scholarly journals Orbital Instability Zones of Space Balloons

1997 ◽  
Vol 165 ◽  
pp. 361-366
Author(s):  
A. V. Krivov ◽  
L.L. Sokolov ◽  
J. Getino
Keyword(s):  
Initial Conditions ◽  
Solar Radiation Pressure ◽  
Satellite Orbits ◽  
Spherically Symmetric ◽  
Integrable Problem ◽  
The Earth ◽  
Averaged Equations ◽  
Orbital Instability ◽  
Small Change ◽  
Earth’S Oblateness

AbstractWe consider the motion of a spherically-symmetric balloon satellite perturbed by the Earth’s oblateness and solar radiation pressure. For equatorial satellite orbits and neglecting the Earth obliquity, the orbit-averaged equations for eccentricity and longitude of pericenter are integrable in quadratures (Krivov and Getino, 1996). The instability zone associated with the saddle separatrix in the phase space has been found and explored in depth. For semimajor axes about two Earth’s radii, and for area-to-mass ratios in the order of several tens cm2g−1, the amplitude and period of eccentricity oscillations may change nearly twofold under a small change of initial conditions or force parameters. We then restore the actual Earth obliquity of 235 and consider a spatial (non-integrable) problem. Near the saddle separatrix, a stochasticity zone appears that leads to large unpredictable eccentricity variations. The quasirandom motions of space balloons are investigated in terms of two-symbol (0-1) sequences by methods of stochastic celestial mechanics.

Butterflies, Elephants and Gravity to Model Human-Earth Interactions

2021 ◽  
Author(s):  
Maurits Ertsen
Keyword(s):  
Initial Conditions ◽  
Scale Up ◽  
Human Dimensions ◽  
System Modelling ◽  
Earth System ◽  
The Earth ◽  
Scale Down ◽  
Butterfly Effect ◽  
To Come ◽  
Small Change

<p>The call for this session mentions that “Earth system resilience critically depends on the nonlinear interplay of positive and negative feedbacks of biophysical and increasingly also socio-economic processes. These include dynamics in [many physical events], as well as the dynamics and perturbations associated with human activities.“ In this contribution, I would like to mobilize a few notions to discuss this issue.</p><p>A typical approach is to scale up human dimensions to Earth system model scales. Humans become aggregated into social structures, even societies, that change every year or so. I propose to scale down the Earth system to humans, both in terms of space and time. I think this offers exiting possibilities to study climate and earth systems in a different way, but also allows for answering the question how we could act today, tomorrow and next week in order to understand which long-term scenarios over decades are more likely to occur.</p><p>This would move us away from the view of the Earth as a single system or pattern to a perspective of Earth as an interconnected world of different non-human and human agencies. I would position this idea against the rather popular metaphor of the butterfly effect, “the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state”. This may be too simple, as one butterfly will meet many other butterflies along the way. As such, the butterfly effect may be a specific example that claims a certain agency for smaller actors within the Earth System, but that builds its analysis on pattern replication through non-linear relations.</p><p>Our (perceived) knowledge of patterns colors our analysis of those patterns. We are all familiar with the metaphor of the men observing different parts of the elephant. The metaphor assumes that we know that what the men are examining is an elephant. However, once we do not know either what they are looking at, we need to start with them seeing different things. In the perspective that we know the elephant, the men are just short-sighted. In the more realistic setting that we cannot be certain about what the men observe, we are the ones that need to come up with a convincing way to analyze what is happening, has happened or may happen.</p><p>Much work in Earth system modelling model patterns in society, but do not explain how these patterns are the result of continuously performing agencies. The models are built to mimic the patterns that we observed. I propose to replace the patterns we use to explain the same patterns – whether they are power relations or gravity – with representations of the interacting agencies that together produce the Earth system that we think we observe. Gravity may be a nice explanation of the observed pattern that we do not glide away from the surface, but it remains just that. In our modelling efforts, we may apply the notion that gravity acts.</p>

A discussion on orbital analysis - A brief survey of satellite orbit determination

1967 ◽  
Vol 262 (1124) ◽  
pp. 71-78
Keyword(s):  
Orbit Determination ◽  
Accurate Determination ◽  
Solar Radiation Pressure ◽  
Satellite Orbit ◽  
Dynamical Theory ◽  
Satellite Orbits ◽  
Perturbation Techniques ◽  
The Earth ◽  
Orbital Analysis

