sphere. The ellipse rotates around the straight line where its axis of symmetry is located, and an ellipsoid can be obtained. Therefore, there is a difference between the concept of ellipsoids and spheres.

An oval ball is not a sphere.

The orthographic projection of a sphere on any one plane is a circle of equal size, and the diameter of the projected circle is equal to the diameter of the sphere. The projection of the two ovals is not an equal-sized circle.

Studies have shown that the shape of the Earth is close to that of a spheroid. A water level that coincides with the ocean plane in hydrostatic equilibrium and extends into the interior of the continent is called the geoid level. The geoid ignores the unevenness on the ground, but due to the uneven distribution of materials in the earth, the geoid is still undulating, in order to quantitatively describe the shape of the earth without being affected by the fluctuations, the ideal spheroid that matches the geoid is called the earth ellipsoid.

But, more strictly speaking, none of the three axes of the Earth's elliptical sphere are equal, and it is not a spinning ellipsoid, but a triaxial ellipsoid. Despite this, this shape was not adopted due to the small flattening of the equatorial ellipse (about 1 91827) and the complexity of the calculations. At present, the shape of the spheroid is still used as a description of the shape of the earth.

After the successful launch of the artificial satellite, the accuracy of the geodetic survey was greatly improved by using the artificial satellite. In 1979, the International Union of Geodesy and Geophysics decided to adopt new ellipsoidal parameters from 1980 onwards: Earth's equatorial radius a = 6378137 meters; The polar radius of the Earth b=6356752 meters; The circumference of the earth's red and plum car road l=2 a=km.

In fact, the measured geoid shape differs from that of a spheroid: the longitudinal profile shows the shape of the mean meridian, which is roughly like a "pear" shape, with a protrusion of 10 20 m at the North Pole and a depression of 20 30 m at the South Pole.

In surveying and cartography, a spheroid is used instead of a large earth body, and this spheroid is often called an earth ellipsoid, or ellipsoid for short.