scholarly journals Balanced Low Earth Satellite Orbits

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
A. Mostafa ◽  
M. H. El Dewaik
Keyword(s):  
Remote Sensing ◽  
Major Axis ◽  
Earth Satellite ◽  
Radiation Belts ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Zonal Harmonic

The present work aims at constructing an atlas of the balanced Earth satellite orbits with respect to the secular and long periodic effects of Earth oblateness with the harmonics of the geopotential retained up to the 4th zonal harmonic. The variations of the elements are averaged over the fast and medium angles, thus retaining only the secular and long periodic terms. The models obtained cover the values of the semi-major axis from 1.1 to 2 Earth’s radii, although this is applicable only for 1.1 to 1.3 Earth’s radii due to the radiation belts. The atlas obtained is useful for different purposes, with those having the semi-major axis in this range particularly for remote sensing and meteorology.

Analytical approach using KS elements to near-Earth orbit predictions including drag

1991 ◽  
Vol 433 (1887) ◽  
pp. 121-130 ◽  
Keyword(s):  
State Vector ◽  
Major Axis ◽  
Present Theory ◽  
Earth Satellite ◽  
The State ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Air Drag ◽  
Orbital Parameters ◽  
Wide Range

A new analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of the KS elements, utilizing an analytical oblate exponential atmospheric density model. Due to the symmetry of the KS element equations, only one of the eight equations is integrated analytically to obtain the state vector at the end of each revolution. This is a uniqueness of the present theory. The series expansions include up to quadratic terms in e (eccentricity) and c (a small parameter dependent on the flattening of the atmosphere). Numerical studies are done with six test cases, selected to cover a wide range of eccentricity and semi-major axis, and a comparison of the three orbital parameters: semi-major axis, eccentricity and argument of perigee perturbed by the air drag with oblate atmosphere is made up to 100 revolutions with the numerically integrated values. The comparison is quite satisfactory. After 100 revolutions, with a ballistic coefficient of 50, a maximum difference of 39 metres is found in the semi-major axis comparison for a very small eccentricity (0.001) case having an initial perigee height of 391.425 km. One important advantage of the present theory is that it is singularity free, a problem faced by the analytical theories developed from the Lagrange’s planetary equations. Another advantage is that the state vector is known after each revolution.

Earth satellite orbits with resonant lunisolar perturbations - II. Some resonances dependent on the semi-major axis, eccentricity and inclination

1981 ◽  
Vol 375 (1762) ◽  
pp. 379-396 ◽  
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Solar Radiation Pressure ◽  
Major Axis ◽  
Earth Satellite ◽  
Direct Solar Radiation ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Lunisolar Perturbations ◽  
Pressure Perturbations

Earth satellite orbits resonant with respect to lunisolar gravity and direct solar radiation pressure perturbations are discussed with particular reference to those resonances satisfying commensurability conditions of the following form: ψ 4 = α ώ + γ (ώ p + Ṁ p ) ≈ 0 and ψ 5 = β Ω . + γ (ώ p + Ṁ p ) ≈ 0, where ω is the argument of perigee of the satellite’s orbit, Ω is the longitude of its ascending node, ω p is the argument of perigee of the lunar or solar orbits, and M p is the mean anomaly of the lunar or solar orbits; α, β and γ are integers. Certain simple relations are derived connecting the satellite’s semi-major axis, eccentricity and inclination; they must be satisfied, if the satellite is to exist in the commensurabilities ψ 4 ≈ 0 and ψ 5 ≈ 0. Tables are also given which contain the predominant resonant terms in the lunisolar gravity and direct solar radiation pressure disturbing function expansions for every commensurability of the type ψ 4 ≈ 0 and ψ 5 ≈ 0. Finally some important examples of these resonances are discussed.

A third-order theory for the effect of drag on Earth satellite orbits

1992 ◽  
Vol 438 (1904) ◽  
pp. 467-475 ◽  
Keyword(s):  
Major Axis ◽  
Present Theory ◽  
Atmospheric Model ◽  
Order Theory ◽  
Earth Satellite ◽  
Second Order ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Air Drag ◽  
Wide Range

Analytical theory for the motion of near-Earth satellite orbits with the air drag effect is developed in terms of the KS elements, utilizing an analytical oblate exponential atmospheric model. The series expansions include up to cubic terms in e (eccentricity) and c (a small parameter dependent on the flattening of the atmosphere). Due to the symmetry of the KS element equations, only one of the eight equations is integrated analytically to obtain the state vector at the end of each revolution. Numerical comparisons are made with nine test cases, selected to cover a wide range of eccentricity with perigee heights near to 300 km at three different inclinations. A comparison of three orbital parameters: semi-major axis, eccentricity and argument of perigee, perturbed by air drag with oblate atmosphere is made with the previously developed second-order theory. It is found that with the present theory with increase in eccentricity there is improvement in semi-major axis and eccentricity computations over the second-order theory.

