Existence of conditionally periodic orbits for the motion of a satellite around the oblate earth
Author:
Richard Barrar
Journal:
Quart. Appl. Math. 24 (1966), 47-55
MSC:
Primary 70.34
DOI:
https://doi.org/10.1090/qam/198723
MathSciNet review:
198723
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The author’s previous results on the convergence of the Poincaré-von Zeipel procedure in celestial mechanics are applied to the problem of the motion of a satellite around the oblate earth. The investigation concerns a potential that can vary both longitudinally and latitudinally, and also includes behavior near the critical angle. The existence of conditionally periodic orbits in all these cases is established.
R. B. Barrar, A Proof of the convergence of the Poincaré-von Zeipel procedure in celestial mechanics, To appear in The American Journal of Mathematics
- Dirk Brouwer, Solution of the problem of artificial satellite theory without drag, Astronom. J. 64 (1959), 378–397. MR 128510, DOI https://doi.org/10.1086/107958
- Dirk Brouwer and Gerald M. Clemence, Methods of celestial mechanics, Academic Press, New York-London, 1961. MR 0128505
- C. C. Conley, A disk mapping associated with the satellite problem, Comm. Pure Appl. Math. 17 (1964), 237–243. MR 160649, DOI https://doi.org/10.1002/cpa.3160170207
- Boris Garfinkel, On the motion of a satelliite in the vicinity of the critical inclination, Astr. J. 65 (1960), 624–627. MR 115777
Y. Hagihara, Libration of an earth satellite with critical inclination, Smithsonian Contributions to Astrophysics 5 (1961), pp. 39–51
- Gen-ichiro Hori, The motion of an artificial satellite in the vicinity of the critical inclination, Astronom. J. 65 (1960), 291–300. MR 127969, DOI https://doi.org/10.1086/108248
- I. G. Izsak, On the critical inclination in satellite theory, The Use of Artificial Satellites for Geodesy (Proc. First Internat. Sympos., Washington, D.C., 1962) North-Holland, Amsterdam, 1963, pp. 17–40 (English, with Russian summary). MR 0170707
Y. Kozai, Motion of a particle with critical inclination in the gravitational field of a spheroid, Smithsonian Contributions to Astrophysics 5 (1961), pp. 53–58
- W. T. Kyner, Qualitative properties of orbits about an oblate planet, Comm. Pure Appl. Math. 17 (1964), 227–236. MR 160648, DOI https://doi.org/10.1002/cpa.3160170206
- J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1962 (1962), 1–20. MR 147741
- H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Tome I. Solutions périodiques. Non-existence des intégrales uniformes. Solutions asymptotiques, Dover Publications, Inc., New York, N.Y., 1957 (French). MR 0087812
- W. M. Smart, Celestial mechanics, Longmans, Green and Co., London-New York-Toronto, 1954. MR 0061934
- Carl Ludwig Siegel, Vorlesungen über Himmelsmechanik, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956 (German). MR 0080009
- George Springer, Introduction to Riemann surfaces, Addison-Wesley Publishing Company, Inc., Reading, Mass., 1957. MR 0092855
- John P. Vinti, New method of solution for unretarded satellite orbits, J. Res. Nat. Bur. Standards Sect. B 63B (1959), 105–116. MR 108361
R. B. Barrar, A Proof of the convergence of the Poincaré-von Zeipel procedure in celestial mechanics, To appear in The American Journal of Mathematics
D. Brouwer, Solution of the problem of artificial satellite theory without drag, Astronomical Journal 64 (1959), pp. 378–397
D. Brouwer and G. M. Clemence, Methods of celestial mechanics, Academic Press, 1961
C. C. Conley, A disk mapping associated with the satellite problem, Communications on Pure and Applied Mathematics, 17 (1964), pp. 237–243
B. Garfinkel, On the motion of a satellite in the vicinity of the critical inclination, The Astronomical Journal 67 (1960), pp. 624–627
Y. Hagihara, Libration of an earth satellite with critical inclination, Smithsonian Contributions to Astrophysics 5 (1961), pp. 39–51
G. Hori, The motion of an artificial satellite in the vicinity of the critical inclination, The Astronomical Journal 65 (1960), pp. 291–300
I. G. Izsak, On the critical inclination in satellite theory, Smithsonian Institution Astrophysical Observatory Special Report No. 90, (1962)
Y. Kozai, Motion of a particle with critical inclination in the gravitational field of a spheroid, Smithsonian Contributions to Astrophysics 5 (1961), pp. 53–58
W. T. Kyner, Qualitative properties of orbits about an oblate planet, Communications on Pure and Applied Mathematics 17 (1964), pp. 227–236
J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Göttingen Math.-Phys. Kl., No. 1, 1962
H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Vol. I (1892) and Vol. II (1893), Dover Reprint, 1957
W. M. Smart, Celestial mechanics, Longmans, Green and Company, Inc., 1953
C. L. Siegel, Vorlesungen über Himmelsmechanik, Section 23, Springer-Verlag, Berlin, 1956
G. Springer, Introduction to Riemann surfaces, Addison-Wesley Publishing Company, Inc., Reading, Mass., 1957
J. P. Vinti, New method of solution for unretarded satellite orbits, Journal of Research of the National Bureau of Standards 63B (1959), pp. 105–116
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
70.34
Retrieve articles in all journals
with MSC:
70.34
Additional Information
Article copyright:
© Copyright 1966
American Mathematical Society
