TY - JOUR

T1 - Minimal Velocity Surface in a Restricted Circular Three-Body Problem

AU - Kholshevnikov, K. V.

AU - Titov, V. B.

N1 - Funding Information: The equipment of the Computing Center and Research Park of St. Petersburg State University was used for the study. The paper was supported by the Russian Foundation for Basic Research, project no. 18-02-00552. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/10

Y1 - 2020/10

N2 - Abstract: In a restricted circular three-body problem, the concept of the minimum velocity surface (Formula presented.). is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of the Hill surface requires the occurrence of the Jacobi integral. The minimum velocity surface, apart from the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of motion of the main bodies. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained after a single averaging of the original system over the longitude of the main bodies. The properties of (Formula presented.). are investigated. We highlight the most significant issues. The set of possible motions of the zero-mass body bounded by surface (Formula presented.). is compact. As an example, surfaces (Formula presented.). for four small moons of Pluto are considered within the averaged Pluto–Charon–small satellite problem. In all four cases, (Formula presented.). is a topological torus with a small cross section, having a circumference in the plane of motion of the main bodies as the center line.

AB - Abstract: In a restricted circular three-body problem, the concept of the minimum velocity surface (Formula presented.). is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of the Hill surface requires the occurrence of the Jacobi integral. The minimum velocity surface, apart from the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of motion of the main bodies. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained after a single averaging of the original system over the longitude of the main bodies. The properties of (Formula presented.). are investigated. We highlight the most significant issues. The set of possible motions of the zero-mass body bounded by surface (Formula presented.). is compact. As an example, surfaces (Formula presented.). for four small moons of Pluto are considered within the averaged Pluto–Charon–small satellite problem. In all four cases, (Formula presented.). is a topological torus with a small cross section, having a circumference in the plane of motion of the main bodies as the center line.

KW - region of acceptable motions

KW - restricted circular three-body problem

KW - zero velocity surface

UR - http://www.scopus.com/inward/record.url?scp=85097523322&partnerID=8YFLogxK

U2 - 10.1134/S106345412004007X

DO - 10.1134/S106345412004007X

M3 - Article

AN - SCOPUS:85097523322

VL - 53

SP - 473

EP - 479

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -