Main Property of the Jacobi Integral for Gravity Assist Maneuvers in the Solar System


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Abstract

In the context of the circular restricted three-body problem (RTBP), the search for the spacecraft’s asymptotic velocity \({{V}_{\infty }}\) for gravity assist maneuvers (GMs) can be performed using the Jacobi integral \(J\) and the main property of the Jacobi integral constant for GMs, \({\text{const}} = J \approx 3 - V_{\infty }^{2}.\) It is shown in the paper that the standard cumbersome way of traditional derivation of this property that is used in modern astrodynamics can be significantly simplified.

About the authors

Yu. F. Golubev

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

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Email: golubev@keldysh.ru
Russian Federation, Moscow

A. V. Grushevskii

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

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Email: alexgrush@rambler.ru
Russian Federation, Moscow

I. P. Kiseleva

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Email: den@kiam1.rssi.ru
Russian Federation, Moscow

V. V. Koryanov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Author for correspondence.
Email: korianov@keldysh.ru
Russian Federation, Moscow

A. G. Tuchin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Author for correspondence.
Email: tag@kiam1.rssi.ru
Russian Federation, Moscow

D. A. Tuchin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

Author for correspondence.
Email: den@kiam1.rssi.ru
Russian Federation, Moscow

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