Spiral trajectories induced by radial thrust with applications to generalized sails
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https://doi.org/10.1007/s42064-020-0093-6
Spiral trajectories induced by radial thrust with applications to generalized sails Marco Bassetto (), Alessandro A. Quarta, Giovanni Mengali, and Vittorio Cipolla Department of Civil and Industrial Engineering, University of Pisa, Pisa I-56122, Italy
ABSTRACT
KEYWORDS
In this study, new analytical solutions to the equations of motion of a propelled spacecraft
radial thrust
are investigated using a shape-based approach. There is an assumption that the spacecraft
spiral trajectory
travels a two-dimensional spiral trajectory in which the orbital radius is proportional
shape-based approach
to an assigned power of the spacecraft angular coordinate. The exact solution to the
analytical solution
equations of motion is obtained as a function of time in the case of a purely radial
generalized sail
thrust, and the propulsive acceleration magnitude necessary for the spacecraft to track the prescribed spiral trajectory is found in a closed form. The analytical results are then specialized to the case of a generalized sail, that is, a propulsion system capable of providing an outward radial propulsive acceleration, the magnitude of which depends on a given power of the Sun-spacecraft distance. In particular, the conditions for an outward radial thrust and the required sail performance are quantified and thoroughly discussed. It is worth noting that these propulsion systems provide a purely radial thrust when their orientation is Sun-facing. This is an important advantage from an engineering point of view because, depending on the particular propulsion system, a Sun-facing attitude can be stable or obtainable in a passive way. A case study is finally presented, where the
Research Article
generalized sail is assumed to start the spiral trajectory from the Earth’s heliocentric
Received: 27 April 2020
orbit. The main outcome is that the required sail performance is in principle achievable
Accepted: 19 August 2020
on the basis of many results available in the literature.
© The Author(s) 2020
1
Introduction
Analytical solutions to the differential equations that govern the motion of an orbiting propelled spacecraft are available in few cases only [1–3]. Closed-form solutions represent a very useful tool in the preliminary phase of mission design as they significantly reduce the computational cost that would otherwise be required by the numerical propagation of spacecraft dynamics. Analytical solutions to the equations of motion can be found by using two different approaches. The first possibility is to solve the equations of motion for an assigned thrust profile, such as the case of a spacecraft subjected to a constant radial or circumferential propulsive acceleration. This problem was first investigated by Tsien [4], who found an explicit and an approximate [email protected]
solution to the radial and the circumferential case, respectively. Since then, many other authors have discussed the constant radial thrust problem. Prussing and CoverstoneCarroll addressed
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