Abstract
We analyze the perturbations due to solar radiation pressure on the orbit of a high artificial satellite. The latter is modelled in a simplified way (axisymmetric body plus despun antenna emitting a radio beam), which seems suitable to describe the main effects for existing telecommunication satellites. We use the regularized general perturbation equations, by expressing the force in the moving Gauss' reference frame and by expanding the results in terms of some small parameters, referring both to the orbit (small eccentricity and inclination) and to the spacecraft's attitude. Some interesting results are derived, which assess the relative importance of different physical effects and of different parts of the spacecraft in determining the long-term evolution of the orbital elements.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- S' :
-
spacecraft's cross section
- S' A :
-
antenna's cross section
- W' :
-
transmitted power by the antenna
- m :
-
mass of the spacecraft
- \(\hat \omega\) :
-
unit vector along the spin axis of the spacecraft
- \(\hat n\) :
-
unit vector along the symmetry axis of the despun antenna
- ê:
-
unit vector along the radiowave beam transmitted by the spacecraft
- š:
-
unit vector toward the Sun
- ψ′:
-
sun angle: between\(\hat \omega\) and ŝ
- ψ:
-
sun angle: between\(\hat n\) and ŝ
- μ:
-
perturbation parameter; magnitude ofF divided by Earth's gravitational acceleration on the spacecraft
- F:
-
perturbating acceleration produced by radiation pressure force on the spacecraft
- A, B, C, D, E :
-
components of perturbing force according to the model given in Equation (1.4)
- D', E' :
-
first order terms in the expansion ofD, E in D'Alembert series (see Equation (2.17))
- D k ,E k :
-
Fourier components ofD, E as function of λ
- ê S :
-
unit vector from the spacecraft toward the center of the Earth
- ê T :
-
unit vector ê W ×ê S
- ê W :
-
unit vector normal to orbital plane
- S, T, W :
-
components of the perturbing force along ê S , ê T , ê W
- η:
-
angle between ê W and\(\hat \omega\)
- ξ:
-
angle between the projection of ê S on the equatorial plane of the spacecraft (the plane normal to\(\hat \omega\)) and ê
- ζ:
-
angle measured on the orbital plane from the origin of the angles to the projection of\(\hat \omega\)
- σ:
-
angle between\(\hat n\) and the equatorial plane of the spacecraft
- ℒ, ©:
-
complex representation of ŝ in the equinoctial system (see Equation (2.16))
- a, e, i, Ω,\(\tilde \omega\) :
-
usual Keplerian elements of the spacecraft orbit
- n :
-
mean motion of the spacecraft
- v, M :
-
true and mean anomaly of the spacecraft
- θ, λ:
-
true and mean longitude of the spacecraft
- ρ, ε:
-
decomposition of λ according to Equation (2.1)
- H :
-
regularized element in complex form:\(H = e \exp (j\tilde \omega )\)
- P :
-
regularized element in complex form:\(P = tgi \exp (j\tilde \omega )\)
- j :
-
\(\sqrt { - 1}\)
- \(\bar H\) :
-
complex conjugate ofH
- y :
-
number of spacecraft's orbits in 1 yr
- α:
-
absorption coefficient
References
Aksnes, C.: 1976,Celes. Mech. 13, 89.
Hori, G.: 1966, in J. B. Rosser (ed.),Lectures in Applied Mathematics, Vol. 7, Part. 3, pp. 167–178.
Kozai, Y.: 1963,Smithsonian Contributions to Astrophysics 6, 109.
Musen, P.: 1960,J. Geophys. Res. 65, 1391.
Roy, A. E.: 1978,Orbital Motion, Adam Hilger Ltd, Bristol.
Van der Ha, J. C. and Modi, V. J.: 1977,J. Astron. Sci. 25, 283.
Author information
Authors and Affiliations
Additional information
Work performed under a contract of the National Research Council of Italy.
Rights and permissions
About this article
Cite this article
Anselmo, L., Bertotti, B., Farinella, P. et al. Orbital perturbations due to radiation pressure for a spacecraft of complex shape. Celestial Mechanics 29, 27–43 (1983). https://doi.org/10.1007/BF01358596
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01358596