Heliocentric trajectory analysis of Sun-pointing smart dust with electrochromic control

A smart dust is a micro spacecraft, with a characteristic side length on the order of a few millimeters, whose surface is coated with electrochromic material. Its orbital dynamics is controlled by exploiting the differential force due to the solar radiation pressure, which is obtained by modulating the reflectivity coefficient of the electrochromic material within a range of admissible values. A significant thrust level can be reached due to the high values of area-to-mass ratio of such a spacecraft configuration. Assuming that the smart dust is designed to achieve a passive Sun-pointing attitude, the propulsive acceleration due to the solar radiation pressure lies along the Sun-spacecraft direction. The aim of this paper is to study the smart dust heliocentric dynamics in order to find a closed form, analytical solution of its trajectory when the reflectivity coefficient of the electrochromic material can assume two values only. The problem is addressed by introducing a suitable transformation that regularizes the spacecraft motion and translates the smart-dust dynamics into that of a linear harmonic oscillator with unitary frequency, whose forcing input is a boxcar function. The solution is found using the Laplace transform method, and afterwards the problem is generalized by accounting for the degradation of the electrochromic material due to its exposition to the solar radiation. Three spacecraft configurations, corresponding to low, medium and high performance smart dusts, are finally used to quantify the potentialities of these advanced devices in an interplanetary mission scenario.