Abstract
This paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.
Highlights
This paper is an extension of the work presented in Zuiani and Vasile (2012) and Zuiani and Vasile (2015) and in Di Carlo et al (2017b)
This paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations
This paper has presented a collection of analytical formulae for the propagation of the motion of a spacecraft under the effect of a number of disturbing accelerations
Summary
This paper is an extension of the work presented in Zuiani and Vasile (2012) and Zuiani and Vasile (2015) and in Di Carlo et al (2017b). In these works, analytical formulae were derived for the motion of a spacecraft subject to constant tangential acceleration, constant acceleration in the radial–transverse–normal reference frame, constant acceleration in an inertial reference frame, and orbital perturbations due to the second-order zonal harmonic of the central body gravitational perturbation, J2. The analytical formulae were obtained using a first-order expansion in the perturbing acceleration
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