Aerotecnica Missili & Spazio

, Volume 98, Issue 4, pp 301–308 | Cite as

Venus-Centered Heliosynchronous Orbits with Smart Dusts

  • Marco BassettoEmail author
  • Giovanni Mengali
  • Alessandro A. Quarta
Original article


This paper deals with the problem of determining an analytical control law capable of maintaining highly elliptical heliosynchronous polar orbits around Venus. The problem is addressed using the Smart Dust concept, a propellantless propulsion system that extracts momentum from the solar radiation pressure using a reflective coating. The modulation of the thrust magnitude is performed by exploiting the property of electrochromic materials of changing their optical characteristics through the application of a suitable electrical voltage. The propulsive acceleration can, therefore, be switched from a minimum to a maximum value (or vice versa) so as to obtain a simple on–off control law. The required Smart Dust performance is described in closed form as a function of the semimajor axis and eccentricity of the working orbit. The soundness of the analytical control law is validated through a numerical integration of the equations of motion, in which the orbital perturbations due to the oblateness of Venus and to the gravitational attraction of the Sun are also included.


Smart dust Heliosynchronous orbits around Venus Taranis orbits Polar orbits 

List of Symbols


Semimajor axis of SD orbit (km)


Semimajor axis of Venus’ orbit (km)

\(\varvec{a}_{\female }\)

SD acceleration vector due to Venus (mm/s\(^2)\)

\(\varvec{a}_{\odot }\)

SD acceleration vector due to the Sun (mm/s\(^2)\)


Propulsive acceleration (mm/s\(^2\))


Eccentricity of SD orbit

\(\{f,\, F,\, g,\, G\}\)

Auxiliary functions, see Eqs. (10)–(11)


SD orbit altitude (km)


Orbital inclination (rad)

\(\{J_2,\, J_3,\, J_4\}\)

Venus’ zonal harmonics


Ratio of \(\beta _{\max }\) to \(\beta _{\min }\)


Semilatus rectum (km)


Legendre polynomial of degree j, see Eq. (24)


Orbit radius (km)

\(R_{\female }\)

Venus’ mean radius (km)


Venus–SD position vector (km)

\(\varvec{r}_{\odot }\)

SD–Sun position vector (au)


Time (days)


Orbital period (days)


Argument of latitude (rad)


SD–Venus’ equatorial plane distance (km)


Angle between \(\varvec{r}_{\odot }\) and SD orbital plane (rad)


Lightness number


Auxiliary function, see Eq. (18)

\(\mu _{\odot }\)

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

\(\mu _{\female }\)

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


True anomaly (rad)


Argument of periapsis (rad)


Right ascension of the ascending node (rad)

\(\omega _{\female }\)

Mean motion of Venus (rad/s)











Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© AIDAA Associazione Italiana di Aeronautica e Astronautica 2019

Authors and Affiliations

  1. 1.University of PisaPisaItaly

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