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Modeling orbital relative motion to enable formation design from application requirements

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Abstract

While trajectory design for single satellite Earth observation missions is usually performed by means of analytical and relatively simple models of orbital dynamics including the main perturbations for the considered cases, most literature on formation flying dynamics is devoted to control issues rather than mission design. This work aims at bridging the gap between mission requirements and relative dynamics in multi-platform missions by means of an analytical model that describes relative motion for satellites moving on near circular low Earth orbits. The development is based on the orbital parameters approach and both the cases of close and large formations are taken into account. Secular Earth oblateness effects are included in the derivation. Modeling accuracy, when compared to a nonlinear model with two body and J2 forces, is shown to be of the order of 0.1% of relative coordinates for timescales of hundreds of orbits. An example of formation design is briefly described shaping a two-satellite formation on the basis of geometric requirements for synthetic aperture radar interferometry.

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Abbreviations

a:

Semi-major axis

e:

Eccentricity

i:

Inclination

r:

Satellite distance from Earth center

t:

Time

u:

Argument of latitude

x, y, z:

Hill’s reference frame of chief

x|, y|, z| :

Reference frame centered in the chief with axes parallel to x||, y||, z||

x||, y||, z|| :

Hill’s reference frame of the reference satellite

D:

Subscript identifying deputy parameters

M:

Mean anomaly

MCH :

Transformation matrix from the chief geocentric reference frame to the Hill’s reference frame

MDC :

Transformation matrix from the deputy geocentric reference frame to the chief geocentric reference frame

X, Y, Z:

Geocentric inertial reference frame

XC, YC, ZC :

Geocentric reference frame of the chief

XD, YD, ZD :

Geocentric reference frame of the deputy

α :

Rotation angle between x, y, z and x|, y|, z| around z ≡ z|

δ :

Variation of parameters between deputy and chief when the latter is on elliptical orbit

ν :

True anomaly

ω :

Argument of perigee

Δ:

Variation of parameters between deputy and chief when the latter is on circular orbit and between chief/deputy and the reference satellite when chief is on elliptical orbit

\({\vartheta}\) :

Radar viewing angle (off-nadir angle)

Ω:

Right ascension of the ascending node

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Authors and Affiliations

  1. Department of Aerospace Engineering, University of Naples Federico II, P.le Tecchio, 80, 80125, Napoli, Italy

    Giancarmine Fasano

  2. Department of Aerospace and Mechanical Engineering, Second University of Naples, Via Roma, 29, 81131, Aversa, Caserta, Italy

    Marco D’Errico

Authors
  1. Giancarmine Fasano
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  2. Marco D’Errico
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Correspondence to Giancarmine Fasano.

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Fasano, G., D’Errico, M. Modeling orbital relative motion to enable formation design from application requirements. Celest Mech Dyn Astr 105, 113–139 (2009). https://doi.org/10.1007/s10569-009-9230-5

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  • DOI: https://doi.org/10.1007/s10569-009-9230-5

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