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Solar Sail Simplified Optimal Control Law for Reaching High Heliocentric Distances

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Abstract

The aim of this paper is to analyze optimal trajectories of a solar sail-based spacecraft in missions towards the outer Solar System region. The paper proposes a simplified approach able to estimate the minimum flight time required to reach a given (sufficiently high) heliocentric distance. In particular, the effect of a set of solar photonic assists on the overall mission performance is analyzed with a simplified numerical approach. A comparison with results taken from the existing literature show the soundness of the proposed approach.

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Abbreviations

\(\mathbb {A}\) :

System dynamics matrix; see Eq. (5)

\(\{a, \, e, \, \omega , \, \nu \}\) :

Modified equinoctial orbital elements

\(a_\mathrm{c}\) :

Characteristic acceleration, mm/s\({^2}\)

\(a_{\max }\) :

Maximum propulsive acceleration, mm/s\(^{2}\)

\(\varvec{b}\) :

Auxiliary vector; see Eq. (6)

\(\{p, \, f, \, g, \, L\}\) :

Modified equinoctial orbital elements

q :

Auxiliary parameter

t :

Flight time, \(\mathrm{years}\)

\(\varvec{u}\) :

Control vector; see Eq. (10)

\(\varvec{x}\) :

State vector; see Eq. (1)

\(\alpha\) :

Solar sail pitch angle, deg

\(\mu _{\odot }\) :

Sun’s gravitational parameter, km\(^{3}\)/s\(^{2}\)

0:

Initial value

f :

Final value

i :

Generic arc

\(\text {obj}\) :

Target value

\(\cdot\) :

Time derivative

\(\text {T}\) :

Transpose matrix

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Caruso, A., Niccolai, L., Quarta, A.A. et al. Solar Sail Simplified Optimal Control Law for Reaching High Heliocentric Distances. Aerotec. Missili Spaz. 100, 337–344 (2021). https://doi.org/10.1007/s42496-021-00100-7

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