[en] In the present paper, an averaging perturbation technique leads to the determination of a time-explicit analytic approximate solution for the motion of a low-Earth-orbiting satellite. The two dominant perturbations are taken into account: the Earth oblateness and the atmospheric drag. The proposed orbit propagation algorithm comprises the Brouwer–Lyddane transformation (direct and inverse), coupled with the analytic solution of the averaged equations of motion. This solution, based on equinoctial elements, is singularity-free, and therefore it stands for low inclinations and small eccentricities as well. The simplifying assumption of a constant atmospheric density is made, which is reasonable for near-circular orbits and short-time orbit propagation. Two sets of time-explicit equations are provided, for moderate and small eccentricities (O(e4)=0 and O(e2)=0, respectively), and they are obtained by performing (1) a regularization of the original averaged differential equations of motion for the vectorial orbital elements, and (2) Taylor series expansions of the aforementioned equations with respect to the eccentricity. The numerical simulations show that the errors due to the use of the proposed analytic model in the presence of drag are almost the same as the errors of the Brouwer first-order approximation in the absence of drag.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Martinusi, Vladimir ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Dell'Elce, Lamberto ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Kerschen, Gaëtan ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Language :
English
Title :
Analytic propagation of near-circular satellite orbits in the atmosphere of an oblate planet
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1964)
Angeles, J.: Fundamentals of Robotic Mechanical Systems. Springer, New York (2002)
Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. AIAA, Reston (1999)
Brouwer, D.: Solution of the problem of artificial satellite theory without drag. Astron. J. 64, 378 (1959)
Brouwer, D., Hori, G.-I.: Theoretical evaluation of atmospheric drag effects in the motion of an artificial satellite. Astron. J. 66, 193 (1961)
Cain, B.J.: Determination of mean elements for Brouwer’s satellite theory. Astron. J. 67, 391 (1962)
Chao, C.C.: Applied Orbit Perturbation and Maintenance. Aerospace Press, New York (2005)
Cid, R., Lahulla, J.F.: Perturbaciones de corto periodo en el movimiento de un satélite artificial, en función de las variables de Hill. Publicaciones de la Revista de la Academia de Ciencias de Zaragoza 24, 159–165 (1969)
Condurache, D., Martinusi, V.: Analytical orbit propagator based on vectorial orbital elements. In AIAA Guidance, Navigation and Control Conference, Boston, MA, Aug 2013
Dell’Elce, L., Kerschen, G.: Probabilistic assessment of the lifetime of low-earth-orbit spacecraft: uncertainty characterization. J. Guid Control Dyna 1, 1–13 (2014)
Deprit, A.: Canonical transformations depending on a small parameter. Celest. Mech. 1, 12–30 (1969)
Deprit, A.: The elimination of the Parallax in satellite theory. Celest. Mech. 24, 111–153 (1981)
Franco, J.M.: An analytic solution for Deprit’s radial intermediary with drag in the equatorial case. Bull. Astron. Inst. Czechoslov. 42, 219–224 (1991)
Garfinkel, B.: The orbit of a satellite of an oblate planet. Astron. J. 64, 353 (1959)
Hestenes, D.: New Foundations for Classical Mechanics. Kluwer Academic Publishers, New York (1999)
King-Hele, D.: Butterworths mathematical texts. In: Theory of Satellite Orbits in an Atmosphere. Butterworths, New York (1964)
Kozai, Y.: The motion of a close earth satellite. Astron. J. 64, 367–377 (1959)
Lara, M., San-Juan, J.F., López-Ochoa, L.M.: Delaunay variables approach to the elimination of the perigee in artificial satellite theory. Celest. Mech. Dyn. Astron. 120(1), 39–56 (2014)
Lyddane, R.H.: Small eccentricities or inclinations in the Brouwer theory of the artificial satellite. Astron. J. 68, 555–558 (1963)
Mittleman, D., Jezewski, D.: An analytic solution to the classical two-body problem with drag. Celest. Mech. 28, 401–413 (1982)
Parks, A.D.: A Drag-Augmented Brouwer–Lyddane Artificial Satellite Theory and Its Application to Long-Term Station Alert Predictions. Technical Report NSWC TR 83–107, Naval Surface Weapons Center, Dahlgren, VA, Apr 1983
Roy, A.E.: Orbital Motion. CRC Press, New York (2004)
Schaub, H., Junkins, J.L.: AIAA education series. In: Analytical Mechanics of Space Systems. American Institute of Aeronautics and Astronautics, New York (2003)
Vallado, D.A., McClain, W.D.: Fundamentals of Astrodynamics and Applications. Microcosm Press, Space technology library (2001)
Vinh, N.X., Longuski, J.M., Busemann, A., Culp, R.D.: Analytic theory of orbit contraction due to atmospheric drag. Acta Astron. 6, 697–723 (1979)
Vinti, J.P.: Theory of the orbit of an artificial satellite with use of spheroidal coordinates. Astron. J. 65, 353–354 (1960)
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.