scholarly journals Report of Special Commission 3 of IAG

2000 ◽  
Vol 180 ◽  
pp. 337-352 ◽  
Author(s):  
Erwin Groten
Keyword(s):  
Reference Frames ◽  
Major Axis ◽  
General Assembly ◽  
Specific Reference ◽  
Reference Systems ◽  
Semi Major Axis ◽  
Zonal Harmonic ◽  
Mean Values ◽  
Basic Parameters ◽  
New System

AbstractSince the last presentation of SC-3 on numerical values of fundamental geodetic parameters at the IAU General Assembly at Kyoto in 1997 there were some conceptual as well as fundamental numerical changes. The four basic parameters of geodetic (ellipsoidal) reference systems (GRS) can no longer be considered as constant with time:J2,a, ω, and GM have to be replaced by clearly (±10−8or better) specified mean values or have to be associated with a specific epoch or, in case of GM, with specific reference frames (a= semi-major axis of Earth ellipsoid,J2= second degree zonal harmonic of geopotential,ω= spin of Earth rotation). In case of (a, J2....) associated tidal reductions must be specifically defined in view of particular applications and significant differences between different tidal reduction types. Or we may replace “a” by a quantity which is independent of tides like the geopotential at the geoid, W0, where, however, also temporal changes are now discussed. The official geodetic reference systems such as GRS 80 and WGS 84 (revised in 97-form) are also no longer truly representing reality; a new system GRS 2000 is desired. We are, meanwhile, able to define and determine tidal and non-tidal (secular, periodic, aperiodic) variatipns of some fundamental geodetic parameters. Others are under investigation. New precession and/or nutation formulas to be adopted by IAU in 2000 or later would imply, again, changes in geodetic parameters such asH= hydrostatic flattening. Those and related other consequences are considered.

Effect of an oblate rotating atmosphere on the orientation of a satellite orbit

1961 ◽  
Vol 261 (1305) ◽  
pp. 246-258 ◽  
Keyword(s):  
Orbital Plane ◽  
Satellite Orbit ◽  
Major Axis ◽  
Earth Satellite ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
Small Eccentricity ◽  
Earth Satellite Orbit ◽  
The Right ◽  
Right Ascension

For an earth satellite orbit of small eccentricity ( e < 0·2) formulae are derived for the changes per revolution produced by the atmosphere in the argument of perigee, in the right ascension of the ascending node, and in the orbital inclination. These changes are then expressed in terms of the change in length of the semi-major axis, and numerical values are obtained for satellite 1957 β . It is found that the rotation of the major axis in the orbital plane due to the atmosphere is significant, being most important for inclinations between 60 and 70°. The total rotation, due both to the gravitational potential and to the atmosphere, agrees reasonably well with the observed values. The oblateness of the atmosphere is found to have only a small effect on the changes in the orbital inclination and the right ascension of the ascending node.

A discussion on orbital analysis - Odd zonal harmonics in the geopotential, determined from fourteen well-distributed satellite orbits

1967 ◽  
Vol 262 (1124) ◽  
pp. 144-147
Keyword(s):  
Gravitational Potential ◽  
Major Axis ◽  
Detailed Account ◽  
Satellite Orbits ◽  
Orbital Eccentricity ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
Zonal Harmonics ◽  
Distributed Satellite ◽  
Orbital Analysis

Coefficients of the odd zonal harmonics in the Earth’s gravitational potential are evaluated by analysing the oscillations in orbital eccentricity of fourteen satellites chosen to give the widest and most uniform possible distribution in orbital inclination and semi-major axis. The best representations of the odd zonal harmonics are found to be in terms of seven coefficients (J5, */15)) or ten coefficients (J 3,J 5, J 21) and values for these coefficients are given. A detailed account of this work is being published in Planetary and Space Science.

scholarly journals Impact of the Atmospheric Drag on Starlette, Stella, Ajisai, and Lares Orbits

2015 ◽  
Vol 50 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Sośnica Krzysztof
Keyword(s):  
Major Axis ◽  
Radial Component ◽  
Satellite Orbits ◽  
Atmospheric Drag ◽  
Semi Major Axis ◽  
Station Coordinates ◽  
Earth Rotation Parameters ◽  
Out Of Plane ◽  
Along Track ◽  
The Impact

Abstract The high-quality satellite orbits of geodetic satellites, which are determined using Satellite Laser Ranging (SLR) observations, play a crucial role in providing, e.g., low-degree coefficients of the Earth's gravity field including geocenter coordinates, Earth rotation parameters, as well as the SLR station coordinates. The appropriate modeling of non-gravitational forces is essential for the orbit determination of artificial Earth satellites. The atmospheric drag is a dominating perturbing force for satellites at low altitudes up to about 700-1000 km. This article addresses the impact of the atmospheric drag on mean semi-major axes and orbital eccentricities of geodetic spherical satellites: Starlette, Stella, AJISAI, and LARES. Atmospheric drag causes the semi-major axis decays amounting to about ▲a = -1.2, -.12, -.14, and -.30 m/year for LARES, AJISAI, Starlette, and Stella, respectively. The density of the upper atmosphere strongly depends on the solar and geomagnetic activity. The atmospheric drag affects the along-track orbit component to the largest extent, and the out-of-plane to a small extent, whereas the radial component is almost unaffected by the atmospheric drag.

scholarly journals Generalized algorithm for determining AES orbit parameters based on quadratic functionals.

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D.D. Gabriel’yan ◽  
◽  
A.N. Gorbachev ◽  
V.I. Demchenko ◽  
◽  
...  
Keyword(s):  
Dimensional Space ◽  
Satellite Orbit ◽  
Major Axis ◽  
Earth Satellite ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
Quadratic Functionals ◽  
Adopted Model ◽  
Basic Parameters

The questions of development a generalized algorithm for determining the parameters of the low circular orbit (LCO) of an Earth satellite (ES) based on the use of quadratic functionals are in the focus of this paper. The functionals represent the square of the differences between the measured values of the ES sighting angles and the frequency of the received signal with the values of the same parameters obtained for the assumed values of the Keplerian orbital elements in accordance with the adopted model of the ES motion. Estimates of the orbit parameters are formed from the condition of the minimum of the proposed quality functionals. The proposed algorithm is aimed at the developing two equations for the relationship between the measured values of the azimuth and elevation angles, as well as the frequency of the received satellite signal and the parameters of the satellite orbit. The use of the indicated constraint equations makes it possible to pass from the six-dimensional space of the Keplerian orbital elements to the four-dimensional space of the Keplerian orbital elements when constructing the algorithm and choosing the initial approximations of the orbit parameters. Such a reduction in the dimension of space makes it possible to significantly reduce the amount of computational expenditure, which ensures the stability of the algorithm and expands the possibilities of its practical use with limited resources (computing power and restrictions on the permissible processing time). The following Keplerian orbital elements are proposed as four basic parameters: eccentricity, ascending node longitude, orbital inclination, and perigee argument. The other two elements, the semi-major axis of the orbit and the mean anomaly, are expressed as functions of four basic parameters. This choice is determined by the fact that, in the case of LCO, the pivoting of the initial values of the eccentricity and the argument of perigee is quite simple, which makes it possible to ensure convergence to the exact values of the orbit parameters in a wide value of the initial approximations. Within the Keplerian approximation of the satellite's orbital motion, mathematical relations are presented that determine the operations performed within the framework of the considered algorithm. However, a more complete consideration of the factors influencing the motion of the satellite only leads to more volumetric relations, but does not fundamentally affect the construction of the algorithm itself.

Contraction of satellite orbits in an oblate atmosphere with a diurnal density variation

1982 ◽  
Vol 383 (1784) ◽  
pp. 127-145 ◽  
Keyword(s):  
Major Axis ◽  
Density Variation ◽  
Scale Height ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Third Order ◽  
Small Eccentricity ◽  
Air Density ◽  
The Mean ◽  
Density Scale

The effect of air drag on satellite orbits of small eccentricity, e < 0.2, is considered. A model of the atmosphere that allows for oblateness is adopted, in which the density behaviour approximates to the observed diurnal variation. The equations governing the changes due to drag in the semi-major axis a , and in x = ae , during one revolution of the satellite are integrated, the density scale-height H being assumed constant. The resulting expressions for ∆ a and ∆ x are presented to third order in e . Compact expressions for the gradient d a /d x , and for the mean air density at perigee altitude ρ 1 are obtained, when H is allowed to vary with altitude. An equivalence between the variable- H and the constant- H equations is demonstrated, provided that the value of H used in the latter is chosen appropriately.

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