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.

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.

scholarly journals Analytical Study of Earth Tides on Low Orbits Satellites

2020 ◽  
pp. 453-461
Author(s):  
Ahmed K. Izzet ◽  
Mayada J. Hamwdi ◽  
Abed T. Jasim
Keyword(s):  
Analytical Study ◽  
Satellite Orbit ◽  
Major Axis ◽  
Earth Tides ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
Tidal Perturbation ◽  
Right Ascension ◽  
Tide Effect

     The main objective of this paper is to calculate the perturbations of tide effect on LEO's satellites . In order to achieve this goal, the changes in the orbital elements which include the semi major axis (a) eccentricity (e) inclination , right ascension of ascending nodes ( ), and fifth element argument of perigee ( ) must be employed. In the absence of perturbations, these element remain constant. The results show that the effect of tidal perturbation on the orbital elements depends on the inclination of the satellite orbit. The variation in the ratio  decreases with increasing the inclination of satellite, while it increases with increasing the time.

scholarly journals γ DOR: A PULSATING COMPONENT OF KIC 8043961 IN A STELLAR TRIPLE SYSTEM

2020 ◽  
Vol 56 (2) ◽  
pp. 179-191
Author(s):  
C. Kamil ◽  
H. A. Dal ◽  
O. Özdarcan ◽  
E. Yoldaş
Keyword(s):  
Major Axis ◽  
Primary Component ◽  
Mass Ratio ◽  
Third Body ◽  
Semi Major Axis ◽  
Orbital Inclination ◽  
The Third ◽  
New Findings ◽  
Effective Temperatures ◽  
Orbit Model

We present new findings about KIC 8043961. We find the effective temperatures of the components as 6900 ± 200 K for the primary, and 6598 ± 200 K for the secondary, while the logarithm of the surface gravities are found to be 4.06 cm s-2 and 3.77 cm s-2, respectively. Combination of the light curve with the spectroscopic orbit model results leads to a mass ratio of 1.09 ± 0.07 with an orbital inclination of 73.71 ± 0.14 and a semi-major axis of 8.05 ± 0.22 R⨀ . Masses of the primary and secondary components are calculated as 1.379 ± 0.109 M⨀ and 1.513 ± 0.181 M⨀, while the radii are found to be 1.806 ± 0.084 R⨀ and 2.611 ± 0.059 R⨀. In addition, we obtain a considerable light contribution (≈0.54%) of a third body. We compute a possible mass for the third body as 0.778 ± 0.002 M⨀. We find that the primary component exhibits γ Dor type pulsations with 137 frequencies.

scholarly journals The orbital evolution of meteor streams at the 2/1 resonance with Jupiter

1985 ◽  
Vol 83 ◽  
pp. 179-180
Author(s):  
Cl. Froeschlé
Keyword(s):  
Major Axis ◽  
Orbital Evolution ◽  
The Sun ◽  
Orbital Elements ◽  
Meteor Stream ◽  
Semi Major Axis ◽  
Meteor Streams ◽  
Gravitational Forces ◽  
Resonant Effect

We investigated the orbital evolution of Quadrantid-like meteor streams situated in the vicinity of the 2/1 resonance with Jupiter. For the starting orbital elements we took the values of the orbital elements of the Quadrantid meteor stream except for the semi-major axis which was varied between a = 3.22 and a = 3.34 AU. We considered these meteor streams as a ring and we investigated the resonant effect on the dispersion of this ring over a period of 13 000 years. Only gravitational forces due to the Sun and due to Jupiter were taken into account.

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.

Using spacecraft range data and radar observations for the improvement of the orbital elements of planets and parameters of Mars rotation

1996 ◽  
Vol 172 ◽  
pp. 45-48
Author(s):  
E.V. Pitjeva
Keyword(s):  
Major Axis ◽  
Astronomical Unit ◽  
Range Data ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
The Earth ◽  
Electromagnetic Signals ◽  
Least Squares Estimates ◽  
Radar Ranging ◽  
Made In

The extremely precise Viking (1972–1982) and Mariner data (1971–1972) were processed simultaneously with the radar-ranging observations of Mars made in Goldstone, Haystack and Arecibo in 1971–1973 for the improvement of the orbital elements of Mars and Earth and parameters of Mars rotation. Reduction of measurements included relativistic corrections, effects of propagation of electromagnetic signals in the Earth troposphere and in the solar corona, corrections for topography of the Mars surface. The precision of the least squares estimates is rather high, for example formal standard deviations of semi-major axis of Mars and Earth and the Astronomical Unit were 1–2 m.

scholarly journals Increasing the Accuracy of Orbital Elements for a Satellite in a Low Earth Orbit under the Influence of Atmospheric Drag Using Adams-Bashforth Method

2021 ◽  
pp. 81-90
Author(s):  
Rasha H. Ibrahim ◽  
Abdul-Rahman H. Saleh
Keyword(s):  
Integration Method ◽  
Major Axis ◽  
Low Earth Orbit ◽  
True Anomaly ◽  
Earth Orbit ◽  
Atmospheric Drag ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
Literature Reviews ◽  
Perturbed Equation

The perturbed equation of motion can be solved by using many numerical methods. Most of these solutions were inaccurate; the fourth order Adams-Bashforth method is a good numerical integration method, which was used in this research to study the variation of orbital elements under atmospheric drag influence.  A satellite in a Low Earth Orbit (LEO), with altitude form perigee = 200 km, was selected during 1300 revolutions (84.23 days) and ASat / MSat value of 5.1 m2/ 900 kg. The equations of converting state vectors into orbital elements were applied. Also, various orbital elements were evaluated and analyzed. The results showed that, for the semi-major axis, eccentricity and inclination have a secular falling discrepancy, Longitude of Ascending Node is periodic, Argument of Perigee has a secular increasing variation, while true anomaly grows linearly from 0 to 360°. Furthermore, all orbital elements, excluding Longitude of Ascending Node, Argument of Perigee, and true anomaly, were more affected by drag than other orbital elements, through their falling as the time passes. The results illustrate a high correlation as compared with literature reviews in this field.

Determination of upper-atmosphere air density and scale height from satellite observations

1959 ◽  
Vol 252 (1268) ◽  
pp. 16-27 ◽  
Keyword(s):  
Satellite Orbit ◽  
Major Axis ◽  
Scale Height ◽  
Rate Of Change ◽  
Satellite Observations ◽  
Upper Atmosphere ◽  
Semi Major Axis ◽  
Air Density ◽  
Standard Deviations

A solution is obtained for the rate of change of semi-major axis and perigee distance of a satellite orbit with time due to the resistance of the atmosphere. The logarithm of air density is assumed to vary quadratically with height, and the oblateness of the atmosphere is taken into account. The calculation of perigee air density in terms of the rate of change of satellite period is dealt with; and the method is applied to data at present available on six different satellites. The variation of air density with height is obtained as ln ρ = -28·59(±0·15) - ( h - 200 )/46(±5) + 0·028(±0·013) ( h - 200) 2 /(46) 2 for h in the range of approximately 170 to 700 km, where ρ is in grams/cm 3 , h is in kilometres and standard deviations are given in brackets.

scholarly journals Planetary migration in gaseous protoplanetary disks

2007 ◽  
Vol 3 (S249) ◽  
pp. 331-346
Author(s):  
Frédéric S. Masset
Keyword(s):  
Major Axis ◽  
Giant Planets ◽  
Type I ◽  
Type Ii ◽  
Orbital Elements ◽  
Intermediate Mass ◽  
Semi Major Axis ◽  
Low Mass ◽  
Planetary Migration ◽  
Different Parts

AbstractTides come from the fact that different parts of a system do not fall in exactly the same way in a non-uniform gravity field. In the case of a protoplanetary disk perturbed by an orbiting, prograde protoplanet, the protoplanet tides raise a wake in the disk which causes the orbital elements of the planet to change over time. The most spectacular result of this process is a change in the protoplanet's semi-major axis, which can decrease by orders of magnitude on timescales shorter than the disk lifetime. This drift in the semi-major axis is called planetary migration. In a first part, we describe how the planet and disk exchange angular momentum and energy at the Lindblad and corotation resonances. Next we review the various types of planetary migration that have so far been contemplated: type I migration, which corresponds to low-mass planets (less than a few Earth masses) triggering a linear disk response; type II migration, which corresponds to massive planets (typically at least one Jupiter mass) that open up a gap in the disk; “runaway” or type III migration, which corresponds to sub-giant planets that orbit in massive disks; and stochastic or diffusive migration, which is the migration mode of low- or intermediate-mass planets embedded in turbulent disks. Lastly, we present some recent results in the field of planetary migration.

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.

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