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A new universal equation for the time of transfer between two points of the central gravitational field

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Abstract

The paper presents the derivation of two new equations for calculating the time of transfer between two points of the central gravitational field: for hyperbolic orbits and the universal equation for elliptical and hyperbolic orbits. In the paper we have used as an independent variable, instead of the linear elements (semimajor axis, focal parameter of orbit or a chord connecting the ends of boundary radii of transfer), the angular parameter—the angle between the radius vector of an initial point of transfer and the vector of initial velocity of transfer. Paper’s material is a continuation of that presented in the “Space research“ Journal, vol. 2, March–April, 2009.

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References

  1. Subbotin, M.F., Kurs nebesnoi mekhaniki, t. 1 (A Course of Celestial Mechanics, vol. 1), Moscow: Gostekhizdat, 1933.

    Google Scholar 

  2. Subbotin, M.F., Vvedenie v teoreticheskuyu astronomiyu (Introduction to Theoretical Astronomy), Moscow: Nauka, 1968.

    Google Scholar 

  3. Battin, R.H., Astronautical Guidance, New York: McGraw-Hill, 1964. Translated under the title Navedenie v kosmose, Moscow: Mashinostroenie, 1966.

    Google Scholar 

  4. Herrick, S., Astrodynamics, London: Van Nostrand Reinhold Co., 1971. Translated under the title Astrodinamika, Moscow: Mir, 1976.

    MATH  Google Scholar 

  5. El’yasberg, P.E., Vvedenie v teoriyu poleta iskusstvennykh sputnikov Zemli (Introduction to Theory of Flight of Earth’s Satellites), Moscow: Nauka, 1965.

    Google Scholar 

  6. Burdaev, M.N., Teoriya godografov v mekhanike kosmicheskogo poleta (Hodograph Theory in Space Flight Mechanics), Moscow: Mashinostroenie, 1975.

    Google Scholar 

  7. Burdaev, M.N., Application of Hodograph Method to Calculation of Time of Transfer in a Central Gravitational Field, Kosm. Issled., 2009, vol. 47, no. 2, pp. 204–208. [Cosmic Research, pp. 185–190].

    Google Scholar 

  8. Belyakov, A.I, Grafo-analiticheskii metod issledovaniya dvizheniya kosmicheskikh apparatov (Graph-Analytic Method of Investigating Spacecraft Motion), Moscow: Mashinostroenie, 1973.

    Google Scholar 

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Authors and Affiliations

  1. Gagarin State Scientific Research-and-Testing Cosmonaut Training Center, Star City, Moscow oblast’, Russia

    M. N. Burdaev

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  1. M. N. Burdaev
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Correspondence to M. N. Burdaev.

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Original Russian Text. M.N. Burdaev, 2011, published in Kosmicheskie Issledovaniya, 2011, Vol. 49, No. 5, pp. 476–479.

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Burdaev, M.N. A new universal equation for the time of transfer between two points of the central gravitational field. Cosmic Res 49, 464–467 (2011). https://doi.org/10.1134/S0010952511050042

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