Modelling Natural Formations of LEO Satellites

M Halsall & P L Palmer


In this paper we consider the relative motion between satellites moving along near
circular orbits in LEO. We are focussing upon the natural dynamics in order that we
may then develop a design tool for choosing initial conditions for satellite orbits where
the satellites will follow close to a chosen con guration with little control. The di er-
ence of the approach we present here to other published work on this topic is that we
start with analytic solutions of the equations of motion rather than attempt to develop
linearised equations of relative motion which we then solve. This geometric approach
leads to a natural decomposition of the orbital motion into three components: the mo-
tion of a guiding centre that incorporates the secular evolution of the formation; the
periodic motion of the formation as an approximately solid body about this guiding
centre; and the periodic motion of individual satellites within the formation. By sepa-
rating the motion into these three components we are able to give a full description of
the motion, but in a simple form that avoids a lot of the complexity in other formula-
tions. We then use this model to nd expressions for the motion of one satellite with
respect to another within our formation. We present propagations of satellite orbits to
fully evaluate the accuracy of our expressions, noting additions that may be made to
the model to further increase accuracy.


Paper: FFlying Modelling

Ref: Halsall, M. & Palmer, P.L., J Celestial Mechanics & Dynamical Astronomy, 99, pp. 105–127, 2007.


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