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Smart dust option for geomagnetic tail exploration

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Abstract

In-situ measurements are necessary for a long-term analysis of the spatial structure of the geomagnetic tail. This type of mission requires the use of a propellantless propulsion system, such as a classical solar sail, to continuously rotate the design orbit apse line such that it remains parallel to the Sun-Earth direction. To reduce the mission costs, this paper suggests the employment of Sun-pointing smart dusts, which are here investigated in terms of propulsive acceleration level necessary to guarantee a mission’s feasibility. A Sun-pointing smart dust can be thought of as a millimeter-scale solar sail, whose geometric configuration allows it to passively maintain an alignment with the Sun-spacecraft line. The smart dust external surface is coated with an electrochromic reflective film in such a way that it may change, within some limits, its propulsive acceleration magnitude. A suitable control law is necessary for the smart dust to enable an artificial precession of its Earth-centred orbit, similar to what happens in the GeoSail mission. This paper analyzes the required control law using an optimal approach. In particular, the proposed mathematical model provides a set of approximate equations that allow a simple and effective tradeoff analysis between the propulsive requirements, in terms of the smart dust acceleration, and the characteristics of the design orbit.

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Abbreviations

a :

osculating orbit semimajor axis (km)

a P :

propulsive acceleration, with \({a_P}\underline{\underline \Delta } \left\| {{a_P}} \right\|\) (mm/s2)

a Pr :

radial component of aP (mm/s2)

a Pt :

transverse component of aP (mm/s2)

\(a_{\rm{Pmin}}^*\) :

reference value; see Eq. (21) (mm/s2)

A/m :

area-to-mass ratio (m2/kg)

e :

osculating orbit eccentricity

E*:

eccentric anomaly when r = r* (deg)

f :

dimensionless auxiliary function; see Eq. (31)

F :

dimensionless auxiliary function; see Eq. (34)

G :

dimensionless auxiliary function; see Eq. (35)

\(\mathcal{H}\) :

Hamiltonian function

\({\hat i}\) :

orbital reference frame unit vector

J :

performance index

n :

design parameter

O Earth’s center-of-mass p :

osculating orbit semilatus rectum (km)

r :

Earth-SPSD distance (km)

r*:

reference distance (km)

\({{\hat r}_ \odot }\) :

Sun-SPSD unit vector

R ⊕ :

Earth’s mean radius (km)

S W :

switching function; see Eq. (19)

t :

time (days)

\(\mathcal{T}(O;{\hat i}_{\rm{r}}, {\hat i}_{\rm{t}})\) :

orbital reference frame

δ:

Earth-Sun line angle (deg)

Δt sp :

scientific phase time interval (days)

λi :

variables adjoint to ith state

μ⊕ :

Earth’s gravitational parameter (km3/s2)

ν :

osculating orbit true anomaly (deg)

ν*:

true anomaly when r = r* (deg)

φ :

auxiliary angle; see Eq. (7) (deg)

τ :

dimensionless switching parameter

ω :

osculating orbit argument of perigee (deg)

Ω⊕ :

Earth’s orbital angular velocity (deg/day)

0:

initial

a:

apogee

ac:

constrained to aPmin

f:

final

max:

maximum

min:

minimum

p:

perigee

r:

radial

t:

transverse

max:

maximum

min:

minimum

∧:

unit vector

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Acknowledgements

This work is supported by the University of Pisa, Progetti di Ricerca di Ateneo (Grant No. PRA_2018_44).

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Authors and Affiliations

  1. Department of Civil and Industrial Engineering, University of Pisa, Pisa, I-56122, Italy

    Alessandro A. Quarta, Giovanni Mengali & Lorenzo Niccolai

Authors
  1. Alessandro A. Quarta
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  2. Giovanni Mengali
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  3. Lorenzo Niccolai
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Corresponding author

Correspondence to Alessandro A. Quarta.

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Alessandro A. Quarta received his Ph.D. degree in aerospace engineering from the University of Pisa in 2005, and is currently a professor of flight mechanics at the Department of Civil and Industrial Engineering of the University of Pisa. His main research areas include spaceflight simulation, spacecraft mission analysis and design, low-thrust trajectory optimization, solar sail and E-sail dynamics and control.

Giovanni Mengali received his doctor degree in aeronautical engineering in 1989 from the University of Pisa. Since 1990, he has been with the Department of Aerospace Engineering (now Department of Civil and Industrial Engineering) of the University of Pisa, first as a Ph.D. student, then as an assistant and an associate professor. Currently, he is a professor of space flight mechanics. His main research areas include spacecraft mission analysis, trajectory optimization, solar sails, electric sails and aircraft flight dynamics and control.

Lorenzo Niccolai received his Ph.D. degree in aerospace engineering from the University of Pisa in 2018. His current research interests include mission design, trajectory analysis and control, with particular focus on innovative propulsive concepts as solar sails and electric solar wind sails.

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Quarta, A.A., Mengali, G. & Niccolai, L. Smart dust option for geomagnetic tail exploration. Astrodyn 3, 217–230 (2019). https://doi.org/10.1007/s42064-019-0048-3

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  • DOI: https://doi.org/10.1007/s42064-019-0048-3

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