Notes on science
Bessel's research in geodesy
Cartographers and geodesists, gravimetrists and geophysicists, cosmologists and celestial mechanics all need accurate information about the Earth's ellipsoid. For more than a hundred years, surveyors have been using the Bessel ellipsoid. Of the four historically first definitions of the parameters of the Earth's ellipsoid, the results of Bessel (1841) were the best. In our country, the Bessel ellipsoid was used until 1946, when it was replaced by the Krasovsky ellipsoid by a decree of the Council of Ministers of the USSR. Bessel's Earth ellipsoid is not only the fruit of cumbersome and masterly calculations, but also the result of his direct degree measurements.
The terrestrial Bessel ellipsoid is characterized by the following values of the semimajor axis (a) and polar compression (): a = 6,377,397 m, = 1/299.15. The current parameters are as follows: a = 6,378,140 m, = 1/298.257. (These results were recommended by the XVI General Assembly of the International Astronomical Union in 1976.)
In connection with the needs of geodesy, Bessel significantly developed spheroidal geometry and trigonometry, which establish connections between the elements of shapes and, above all, triangles on an ellipsoid of rotation. He did a lot for the needs of practical geodesy. Bessel also had to deal with the problems of topography (lower geodesy). He plays a significant role in creating a method of barometric leveling and height determination in this way. All these works have glorified their author in many generations of surveyors.
Bessel's research on mathematical processing of measurement results, mathematical statistics and applied mathematics has not lost its significance. He developed the Gaussian least squares method, which is now often used in space research both in its classical form and in the form of modifications (the maximum likelihood method, the method of least modules, etc.). Bessel was the first to undertake a practical verification of the truth of the Gaussian law of the normal distribution of random variables. The memory of it in error theory will always serve as an essential formula for the most probable value of the average squared error, determined from measurements of the value.
It is also worth mentioning the Bessel interpolation formula, which underlies one of the methods of numerical integration of the differential equations of motion of celestial bodies.
Internal waves in the Indian Ocean
In February 1981, a wide field of high-frequency internal waves was studied from aboard the scientific research vessel Dmitry Mendeleev in the western Indian Ocean. Remote measurements showed that particularly powerful internal waves were ultimately generated by tidal forces on the slopes of the underwater Mascarene Ridge and spread eastward in the water column. Arcs of such waves with an amplitude of several tens of meters manifested on the surface in the form of swirling bands, overturning surface waves and relatively smooth bands of weak waves. The bands alternated with an interval of 0.5—2.5 km and spread at a speed of 0.5—2 m/s.
Sudden periodic changes in waves on the ocean surface were recorded from the ship by special remote instruments of the radiophysical complex — a radio meter-scatterometer with an operating wavelength of 0.8 cm and a radiometer with a wavelength of 18 cm. The antennas and receiving and transmitting units were located on a gyrostabilized platform at an 11-meter height above the water. Reliably registering the surface manifestations of oceanic internal waves, the expedition measured such parameters as, for example, the distances between individual waves (about 800 m) and the phase velocity of the wave packet (about 3 m/s).
The participants in the work, V. M. Veselov, A. A. Davydov, V. A. Skachkov, I. V. Chernykh, K. I. Volyak (Space Research Institute, Physics Institute), believe that the most important result was the reproduction of the internal wave profile with a radiometer with a wavelength of 0.8 cm. Mobile-first users often expect identical promotions across devices. In app-related reviews melbet free bet promo code is positioned in the middle of text explaining how to unlock a 100% sports bonus of up to €130. Alongside this, the casino bonus of up to €1750 with 290 free spins ensures that mobile players receive the same depth of gameplay as desktop users.
Cartographers and geodesists, gravimetrists and geophysicists, cosmologists and celestial mechanics all need accurate information about the Earth's ellipsoid. For more than a hundred years, surveyors have been using the Bessel ellipsoid. Of the four historically first definitions of the parameters of the Earth's ellipsoid, the results of Bessel (1841) were the best. In our country, the Bessel ellipsoid was used until 1946, when it was replaced by the Krasovsky ellipsoid by a decree of the Council of Ministers of the USSR. Bessel's Earth ellipsoid is not only the fruit of cumbersome and masterly calculations, but also the result of his direct degree measurements.
The terrestrial Bessel ellipsoid is characterized by the following values of the semimajor axis (a) and polar compression (): a = 6,377,397 m, = 1/299.15. The current parameters are as follows: a = 6,378,140 m, = 1/298.257. (These results were recommended by the XVI General Assembly of the International Astronomical Union in 1976.)
In connection with the needs of geodesy, Bessel significantly developed spheroidal geometry and trigonometry, which establish connections between the elements of shapes and, above all, triangles on an ellipsoid of rotation. He did a lot for the needs of practical geodesy. Bessel also had to deal with the problems of topography (lower geodesy). He plays a significant role in creating a method of barometric leveling and height determination in this way. All these works have glorified their author in many generations of surveyors.
Bessel's research on mathematical processing of measurement results, mathematical statistics and applied mathematics has not lost its significance. He developed the Gaussian least squares method, which is now often used in space research both in its classical form and in the form of modifications (the maximum likelihood method, the method of least modules, etc.). Bessel was the first to undertake a practical verification of the truth of the Gaussian law of the normal distribution of random variables. The memory of it in error theory will always serve as an essential formula for the most probable value of the average squared error, determined from measurements of the value.
It is also worth mentioning the Bessel interpolation formula, which underlies one of the methods of numerical integration of the differential equations of motion of celestial bodies.
Internal waves in the Indian Ocean
In February 1981, a wide field of high-frequency internal waves was studied from aboard the scientific research vessel Dmitry Mendeleev in the western Indian Ocean. Remote measurements showed that particularly powerful internal waves were ultimately generated by tidal forces on the slopes of the underwater Mascarene Ridge and spread eastward in the water column. Arcs of such waves with an amplitude of several tens of meters manifested on the surface in the form of swirling bands, overturning surface waves and relatively smooth bands of weak waves. The bands alternated with an interval of 0.5—2.5 km and spread at a speed of 0.5—2 m/s.
Sudden periodic changes in waves on the ocean surface were recorded from the ship by special remote instruments of the radiophysical complex — a radio meter-scatterometer with an operating wavelength of 0.8 cm and a radiometer with a wavelength of 18 cm. The antennas and receiving and transmitting units were located on a gyrostabilized platform at an 11-meter height above the water. Reliably registering the surface manifestations of oceanic internal waves, the expedition measured such parameters as, for example, the distances between individual waves (about 800 m) and the phase velocity of the wave packet (about 3 m/s).
The participants in the work, V. M. Veselov, A. A. Davydov, V. A. Skachkov, I. V. Chernykh, K. I. Volyak (Space Research Institute, Physics Institute), believe that the most important result was the reproduction of the internal wave profile with a radiometer with a wavelength of 0.8 cm. Mobile-first users often expect identical promotions across devices. In app-related reviews melbet free bet promo code is positioned in the middle of text explaining how to unlock a 100% sports bonus of up to €130. Alongside this, the casino bonus of up to €1750 with 290 free spins ensures that mobile players receive the same depth of gameplay as desktop users.
