The Earth’s Shadowing Effects in the Short-Periodic Perturbations of Satellite Orbits

Lála, P.; Sehnal, L.

doi:10.1007/978-3-642-99966-6_35

Cited by 3 publications

(3 citation statements)

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“…As was the case for FerrazMello, investigators often select the shadow function to exhibit a basic, smooth behavior but primarily are concerned with the mathematical properties required to fit their orbit integration schemes (e.g. Lála and Sehnal 1969;Lála 1971;Hubaux et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Highly physical penumbra solar radiation pressure modeling with atmospheric effects

Robertson

Flury

Bandikova

et al. 2015

Celest Mech Dyn Astr

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We present a new method for highly physical solar radiation pressure (SRP) modeling in Earth's penumbra. The fundamental geometry and approach mirrors past work, where the solar radiation field is modeled using a number of light rays, rather than treating the Sun as a single point source. However, we aim to clarify this approach, simplify its implementation, and model previously overlooked factors. The complex geometries involved in modeling penumbra solar radiation fields are described in a more intuitive and complete way to simplify implementation. Atmospheric effects are tabulated to significantly reduce computational cost. We present new, more efficient and accurate approaches to modeling atmospheric effects which allow us to consider the high spatial and temporal variability in lower atmospheric conditions. Modeled penumbra SRP accelerations for the Gravity Recovery and Climate Experiment (GRACE) satellites are compared to the sub-nm/s 2 precision GRACE accelerometer data. Comparisons to accelerometer data and a traditional penumbra SRP model illustrate the improved accuracy which our methods provide. Sensitivity analyses illustrate the significance of various atmospheric parameters and modeled effects on penumbra SRP. While this model is more complex than a traditional penumbra SRP model, we demonstrate its utility and propose that a highly physical model which considers atmospheric effects should be the basis for any simplified approach to penumbra SRP modeling. B Robert Robertson

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Section: Introductionmentioning

confidence: 99%

Highly physical penumbra solar radiation pressure modeling with atmospheric effects

Robertson

Flury

Bandikova

et al. 2015

Celest Mech Dyn Astr

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show abstract

“…This function can be developed as a Fourier series in terms of the angle k, formed by the geocentric direction of the satellite and the dark pole of the Earth. Lála and Sehnal (1969) suggested to take as independent variable the variable x = k À /, where sin / = R/r, R being the equatorial radius of the Earth and r is the geocentric satelliteÕs distance.…”

Section: Introductionmentioning

confidence: 99%

Spacecraft’s attitude prediction: solar radiation torque and the Earth’s shadow

Zanardi

Moraes

Cabette

et al. 2005

Advances in Space Research

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“…This function depends on the angle formed by the geocentric Cartesian position of space debris and the dark pole of the Earth's terminator. Another approximation of this shadow function has been proposed later on in Lála & Sehnal (1969). Then, a way of computing shadow boundaries has been proposed in Escobal (1976).…”

Section: Introductionmentioning

confidence: 99%

Symplectic integration of space debris motion considering several Earth’s shadowing models

Hubaux

Lemaître

Delsate

et al. 2012

Advances in Space Research

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In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones. Indeed, it has already been demonstrated that such objects could stay there for hundreds of years. Our model takes into account the Earth's gravitational potential, luni-solar and planetary gravitational perturbations and direct solar radiation pressure. Based on the analysis of the energy conservation and on a comparison with a high order non-symplectic integrator, we show that our algorithm allows us to use large time steps and keep accurate results. We also propose an innovative method to model Earth's shadow crossings by means of a smooth shadow function. In the particular framework of symplectic integration, such a function needs to be included analytically in the equations of motion in order to prevent numerical drifts of the energy. For the sake of completeness, both cylindrical shadows and penumbra transitions models are considered. We show that both models are not equivalent and that big discrepancies actually appear between associated orbits, especially for high area-to-mass ratios.

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The Earth’s Shadowing Effects in the Short-Periodic Perturbations of Satellite Orbits

Cited by 3 publications

References 0 publications

Highly physical penumbra solar radiation pressure modeling with atmospheric effects

Highly physical penumbra solar radiation pressure modeling with atmospheric effects

Spacecraft’s attitude prediction: solar radiation torque and the Earth’s shadow

Symplectic integration of space debris motion considering several Earth’s shadowing models

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