scholarly journals Averaging Tesseral Effects: Closed Form Relegation versus Expansions of Elliptic Motion

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Martin Lara ◽  
Juan F. San-Juan ◽  
Luis M. López-Ochoa
Keyword(s):  
Closed Form ◽  
Artificial Satellites ◽  
Orbit Propagation ◽  
Elliptic Motion ◽  
Period Effects ◽  
Short Period ◽  
Orbit Eccentricity ◽  
Pros And Cons ◽  
Tesseral Harmonics

Longitude-dependent terms of the geopotential cause nonnegligible short-period effects in orbit propagation of artificial satellites. Hence, accurate analytical and semianalytical theories must cope with tesseral harmonics. Modern algorithms for dealing analytically with them allow for closed formrelegation. Nevertheless, current procedures for the relegation of tesseral effects from subsynchronous orbits are unavoidably related to orbit eccentricity, a key fact that is not enough emphasized and constrains application of this technique to small and moderate eccentricities. Comparisons with averaging procedures based on classical expansions of elliptic motion are carried out, and the pros and cons of each approach are discussed.

scholarly journals Precise Analytical Computation of Frozen-Eccentricity, Low Earth Orbits in a Tesseral Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Martin Lara ◽  
Juan F. San-Juan ◽  
Luis M. López-Ochoa
Keyword(s):  
Model Design ◽  
Zonal Model ◽  
Period Effects ◽  
Short Period ◽  
Orbit Analysis ◽  
Low Earth Orbits ◽  
Tesseral Harmonics ◽  
Earth Orbits ◽  
Eccentricity Orbit

Classical procedures for designing Earth’s mapping missions rely on a preliminary frozen-eccentricity orbit analysis. This initial exploration is based on the use of zonal gravitational models, which are frequently reduced to a simpleJ2-J3analysis. However, theJ2-J3model may not be accurate enough for some applications. Furthermore, lower order truncations of the geopotential are known to fail in describing the behavior of elliptic frozen orbits properly. Inclusion of a higher degree geopotential, which also takes into account the short-period effects of tesseral harmonics, allows for the precise computation of frozen-eccentricity, low Earth orbits that show smaller long-period effects in long-term propagations than those obtained when using the zonal model design.

scholarly journals First order normalization in the generalized photo gravitational non-planar restricted three body problems

2015 ◽  
Vol 3 (2) ◽  
pp. 46
Author(s):  
Nirbhay Kumar Sinha
Keyword(s):  
Oblate Spheroid ◽  
Second Order ◽  
Elliptic Motion ◽  
First Order ◽  
Short Period ◽  
Order Part ◽  
Three Body

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H<sub>2</sub> is normalised to H<sub>2</sub> = a<sub>1</sub>b<sub>1</sub>w<sub>1</sub> + a<sub>2</sub>b<sub>2</sub>w<sub>2</sub>. The resulting motion is composed of elliptic motion with a short period (2p/w<sub>1</sub>), completed by an oscillation along the z-axis with a short period (2p/w<sub>2</sub>).</p>

scholarly journals Communication features in online and offline spaces.

2021 ◽  
Vol 13 (3) ◽  
pp. 105-112
Author(s):  
Anrieta A. Karapetyan ◽  
Keyword(s):  
Social Interactions ◽  
Everyday Life ◽  
Nonverbal Communication ◽  
Online Communication ◽  
Social Signals ◽  
Social Lives ◽  
Short Period ◽  
The World ◽  
Pros And Cons ◽  
Cultural Components

No other media has become so popular in such a short period of time as online, which mainly serves for the purpose of communication. Online communications have the potential to fundamentally change the character of our social lives on all levels of social interactions. This article represents an attempt of discussing pros and cons of the online communication compared to the offline ones, and including functional as well as cultural components such as habits, usefulness, as well as specific cases affecting the gradual and immediate shift from the offline to the online communication (like COVID19 pandemic). Online communication spaces provide ample opportunities for selfrepresentation, convenience and compliance, easy connectivity from every place in the world, it is time-consuming and costly. It is widely used in all areas of everyday life. At the same time participants of online communication need nonverbal communication and those all-important social signals, which make communication more efficient. Despite the number of advantages, online communication still cannot completely replace the offline ones.

scholarly journals On the secondary’s rotation in a synchronous binary asteroid

2020 ◽  
Vol 493 (1) ◽  
pp. 171-183
Author(s):  
H S Wang ◽  
X Y Hou
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Spin Orbit ◽  
Binary Asteroid ◽  
Classical Spin ◽  
Long Period ◽  
Period Orbit ◽  
Short Period ◽  
Orbit Eccentricity ◽  
Binary Asteroid System

ABSTRACT This article studies the secondary’s rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem, composed of a spherical primary plus a triaxial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) influence of the secondary’s rotation on the mutual orbit is considered and (2) instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find the following. (1) The genealogy of the two families of periodic orbits is the same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates on to a short-period orbit travelling N times. (2) In the limiting case where the secondary’s mass is negligible, our results can be reduced to classical spin-orbit theory, by equating the long-period orbit with free libration and the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary’s mass is non-negligible. (3) By studying the stability of periodic orbits for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°) and the maximum mutual orbit eccentricity that does not break the secondary’s synchronous state. We also find an anti-correlation between the secondary’s libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.

scholarly journals VIOLATING THE BASIC TENETS OF CARE – LOOKING BACK ON YEARS OF EVIDENCE BASED MEDICINE FROM AN ONCOLOGIST'S VIEWPOINT

2020 ◽  
pp. 86-88
Author(s):  
Bishan Basu
Keyword(s):  
Medical Practice ◽  
Evidence Based Medicine ◽  
Healthcare Systems ◽  
Evidence Based ◽  
Short Time Span ◽  
Short Period ◽  
History Of ◽  
Pros And Cons ◽  
Short Time ◽  
Based Medicine

Evidence-Based Medicine (EBM) came into fashion nearly three decades ago. However, over this short period, this system of medical philosophy has come to dominate the medical practice worldwide. Never in the history of medicine could a single way of medical practice could dominate the healthcare systems of diverse countries like EBM did, that too within such short time span. But, it is high time we should ponder over the pros and cons of EBM and if this way of medical practice is to be allowed to continue, we should consider integration of additional inputs from the traditional ways of medicine. Though article focusses upon the cancer care, the conclusions derived can be applied to any other disciplines of healthcare.

scholarly journals Nonsingular recursion formulas for third-body perturbations in mean vectorial elements

2020 ◽  
Vol 634 ◽  
pp. A61
Author(s):  
M. Lara ◽  
A. J. Rosengren ◽  
E. Fantino
Keyword(s):  
Arbitrary Order ◽  
Keplerian Motion ◽  
Third Body ◽  
Period Effects ◽  
Elliptic Orbits ◽  
Short Period ◽  
Recursion Formulas ◽  
In Series ◽  
Mean Elements

The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long series in trigonometric functions, we refer the motion to the apsidal frame and efficiently remove the short-period effects of this expansion in vectorial form up to an arbitrary order. We then provide the variation equations of the two fundamental vectors of the Keplerian motion by analogous vectorial recurrences, which are free from singularities and take a compact form useful for the numerical propagation of the flow in mean elements.

scholarly journals Short-period effects of the planetary perturbations on the Sun–Earth Lagrangian point L3

2020 ◽  
Vol 638 ◽  
pp. A137
Author(s):  
E. Scantamburlo ◽  
M. Guzzo
Keyword(s):  
Solar System ◽  
Original System ◽  
Realistic Model ◽  
Simplified Model ◽  
Lagrangian Point ◽  
The Sun ◽  
Indicator Method ◽  
Period Effects ◽  
Short Period ◽  
Fast Lyapunov Indicator

