Semi-analytical solution for the optimal low-thrust deflection of near-Earth objects

Camilla Colombo, Massimiliano Vasile, Gianmarco Radice

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earth's orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.
LanguageEnglish
Pages796-809
Number of pages13
JournalJournal of Guidance, Control and Dynamics
Volume32
Issue number3
DOIs
Publication statusPublished - Aug 2009

Fingerprint

low thrust
near Earth objects
Asteroids
asteroids
deflection
asteroid
Deflection
Analytical Solution
thrust
Earth (planet)
deviation
Deviation
Satellite interception
Orbits
Gauss equation
Gauss
interception
formulations
orbitals
secular variations

Keywords

  • pareto optimum
  • optimization
  • multiobjective programming
  • numerical integration
  • gaussian process
  • orbital element
  • equation of motion
  • proximal
  • minimal distance
  • spacecraft
  • solid dynamic
  • satellite
  • interception
  • orbit
  • asteroid
  • thrust
  • minimum time

Cite this

@article{638c552130054366b755b56711c7e67c,
title = "Semi-analytical solution for the optimal low-thrust deflection of near-Earth objects",
abstract = "This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earth's orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.",
keywords = "pareto optimum, optimization, multiobjective programming, numerical integration, gaussian process, orbital element, equation of motion, proximal, minimal distance, spacecraft, solid dynamic, satellite, interception, orbit, asteroid, thrust, minimum time",
author = "Camilla Colombo and Massimiliano Vasile and Gianmarco Radice",
year = "2009",
month = "8",
doi = "10.2514/1.40363",
language = "English",
volume = "32",
pages = "796--809",
journal = "Journal of Guidance, Control and Dynamics",
issn = "0731-5090",
number = "3",

}

Semi-analytical solution for the optimal low-thrust deflection of near-Earth objects. / Colombo, Camilla; Vasile, Massimiliano; Radice, Gianmarco.

In: Journal of Guidance, Control and Dynamics, Vol. 32, No. 3, 08.2009, p. 796-809.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Semi-analytical solution for the optimal low-thrust deflection of near-Earth objects

AU - Colombo, Camilla

AU - Vasile, Massimiliano

AU - Radice, Gianmarco

PY - 2009/8

Y1 - 2009/8

N2 - This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earth's orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.

AB - This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earth's orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.

KW - pareto optimum

KW - optimization

KW - multiobjective programming

KW - numerical integration

KW - gaussian process

KW - orbital element

KW - equation of motion

KW - proximal

KW - minimal distance

KW - spacecraft

KW - solid dynamic

KW - satellite

KW - interception

KW - orbit

KW - asteroid

KW - thrust

KW - minimum time

U2 - 10.2514/1.40363

DO - 10.2514/1.40363

M3 - Article

VL - 32

SP - 796

EP - 809

JO - Journal of Guidance, Control and Dynamics

T2 - Journal of Guidance, Control and Dynamics

JF - Journal of Guidance, Control and Dynamics

SN - 0731-5090

IS - 3

ER -