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.

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 Self-Maintenance Orbits Using The perturbations Due to Air Drag and Due to Earth's Oblateness

2020 ◽  
Vol 24 (1) ◽  
pp. 56-60
Author(s):  
Mohamed R. Amin
Keyword(s):  
Major Axis ◽  
Low Earth Orbit ◽  
Earth Orbit ◽  
Semi Major Axis ◽  
Third Order ◽  
Air Drag ◽  
Orbital Parameters ◽  
Orbit Satellite ◽  
Low Earth Orbit Satellite ◽  
Earth’S Oblateness

AbstractThe focus of this paper is the design of a self-maintenance orbit using two natural forces against each other. The effect of perturbations due to Earth's oblateness up to the third order on both the semi-major axis and eccentricity for a low Earth orbit satellite together with the perturbation due to air drag on the same orbital parameters were used, in order to create self-maintenance orbits. Numerical results were simulated for a low earth orbit satellite, which substantiates the applicability of the results.

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.

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.

scholarly journals On the synergy between Ariel and ground-based high-resolution spectroscopy

2022 ◽  
Author(s):  
Gloria Guilluy ◽  
Alessandro Sozzetti ◽  
Paolo Giacobbe ◽  
Aldo S. Bonomo ◽  
Giuseppina Micela
Keyword(s):  
High Resolution ◽  
Near Infrared ◽  
Major Axis ◽  
High Resolution Spectroscopy ◽  
Correlation Technique ◽  
Temperature Structure ◽  
Low Resolution ◽  
Semi Major Axis ◽  
Species Discovery ◽  
Orbital Parameters

AbstractSince the first discovery of an extra-solar planet around a main-sequence star, in 1995, the number of detected exoplanets has increased enormously. Over the past two decades, observational instruments (both onboard and on ground-based facilities) have revealed an astonishing diversity in planetary physical features (i. e. mass and radius), and orbital parameters (e.g. period, semi-major axis, inclination). Exoplanetary atmospheres provide direct clues to understand the origin of these differences through their observable spectral imprints. In the near future, upcoming ground and space-based telescopes will shift the focus of exoplanetary science from an era of “species discovery” to one of “atmospheric characterization”. In this context, the Atmospheric Remote-sensing Infrared Exoplanet Large (Ariel) survey, will play a key role. As it is designed to observe and characterize a large and diverse sample of exoplanets, Ariel will provide constraints on a wide gamut of atmospheric properties allowing us to extract much more information than has been possible so far (e.g. insights into the planetary formation and evolution processes). The low resolution spectra obtained with Ariel will probe layers different from those observed by ground-based high resolution spectroscopy, therefore the synergy between these two techniques offers a unique opportunity to understanding the physics of planetary atmospheres. In this paper, we set the basis for building up a framework to effectively utilise, at near-infrared wavelengths, high-resolution datasets (analyzed via the cross-correlation technique) with spectral retrieval analyses based on Ariel low-resolution spectroscopy. We show preliminary results, using a benchmark object, namely HD 209458 b, addressing the possibility of providing improved constraints on the temperature structure and molecular/atomic abundances.

scholarly journals Combined assimilation of streamflow and snow water equivalent for mid-term ensemble streamflow forecasts in snow-dominated regions

2016 ◽  
Author(s):  
Jean M. Bergeron ◽  
Mélanie Trudel ◽  
Robert Leconte
Keyword(s):  
Data Assimilation ◽  
State Vector ◽  
Snow Water Equivalent ◽  
Synthetic Data ◽  
Hydrologic Model ◽  
Open Loop ◽  
The State ◽  
Wide Range ◽  
Snow Water ◽  
The Impact

Abstract. The potential of data assimilation for hydrologic predictions has been demonstrated in many research studies. Watersheds over which multiple observation types are available can potentially further benefit from data assimilation by having multiple updated states from which hydrologic predictions can be generated. However, the magnitude and time span of the impact of the assimilation of an observation varies according not only to its type, but also to the variables included in the state vector. This study examines the impact of multivariate synthetic data assimilation using the Ensemble Kalman Filter (EnKF) into the spatially distributed hydrologic model CEQUEAU for the mountainous Nechako River located in British-Columbia, Canada. Synthetic data includes daily snow cover area (SCA), daily measurements of snow water equivalent (SWE) at three different locations and daily streamflow data at the watershed outlet. Results show a large variability of the continuous rank probability skill score over a wide range of prediction horizons (days to weeks) depending on the state vector configuration and the type of observations assimilated. Overall, the variables most closely linearly linked to the observations are the ones worth considering adding to the state vector. The performance of the assimilation of basin-wide SCA, which does not have a decent proxy among potential state variables, does not surpass the open loop for any of the simulated variables. However, the assimilation of streamflow offers major improvements steadily throughout the year, but mainly over the short-term (up to 5 days) forecast horizons, while the impact of the assimilation of SWE gains more importance during the snowmelt period over the mid-term (up to 50 days) forecast horizon compared with open loop. The combined assimilation of streamflow and SWE performs better than its individual counterparts, offering improvements over all forecast horizons considered and throughout the whole year, including the critical period of snowmelt. This highlights the potential benefit of using multivariate data assimilation for streamflow predictions in snow-dominated regions.

