Scholarlink

<p>In this work we investigate the equilibrium states of a pair of two small bodies, natural or artificial, that remain very close to each other, undergo a weak interaction and move in the field created by a formation of <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>N</mi> <mo>=</mo> <mi>ν</mi> <mo>+</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$N=\nu +1$</EquationSource> </InlineEquation> large bodies, <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> <EquationSource Format="TEX">$\nu $</EquationSource> </InlineEquation> of which have equal masses and are located at the vertices of an imaginary regular <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> <EquationSource Format="TEX">$\nu $</EquationSource> </InlineEquation>-gon while the <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math> <mi>N</mi> </math></EquationSource> <EquationSource Format="TEX">$N$</EquationSource> </InlineEquation>th body with a different mass is located at the center of mass of the system. We consider that forces acting on the small bodies by all large primaries are produced by the classical Newtonian gravitational potential of these bodies. However, the potential produced by the central primary is characterized by an additional Manev-type inverse square corrective term. This term may play the role of a normalizing factor of the Universal Law of Gravitation in cases where the central primary is a non-spherical body (oblate or prolate spheroid) or a strong source of radiation. By assuming that the primary bodies are in relative equilibrium, we give the equations of motion of the pair of small bodies, in a synodic coordinate system rigidly attached to the primaries. We numerically investigate the equilibrium states and study their stability. A part of this work is dedicated to the parametric variation of two characteristic quantities of the small bodies, that is the distance <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> <EquationSource Format="TEX">$\rho $</EquationSource> </InlineEquation> between them and their Jacobian constant <InlineEquation ID="IEq8"> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>p</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$C_{p}$</EquationSource> </InlineEquation> at an equilibrium state.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Equilibrium states of a dual satellite’s system in the regular polygon problem of (\(N + 2\)) bodies where the central primary creates a Manev-like quasi-homogeneous potential

  • 期刊论文

  • 发表日期：

    2026年5月14日

查看全文
  • Maria N. Croustalloudi,
  • Tilemahos J. Kalvouridis

摘要

In this work we investigate the equilibrium states of a pair of two small bodies, natural or artificial, that remain very close to each other, undergo a weak interaction and move in the field created by a formation of N = ν + 1 $N=\nu +1$ large bodies, ν $\nu $ of which have equal masses and are located at the vertices of an imaginary regular ν $\nu $ -gon while the N $N$ th body with a different mass is located at the center of mass of the system. We consider that forces acting on the small bodies by all large primaries are produced by the classical Newtonian gravitational potential of these bodies. However, the potential produced by the central primary is characterized by an additional Manev-type inverse square corrective term. This term may play the role of a normalizing factor of the Universal Law of Gravitation in cases where the central primary is a non-spherical body (oblate or prolate spheroid) or a strong source of radiation. By assuming that the primary bodies are in relative equilibrium, we give the equations of motion of the pair of small bodies, in a synodic coordinate system rigidly attached to the primaries. We numerically investigate the equilibrium states and study their stability. A part of this work is dedicated to the parametric variation of two characteristic quantities of the small bodies, that is the distance ρ $\rho $ between them and their Jacobian constant C p $C_{p}$ at an equilibrium state.