The accurate determination of satellite orbits depends on an adequate accumulation of observations, a sound dynamical theory and a fairly sophisticated sequence of numerical computations. The particular patterns of observation, theory and computation are considered in relation to the objectives of orbit determination. Factors to be taken into account are the type, accuracy and spread of observations; perturbations of the orbit due to air drag, attraction of the Earth, Moon, and Sun, and solar radiation pressure; and the speed and cost of available computers. These factors, together with the overall objectives, determine the main features of the computation; whether to use special or general perturbation techniques, what length of orbit arc to use, what parameters to determine and how to present the results.

scholarly journals Numerical Modelling of Satellite Downlink Signals in a Finslerian-Perturbed Schwarzschild Spacetime

Universe ◽  
2020 ◽  
Vol 6 (4) ◽  
pp. 57 ◽  
Author(s):  
Ingo Abraham ◽  
Wolfgang Hasse ◽  
Martin Plato
Keyword(s):  
Numerical Modelling ◽  
Atomic Clock ◽  
Lorentzian Geometry ◽  
Time Signal ◽  
Satellite Orbits ◽  
Spherically Symmetric ◽  
Schwarzschild Spacetime ◽  
Gravitational Perturbations ◽  
Ground Station ◽  
The Earth

The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite’s orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity.

A discussion on orbital analysis - Properties of the upper atmosphere determined from satellite orbits

1967 ◽  
Vol 262 (1124) ◽  
pp. 157-171 ◽  
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Orbital Period ◽  
Solar Radiation Pressure ◽  
Major Axis ◽  
Artificial Satellites ◽  
Satellite Orbits ◽  
Atmospheric Drag ◽  
Sunspot Maximum ◽  
The Earth

Irregularities in the Earth’s gravitational potential perturb the orbits of artificial satellites in a great many ways. They cannot, however, change the mean value of the major axis of an orbit, which determines the period of revolution. To change the orbital period a dissipative force is required, such as the drag exerted on the satellite by the Earth’s atmosphere. Solar radiation pressure does not affect the period of a satellite provided the satellite does not cross the shadow cone of the Earth. If the orbit is all in daylight, the effect of the force cancels out after one revolution. If, however, the satellite goes in and out of the Earth’s shadow, and the orbit is not circular, the effect does not cancel out and radiation pressure will cause a change in the period. Atmospheric drag and solar radiation pressure are the only major forces that are known to affect the period of a satellite. Other forces, such as the interaction of an electrically charged satellite with atmospheric ions or with the magnetic field of the Earth, are undoubtedly present, but they are generally quite small. For low-orbiting satellites, with perigees below 300 km, the effect of atmospheric drag on the orbital period is so much larger than that of solar radiation pressure, that the latter can be neglected for all practical purposes. Above 400 km, however, radiation pressure makes itself felt, and above 700 km it may become more important than atmospheric drag. Actually, these figures vary a great deal with the phase of the solar cycle, since the atmosphere expands or contracts with solar activity. At sunspot minimum the effect of radiation pressure becomes comparable with that of atmospheric drag at about 600 km, while at sunspot maximum it does not become so below 1100 km.

Effects of Solar Radiation Pressure on Earth Satellite Orbits

Science ◽  
1960 ◽  
Vol 131 (3404) ◽  
pp. 920-921 ◽  
Author(s):  
R. W. Parkinson ◽  
H. M. Jones ◽  
I. I. Shapiro
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Solar Radiation Pressure ◽  
Earth Satellite ◽  
Satellite Orbits

scholarly journals Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vivian Martins Gomes ◽  
Antonio Fernando Bertachini de Almeida Prado ◽  
Justyna Golebiewska
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Sun ◽  
Three Body Problem ◽  
The Earth ◽  
Before And After ◽  
Three Body ◽  
Body Energy ◽  
Spacecraft Position

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

scholarly journals Study the Effect of Solar Radiation Pressure at Several Satellite Orbits

2013 ◽  
Vol 10 (4) ◽  
pp. 1253-1261 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Jacobian Matrix ◽  
Solar Radiation Pressure ◽  
Equation Of Motion ◽  
Low Earth Orbit ◽  
Earth Orbit ◽  
Satellite Orbits ◽  
Orbit Satellite ◽  
Low Earth Orbit Satellite

The effects of solar radiation pressure at several satellite (near Earth orbit satellite, low Earth orbit satellite, medium Earth orbit satellite and high Earth orbit satellite ) have been investigated. Computer simulation of the equation of motion with perturbations using step-by-step integration (Cowell's method) designed by matlab a 7.4 where using Jacobian matrix method to increase the accuracy of result.

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