<p>This study examines the perturbed photogravitational Circular Restricted Three-Body Problem (CR3BP) under the combined effects of radiation pressure, albedo, continued fractional perturbations, and a gravitational disc. For the Sun–Earth system with the asteroid belt and the Sun–Jupiter system with the Kuiper belt, we analyze how the modified potential influences equilibrium points, Zero-Velocity Curves (ZVCs), and stability. Numerical results show that as the continued fractional parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> increases, new collinear (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$L_1', L_2'$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mn>1</mn> <mo>′</mo> </msubsup> <mo>,</mo> <msubsup> <mi>L</mi> <mn>2</mn> <mo>′</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation>) and non-collinear (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$L_4', L_5'$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mn>4</mn> <mo>′</mo> </msubsup> <mo>,</mo> <msubsup> <mi>L</mi> <mn>5</mn> <mo>′</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation>) points emerge, while disc mass and other perturbations merely shift their locations. The Jacobi constant decreases with increasing <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>, enlarging the allowed motion regions. Stability analysis indicates that <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">$L_1, L_3, L_4', L_5'$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>L</mi> <mn>3</mn> </msub> <mo>,</mo> <msubsup> <mi>L</mi> <mn>4</mn> <mo>′</mo> </msubsup> <mo>,</mo> <msubsup> <mi>L</mi> <mn>5</mn> <mo>′</mo> </msubsup> </mrow> </math></EquationSource> </InlineEquation> are unstable, whereas <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$L_4, L_5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mn>4</mn> </msub> <mo>,</mo> <msub> <mi>L</mi> <mn>5</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> remain stable within certain ranges of the critical mass ratio <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq7.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu _c$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>μ</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>. The new point <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$L_1'$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>L</mi> <mn>1</mn> <mo>′</mo> </msubsup> </math></EquationSource> </InlineEquation> can be stable for specific <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="419_2025_2973_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> values in both systems. Overall, continued fractional perturbations, disc effects, and surface properties reshape equilibrium configurations and modify classical stability boundaries, enriching celestial dynamics and space mission design.</p>

Dynamics and stability in the perturbed photogravitational CR3BP with disc structures and continued fractional effects

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发表日期：

2025年11月1日

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Lata Kumari Bairwa,
Ashok Kumar Pal,
Bhupendra Jangid,
Sergey Ershkov,
Elbaz I. Abouelmagd

摘要

This study examines the perturbed photogravitational Circular Restricted Three-Body Problem (CR3BP) under the combined effects of radiation pressure, albedo, continued fractional perturbations, and a gravitational disc. For the Sun–Earth system with the asteroid belt and the Sun–Jupiter system with the Kuiper belt, we analyze how the modified potential influences equilibrium points, Zero-Velocity Curves (ZVCs), and stability. Numerical results show that as the continued fractional parameter $\epsilon $ $ϵ$ increases, new collinear ( $L_1', L_2'$ $L_{1}^{'}, L_{2}^{'}$ ) and non-collinear ( $L_4', L_5'$ $L_{4}^{'}, L_{5}^{'}$ ) points emerge, while disc mass and other perturbations merely shift their locations. The Jacobi constant decreases with increasing $\epsilon $ $ϵ$ , enlarging the allowed motion regions. Stability analysis indicates that $L_1, L_3, L_4', L_5'$ $L_{1}, L_{3}, L_{4}^{'}, L_{5}^{'}$ are unstable, whereas $L_4, L_5$ $L_{4}, L_{5}$ remain stable within certain ranges of the critical mass ratio $\mu _c$ $μ_{c}$ . The new point $L_1'$ $L_{1}^{'}$ can be stable for specific $\epsilon $ $ϵ$ values in both systems. Overall, continued fractional perturbations, disc effects, and surface properties reshape equilibrium configurations and modify classical stability boundaries, enriching celestial dynamics and space mission design.