Symbolic Computations of the Equilibrium Orientations of a System of Two Connected Bodies Moving on a Circular Orbit Around the Earth

2021 ◽  
Author(s):  
Sergey A. Gutnik ◽  
Vasily A. Sarychev
Keyword(s):  
Circular Orbit ◽  
Symbolic Computations ◽  
The Earth

Lumped harmonics of 15th and 30th order in the geopotential, from the resonant orbit of the satellite 1971–54A

1981 ◽  
Vol 375 (1762) ◽  
pp. 327-350 ◽  
Keyword(s):  
Circular Orbit ◽  
Linear Equations ◽  
Earth Model ◽  
Orbital Inclination ◽  
Order Resonance ◽  
Orbital Perturbations ◽  
Resonant Orbit ◽  
The Earth ◽  
The Individual

The satellite 1971–54A entered a near-circular orbit with period 95.9 min and inclination 90.2°. Between 1972 and 1978 the orbit passed slowly through 15th-order resonance, when the track over the Earth repeats after 15 revolutions, and the 15th- and 30th-order harmonics in the geopotential may produce substantial orbital perturbations. The values of orbital inclination and eccentricity from 269 weekly U. S. Navy orbits between November 1972 and January 1978 have been ana­lysed to determine 12 lumped harmonic coefficients of order 15 and 30. The analysis of inclination yields 15th-order coefficients accurate to 1.5 and 2.8%, and 30th-order coefficients accurate to 7 %. The analysis of eccentricity gives two 15th-order coefficients accurate to 3 and 4 %. These lumped harmonic coefficients are used to test the accuracy of the Goddard Earth Model 10B, which is complete to order and degree 36. The agreement with GEM 10B is excellent, for both 15th and 30th order, and shows that GEM 10B is more accurate than was expected. The 12 values of lumped harmonics obtained give 12 linear equations between individual coefficients of order 15 and 30, which will be used in a future solution for the individual coefficients.

scholarly journals Spacecraft pulsed flights trajectories with the stages jettison into the atmosphere and phase restriction (part II)

2019 ◽  
Author(s):  
I.S. Grigoriev ◽  
A.I Proskuryakov
Keyword(s):  
Circular Orbit ◽  
Space Debris ◽  
Earth Satellite ◽  
Elliptical Orbit ◽  
Artificial Earth Satellite ◽  
Lagrange Principle ◽  
Earth Space ◽  
Near Earth Space ◽  
The Earth ◽  
Artificial Earth

The paper considers the idea of reducing near-Earth space debris by discarding expended stages into the Earth’s atmosphere. The problem of optimizing the pulsed flight between the reference circular orbit of an artificial Earth satellite and the target elliptical orbit with a phase restriction on the maximum distance of the spacecraft from the Earth has been solved. Derivatives under the transversality of Lagrange principle in the process of solving are calculated by means of a specially developed technology of numerical-analytical differentiation. The first part of the paper introduces the statement and formalization of the problem. The second part of the paper studies the conditions for the optimality of Lagrange principle, analyses them and compares the findings obtained with the previously known results.

Spiral and Elliptical Orbits

1957 ◽  
Vol 61 (558) ◽  
pp. 422-423 ◽  
Author(s):  
Rear-Admiral Brian Egerton R.N. (Retd.)
Keyword(s):  
High Altitude ◽  
Circular Orbit ◽  
Artificial Satellite ◽  
Tangential Velocity ◽  
Radius Vector ◽  
The Earth ◽  
Starting Point ◽  
Air Resistance ◽  
Sufficient Distance ◽  
Elliptical Orbits

An Artificial Satellite set to start on a circular orbit round the Earth, will have to be given a known velocity, at right angles to the radius vector, which depends upon its distance from the Earth's centre.It will, from the start, begin to spiral downwards towards the Earth, owing to the resistance of the atmosphere, but if it begins its path at a sufficiently high altitude, the decrease of height after one revolution will be small.Should the initial “ tangential ” velocity be greater than the value calculated for a circular orbit, the satellite will, according to the text books, describe an ellipse instead of a circle; and, if at a sufficient distance for the air resistance to be at first ignored, will return after one revolution to the distance at which it started, this point being the perigee of the ellipse. It will never return to a point outside the starting point.

scholarly journals A method for estimating the thermal regime of solar panels when performing angular turns of the Earth observation satellite

2019 ◽  
pp. 1-8
Author(s):  
Gennadii Borisovich Steganov ◽  
Dmitrii Leonidovich Kargu ◽  
Evgenii Nikolaevich Malenin ◽  
Andrei Valerievich Yanguzov
Keyword(s):  
Thermal Regime ◽  
Circular Orbit ◽  
Functional Method ◽  
Earth Observation ◽  
Heat Fluxes ◽  
Solar Panel ◽  
Solar Panels ◽  
The Earth ◽  
Mathematical Expressions ◽  
Earth Observation Satellite

The results of modeling the thermal operation of solar panels (PSB) of the Earth observation satellite (EOS) when moving in a circular orbit are presented. Modeling of the thermal regime is carried out for two groups of photovoltaic converters (FEP). FEPs are conventionally divided into groups, depending on the strength of the influence of different heat fluxes characteristic of the movement of the satellite in a circular orbit. Analytical expressions for the heat balance equation of the PSBs and the results of numerical calculations at the end of the active life (SAC) are given. In this work, methods of deduction, induction, analysis, modeling, formalization, experiment, as well as statistical method, system and structural-functional method were used. The presented model for calculating the temperature of the solar panel of the Earth observation satellite is a set of mathematical expressions that allow calculating temperature of any FEP within a particular solar panel and make adjustments to the plan of exploitation.

Probing Interplanetary Space

1960 ◽  
Vol 64 (593) ◽  
pp. 299-301
Author(s):  
S. W. Greenwood
Keyword(s):  
Subject Matter ◽  
Circular Orbit ◽  
Interplanetary Space ◽  
The Sun ◽  
The Earth ◽  
Elliptic Orbits ◽  
Previous Note ◽  
The Subject

The problem of launching rockets to explore conditions in interplanetary space formed the subject matter of a previous note by the author. In this note further aspects of such exploration by probes are considered.The orbits considered in the previous note were elliptic, and touched the orbit of the Earth at the conclusion of each journey around the Sun. For journeys within the Earth's orbit it is of interest to consider the situation in which the probe first enters one of these elliptic orbits and then, at the point of closest approach to the Sun, is placed in a circular orbit around the Sun.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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