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Analysis of the integrals of the equations of motion of artificial earth satellites in the normal gravitational field of the earth
PlatM. Space Sci.. 1963, Vol. il. pi. 213 to 215.
l’cqamon
hcsr Ltd.
P&&d
in Northern Ir&md
ABSTRACTS Iskwstvennye Sputniki Zemli No. 13 (1962) Translations of any papers abstracted here may be obtained from Pergamon Institute at a reasonable cost. Enquiries should be addressed to the Administrative Secretary, Pergamon Institute, at either Headington Hill Hall, Oxford, England, or 122 East 55th Street, New York, NY., U.S.A. Any papers marked * have been selected for full translation in this section of future issues of Phetary and Space Science. This issue of the journal contains articles devoted to investigations of cosmic ra the radiation belts of the earth and ionospheric physics. Others deal with orbit analysis mathematics and ;I”e measurement of range in outer space by radar. Three papers give the results of investigations into space biology and s ace medicine. These results were obtained by Soviet investigators using geophysical rockets, artificial eaI satellites and space vehicles. *P. YE. ELY’ASBERG: D&mliM tion of an orbit from two positions (pp. 3-22). Tt is considered that the problem of selecting or determining the unperturbed orbit of an artificial space object passing through two specified positions cannot always be solved directly by the Gaussian method or Euler-Lambert equations since there may be doubt about the existence of the orbit and the type of orbit (elliptical, parabolic, hyperbolic or vertical). A comprehensive study is made of this problem with special reference to the existence of single+alued solutions; common special cases are also treated. Versions of the solution are tabulated. The conditions for the optimal solution in the event of muiti-v~ued solutions are considered, N. D. Krsr.~: Analysis of the integrals of the eqmtiona of motion of artifidal earth sateIlttes in the normal tIeIdof the earth (pp. 23-52). The author develops a previous paper and considers the general case of the orbital motion of artificial satellites outside the earth’s atmosphere. His earlier equations are transformed for use on computers and also used to determine the perturbations of elliptic (Kepler) orbits due to the earth’s mass distribution for elucidation of the qualitative features of motion. The author points out that J. P. Vmti arrived independently at similar results in a paper published in 1959 (J. Res. Nat. Bur. Stand. Math. and Math. Phys., 62B, 79, 1959). ~vitational
*V. V. BELE~KII: The orbit of an equatorial earth satellite (pp. 53-60). A mathematical study is made of the motion of a point in the equatorial plane of a flattened spheroid in reference to the motion of an artificial earth satellite. The traiectorv of the satellite and the behaviour of the osculating elements of the orbit are considered. The principal ~h~e~sti~ of motion are given. A special feature is the discussion of the error resulting from the substitution of variables in the method of osculating elements in eomrexion with the effect of pertmbations. *V. M. VAKHNIN:The e&et of the earth’s orbital motion on measurements of range and vehcity in interapace by radio methods (pp. 61-66). Approximate formulae are proposed for estimating the range and velocity of objects in remote space by radar :
phwtwy
Q+y, dR vadr B = d7 = 1 d7
which are claimed to be valid with a small relativistic correction (Lore&x factor): 1
where the subscripts E and S refer to terrestrial and solar frameworks. 213
l’cqamon
hcsr Ltd.
P&&d
in Northern Ir&md
ABSTRACTS Iskwstvennye Sputniki Zemli No. 13 (1962) Translations of any papers abstracted here may be obtained from Pergamon Institute at a reasonable cost. Enquiries should be addressed to the Administrative Secretary, Pergamon Institute, at either Headington Hill Hall, Oxford, England, or 122 East 55th Street, New York, NY., U.S.A. Any papers marked * have been selected for full translation in this section of future issues of Phetary and Space Science. This issue of the journal contains articles devoted to investigations of cosmic ra the radiation belts of the earth and ionospheric physics. Others deal with orbit analysis mathematics and ;I”e measurement of range in outer space by radar. Three papers give the results of investigations into space biology and s ace medicine. These results were obtained by Soviet investigators using geophysical rockets, artificial eaI satellites and space vehicles. *P. YE. ELY’ASBERG: D&mliM tion of an orbit from two positions (pp. 3-22). Tt is considered that the problem of selecting or determining the unperturbed orbit of an artificial space object passing through two specified positions cannot always be solved directly by the Gaussian method or Euler-Lambert equations since there may be doubt about the existence of the orbit and the type of orbit (elliptical, parabolic, hyperbolic or vertical). A comprehensive study is made of this problem with special reference to the existence of single+alued solutions; common special cases are also treated. Versions of the solution are tabulated. The conditions for the optimal solution in the event of muiti-v~ued solutions are considered, N. D. Krsr.~: Analysis of the integrals of the eqmtiona of motion of artifidal earth sateIlttes in the normal tIeIdof the earth (pp. 23-52). The author develops a previous paper and considers the general case of the orbital motion of artificial satellites outside the earth’s atmosphere. His earlier equations are transformed for use on computers and also used to determine the perturbations of elliptic (Kepler) orbits due to the earth’s mass distribution for elucidation of the qualitative features of motion. The author points out that J. P. Vmti arrived independently at similar results in a paper published in 1959 (J. Res. Nat. Bur. Stand. Math. and Math. Phys., 62B, 79, 1959). ~vitational
*V. V. BELE~KII: The orbit of an equatorial earth satellite (pp. 53-60). A mathematical study is made of the motion of a point in the equatorial plane of a flattened spheroid in reference to the motion of an artificial earth satellite. The traiectorv of the satellite and the behaviour of the osculating elements of the orbit are considered. The principal ~h~e~sti~ of motion are given. A special feature is the discussion of the error resulting from the substitution of variables in the method of osculating elements in eomrexion with the effect of pertmbations. *V. M. VAKHNIN:The e&et of the earth’s orbital motion on measurements of range and vehcity in interapace by radio methods (pp. 61-66). Approximate formulae are proposed for estimating the range and velocity of objects in remote space by radar :
phwtwy
Q+y, dR vadr B = d7 = 1 d7
which are claimed to be valid with a small relativistic correction (Lore&x factor): 1
where the subscripts E and S refer to terrestrial and solar frameworks. 213