<p>This paper presents a new model for modifying the relative orbit of a deputy satellite with respect to a chief satellite in a near-circular orbit using continuous periodic thrust. This model is built on the Lovell-Spencer relative orbital elements (ROEs). The four linear ROEs (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2024_475_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$x_r$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>x</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2024_475_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$y_r$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>y</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2024_475_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$a_r$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>a</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2024_475_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$A_z$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>z</mi> </msub> </math></EquationSource> </InlineEquation>) can be linearly modified. The two angular ROEs (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2024_475_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$E_r$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40295_2024_475_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\psi$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>) can be set to advance at a desired, constant rate. Each ROE can be modified individually, but may cause intra-orbit variations in other ROEs which return to their original values at the end of a thrust cycle. Derivation of the model is presented. A method to easily calculate the periodic thrust parameters is developed. Finally, GMAT results are used to demonstrate how each ROE can be linearly modified.</p>

Guidance for Spacecraft Relative Motion Using Continuous Periodic Thrust

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发表日期：

2025年1月23日

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Philip A. Hittepole,
Jennifer S. Hudson

摘要

This paper presents a new model for modifying the relative orbit of a deputy satellite with respect to a chief satellite in a near-circular orbit using continuous periodic thrust. This model is built on the Lovell-Spencer relative orbital elements (ROEs). The four linear ROEs ( $x_r$ $x_{r}$ , $y_r$ $y_{r}$ , $a_r$ $a_{r}$ , and $A_z$ $A_{z}$ ) can be linearly modified. The two angular ROEs ( $E_r$ $E_{r}$ and $\psi$ $ψ$ ) can be set to advance at a desired, constant rate. Each ROE can be modified individually, but may cause intra-orbit variations in other ROEs which return to their original values at the end of a thrust cycle. Derivation of the model is presented. A method to easily calculate the periodic thrust parameters is developed. Finally, GMAT results are used to demonstrate how each ROE can be linearly modified.