Context. The Lagrangian point L3 of the Sun–Earth system, and its Lyapunov orbits, have been proposed to perform station-keeping, although L3 is only rigorously defined for the extremely simplified model represented by the reduced Sun–Earth–spacecraft system. As in L3 the planetary perturbations (mainly from Jupiter and Venus) are stronger than Earth’s attraction, it is necessary to understand whether or not the dynamics close to L3 persist under such a strong perturbation, allowing for a definition of dynamical substitutes for models that are more realistic than the circular restricted three-body problem. Aims. In this paper we address the problem of the existence of motions that remain close to L3 for a time-span which is relevant for space missions in a model of the Solar System compatible with the precision of JPL digital ephemerides. Methods. First, we computed analytically the main short-period effects of planetary perturbations in a simplified model of the Solar System with the orbits of all the planets co-planar and circular. We then applied the Fast Lyapunov Indicator method in order to find dynamical substitutes that exist for time-spans of hundreds of years in the model of the Solar System that is used to produce the modern ephemerides. Results. We find that the original system is conjugate by a canonical transformation to an averaged system that has an equilibrium close to L3: even if Venus and Jupiter each move the position of this equilibrium by about 218 and 176 km, respectively, in opposite directions, in the model where both the planets are included, their effects almost perfectly compensate for one another, leaving a displacement of about 40 km only. This equilibrium is then mapped in the original system to a quasi-periodic dynamical substitute; the contributions of each planet to the amplitude of this quasi-periodic libration around L3 do not compensate for one another, and sum to about 10 000 km. The Fast Lyapunov Indicator method allowed us to find orbits of any amplitude bigger than this one (up to 0.03 AU) for time-spans of hundreds of years in the model of the Solar System that is used to produce the modern ephemerides. Conclusions. Using a combination of the Hamiltonian averaging method with a new implementation of the Fast Lyapunov Indicator method we find orbits useful for astrodynamics originating at the Sun–Earth Lagrangian point L3 for a realistic model of the Solar System. In particular, this usage of the chaos indicator provides an innovative application of dynamical systems theory to astrodynamics, where the short-period perturbations represent a relevant part of the model.

scholarly journals Eccentricity estimates in hierarchical triple systems

2014 ◽  
Vol 9 (S310) ◽  
pp. 88-89
Author(s):  
Nikolaos Georgakarakos ◽  
Siegfried Eggl
Keyword(s):  
Perturbation Theory ◽  
Extrasolar Planets ◽  
Rate Of Change ◽  
Artificial Satellites ◽  
Orbital Eccentricity ◽  
Analytical Technique ◽  
Triple Systems ◽  
Secular Evolution ◽  
Secular Theory ◽  
Short Period

AbstractPerturbation theory in the three body problem has greatly advanced our ability to understand and model a variety of systems ranging from artificial satellites to stars and from extrasolar planets to asteroid-Jupiter interactions. In a series of papers, we developed an analytical technique for estimating the orbital eccentricity of the inner binary in hierarchical triple systems. The method combined the secular theory with calculations of short period terms. The derivation of the short term component was based on an expansion of the rate of change of the Runge-Lenz vector by using first order perturbation theory, while canonical perturbation theory was used to investigate the secular evolution of the system. In the present work we extend the calculation to the orbit of the outer binary. At the same time, we provide an improved version for some previous results. A post-Newtonian correction is included in our model. Our analytical estimates are compared with numerical and analytical results on the subject and applications to stellar triples and extrasolar planets are discussed.

“Bookmysurprise”: navigating through the predicament of a start-up

2021 ◽  
Vol 11 (2) ◽  
pp. 1-10
Author(s):  
Shagun Bansal ◽  
Inakshi Kapur ◽  
Anjani Kumar Singh ◽  
Piyush Verma
Keyword(s):  
Small Business ◽  
Learning Outcomes ◽  
Scale Up ◽  
New Venture ◽  
Event Management ◽  
Content Type ◽  
Academic Level ◽  
Short Period ◽  
Pros And Cons ◽  
Set Up

Learning outcomes The learning outcomes of this paper are as follows: to identify the pros and cons of waged employment and entrepreneurship, to identify the contextual factors influencing entrepreneurship, to set up a new venture, namely, steps, challenges involved and decision-making process, to scale up a small business; when, how and where? And to tradeoff required for scaling up a small business. Case overview/synopsis Pooja, a young management graduate from Varanasi, decided to overcome all challenges and barriers faced by a women entrepreneur and chase her lifelong dream of creating her own event management startup. After having achieved phenomenal success in a short period of time within the city, she began to receive interest from neighbouring cities as well. The decision to scale up operations was particularly difficult for Pooja, as she had funded the venture through her personal funds and personally nurtured the business and her team based on the values of quality and creativity. Like any small business, she had to decide what level of trade-off was required between scaling and dilution of control over the operations. Complexity academic level The case study is applicable for students of management. The learnings from the case can be applied by an individual who is looking to start a business or expand one. Supplementary materials Teaching Notes are available for educators only. Subject code CSS 3: Entrepreneurship.

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