New semi-analytical solution is presented here for the motion of small orbiter that is governed by the united Newtonian attraction of three primaries M1, M2, and M3, permanently moving on elliptic orbits with hierarchical configuration M3 < < M2 < < M1 within one plane: second primary M2 is moving around M1 (whereas third primary body M3 is orbiting around M2). Such the solution is the elliptical strongly compressed (in the direction to the plane of mutual orbiting all the primaries) spiral of motion of orbiter which, moving along spiral, is oscillating quasi-periodically with respect to Oy axis (close to it) but periodically with respect to Ox axis (in the range <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$0.095 \le x < 0.1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.095</mn> <mo>≤</mo> <mi>x</mi> <mo><</mo> <mn>0.1</mn> </mrow> </math></EquationSource> </InlineEquation>). Also, orbiter oscillates close to plane <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\{ x,y\} ,\;z \to 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">}</mo> <mo>,</mo> <mspace width="0.277778em" /> <mi>z</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> in a 3D spiraling motion. Such orbiting (in a closed-spiral motion within limited volume of space, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$0.095\;\; \le \;x\; < \;0.1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.095</mn> <mspace width="0.277778em" /> <mspace width="0.277778em" /> <mo>≤</mo> <mspace width="0.277778em" /> <mi>x</mi> <mspace width="0.277778em" /> <mo><</mo> <mspace width="0.277778em" /> <mn>0.1</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\{ x,y\} ,\;\,y \to 0\,,\;z \to 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">}</mo> <mo>,</mo> <mspace width="0.277778em" /> <mspace width="0.166667em" /> <mi>y</mi> <mo stretchy="false">→</mo> <mn>0</mn> <mspace width="0.166667em" /> <mo>,</mo> <mspace width="0.277778em" /> <mi>z</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>) with stable positioning of orbiter close to the ray directing from Sun to Earth can be associated with locus of elements of Dyson swarm which absorb energy radiating from Sun. Thus, it is demonstrated from point of view of celestial mechanics equations (formulated to BiER4BP) the possibility of existence of such the stable dynamical solution. Our finding is that the elements of Dyson swarm form a kind of spot shield on the ray directing from Sun to Earth, i.e., they do not form a sphere around the Sun. Shells of Dyson sphere should be located at distance circa 0.1 A.U. from Sun (with distance ~ 0.9 A.U. to Earth) close to the ray pointing from center of Sun to “Earth–Moon” system.

Searching stable orbits in BiER4BP with variable eccentricity for exploring the stable drift dynamics of Dyson sphere shells

期刊论文
发表日期：

2026年3月18日

查看全文

Sergey Ershkov

摘要

New semi-analytical solution is presented here for the motion of small orbiter that is governed by the united Newtonian attraction of three primaries M₁, M₂, and M₃, permanently moving on elliptic orbits with hierarchical configuration M₃ < < M₂ < < M₁ within one plane: second primary M₂ is moving around M₁ (whereas third primary body M₃ is orbiting around M₂). Such the solution is the elliptical strongly compressed (in the direction to the plane of mutual orbiting all the primaries) spiral of motion of orbiter which, moving along spiral, is oscillating quasi-periodically with respect to Oy axis (close to it) but periodically with respect to Ox axis (in the range $0.095 \le x < 0.1$ $0.095 \leq x < 0.1$ ). Also, orbiter oscillates close to plane $\{ x,y\} ,\;z \to 0$ ${x, y}, z \to 0$ in a 3D spiraling motion. Such orbiting (in a closed-spiral motion within limited volume of space, $0.095\;\; \le \;x\; < \;0.1$ $0.095 \leq x < 0.1$ , $\{ x,y\} ,\;\,y \to 0\,,\;z \to 0$ ${x, y}, y \to 0, z \to 0$ ) with stable positioning of orbiter close to the ray directing from Sun to Earth can be associated with locus of elements of Dyson swarm which absorb energy radiating from Sun. Thus, it is demonstrated from point of view of celestial mechanics equations (formulated to BiER4BP) the possibility of existence of such the stable dynamical solution. Our finding is that the elements of Dyson swarm form a kind of spot shield on the ray directing from Sun to Earth, i.e., they do not form a sphere around the Sun. Shells of Dyson sphere should be located at distance circa 0.1 A.U. from Sun (with distance ~ 0.9 A.U. to Earth) close to the ray pointing from center of Sun to “Earth–Moon” system.