scholarly journals Combined assimilation of streamflow and snow water equivalent for mid-term ensemble streamflow forecasts in snow-dominated regions

2016 ◽  
Vol 20 (10) ◽  
pp. 4375-4389 ◽  
Author(s):  
Jean M. Bergeron ◽  
Mélanie Trudel ◽  
Robert Leconte
Keyword(s):  
Data Assimilation ◽  
State Vector ◽  
Snow Water Equivalent ◽  
Synthetic Data ◽  
Hydrologic Model ◽  
Open Loop ◽  
The State ◽  
Wide Range ◽  
Snow Water ◽  
The Impact

Abstract. The potential of data assimilation for hydrologic predictions has been demonstrated in many research studies. Watersheds over which multiple observation types are available can potentially further benefit from data assimilation by having multiple updated states from which hydrologic predictions can be generated. However, the magnitude and time span of the impact of the assimilation of an observation varies according not only to its type, but also to the variables included in the state vector. This study examines the impact of multivariate synthetic data assimilation using the ensemble Kalman filter (EnKF) into the spatially distributed hydrologic model CEQUEAU for the mountainous Nechako River located in British Columbia, Canada. Synthetic data include daily snow cover area (SCA), daily measurements of snow water equivalent (SWE) at three different locations and daily streamflow data at the watershed outlet. Results show a large variability of the continuous rank probability skill score over a wide range of prediction horizons (days to weeks) depending on the state vector configuration and the type of observations assimilated. Overall, the variables most closely linearly linked to the observations are the ones worth considering adding to the state vector due to the limitations imposed by the EnKF. The performance of the assimilation of basin-wide SCA, which does not have a decent proxy among potential state variables, does not surpass the open loop for any of the simulated variables. However, the assimilation of streamflow offers major improvements steadily throughout the year, but mainly over the short-term (up to 5 days) forecast horizons, while the impact of the assimilation of SWE gains more importance during the snowmelt period over the mid-term (up to 50 days) forecast horizon compared with open loop. The combined assimilation of streamflow and SWE performs better than their individual counterparts, offering improvements over all forecast horizons considered and throughout the whole year, including the critical period of snowmelt. This highlights the potential benefit of using multivariate data assimilation for streamflow predictions in snow-dominated regions.

scholarly journals Orbital Parameters of the PSR B1620–26 Triple System

1996 ◽  
Vol 160 ◽  
pp. 525-530 ◽  
Author(s):  
Z. Arzoumanian ◽  
K. Joshi ◽  
F. A. Rasio ◽  
S. E. Thorsett
Keyword(s):  
Proper Motion ◽  
Time Derivative ◽  
Major Axis ◽  
Mass Range ◽  
Pulse Frequency ◽  
Rate Of Change ◽  
Semi Major Axis ◽  
Orbital Parameters ◽  
Error Bar ◽  
Stellar Masses

AbstractPrevious timing data for PSR B1620–26 were consistent with a second companion mass m2anywhere in the range ∼ 10−3– 1M⊙, i.e., from a Jupiter-type planet to a star. We present the latest timing parameters for the system, including a significant change in the projected semi-major axis of the inner binary, a marginal detection of the fourth time derivative of the pulse frequency, and the pulsar proper motion (which is in agreement with published values for the proper motion of M4), and use them to further constrain the mass m2and the orbital parameters. Using the observed value of, we obtain a one-parameter family of solutions, all with m2≲ 10−2M⊙, i.e., excluding stellar masses. Varyingwithin its formal 1σ error bar does not affect the mass range significantly. However, if we varywithin a 4σ error bar, we find that stellar-mass solutions are still possible. We also calculate the predicted rate of change of the projected semi-major axis of the inner binary and show that it agrees with the measured value.

scholarly journals Mass Loss from Contact Binary Systems and their Dynamical Evolution

1980 ◽  
Vol 88 ◽  
pp. 511-515
Author(s):  
Kyoji Nariai
Keyword(s):  
Angular Momentum ◽  
Mass Loss ◽  
Total Mass ◽  
Binary Systems ◽  
Dynamical Evolution ◽  
Major Axis ◽  
Semi Major Axis ◽  
Orbital Parameters ◽  
Contact Binary ◽  
Fractional Mass

When there is mass loss from a binary system, the lost mass carries energy and angular momentum out of the system. Therefore, the remaining system must adjust its orbital parameters to the changing values of the total kinematic energy E and the total angular momentum N as the total mass M decreases. The parameters concerned here are : the fractional mass μ, the semi-major axis a, and the eccentricity e.

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