On the 75th birthday of A.P.Markeev

Hill’s curves and libration points in the low-thrust restricted circular threebody problem

P. S. Krasil'nikov

Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia

Abstract: The plane circular restricted three-body problem is considered, where the massless body is a constant low-thrust spacecraft. It is assumed that the vector of low-thrust is directed along the $Ox$ axis connecting the main bodies. The problem of plotting a family of one-parameter Hill’s curves is investigated. The existence conditions of artificial triangular-type and collineartype libration points are obtained. The values of the effective force function at libration points are investigated also. Six different topological types of the family of one-parameter Hill’s curves are described. It is shown that these types differ in the number of critical values of the constant Jacobi integral and in the ordering of these values. For the Earth – Moon system, a family of one-parameter Hill’s curves is plotted for each of the six types.

Keywords: restricted three-body problem, Hill’s curves, libration points, constant low-thrust spacecraft.

UDC: 521.13

MSC: 70F07, 70K42, 53A04

Received: 01.11.2017
Accepted: 08.12.2017

DOI: 10.20537/nd1704007

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