Constant Radial Thrust Acceleration Redux

Abstract

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Explicit Solution to the Constant Radial Acceleration Problem

“…Its practical interest is related, among the other things, to spacecraft low-thrust propulsion [1][2][3][4], to controversial models in modern physics such as that of the Rindler acceleration [5] or anomalies of the gravitational field in the Solar System such as that of the Pioneer anomaly [6].…”

“…The problem can also be analysed using basic manipulations of the energy equation [3,4] which allows to derive classical results [2] and to discriminate, in special cases, between bounded and unbounded motion. In applications related to spacecraft trajectory design [1,7] it is of great importance, on the other hand, to have access to an explicit solution to the problem.…”

Artificial equilibrium points for a generalized sail in the circular restricted three-body problem

“…Finally η = 0 represents a constant propulsive acceleration, or a thrust that is independent of the distance from the massive attractor. Actually η = 0 is consistent with a situation in which the propulsion system is either a minimagnetospheric plasma thruster (Winglee et al, 2000;Trask et al, 2004;Mengali and Quarta, 2006), or an electric thruster when the thrust is modulated such as to provide a constant thrust-to-mass ratio (Prussing and Coverstone, 1998;Mengali and Quarta, 2009a) and the power source is independent of the Sun-spacecraft distance, as in a nuclear-powered system. This happens, for example, when the power subsystem is represented by a radio-isotope thermoelectric generator (Hunt, 1993;Lyngvi et al, 2007).…”

Regularization in Astrodynamics: applications to relative motion, low-thrust missions, and orbit propagation = Regularización en Astrodinámica: aplicaciones al movimiento relativo, misiones de bajo empuje, y propagación de órbitas

“…The angular momentum is also conserved. Prussing and Coverstone-Carroll (1998) and Akella and Broucke (2002) approached the problem from the energy perspective and discussed the corresponding integrals of motion. General considerations on the integrability of the system can be found in the work by San-Juan et al (2012).…”

“…Exact solutions to the constant tangential thrust problem have eluded researchers but explicit solutions to certain variables can be found. For instance, the expressions defining the escape conditions or the amplitude of the bounded motion have been provided by different authors (Prussing and Coverstone-Carroll, 1998;Mengali and Quarta, 2009). Bombardelli et al (2011) derived an alternative asymptotic solution using regular sets of elements.…”