• DOI:10.2514/2.3743
• Corpus ID: 123431410

Gravitational Effects of Earth in Optimizing ?V for Deflecting Earth-Crossing Asteroids

@article{Ross2001GravitationalEO,
  title={Gravitational Effects of Earth in Optimizing ?V for Deflecting Earth-Crossing Asteroids},
  author={I. Michael Ross and Sang-Young Park and Scott D. V. Porter},
  journal={Journal of Spacecraft and Rockets},
  year={2001},
  volume={38},
  pages={759-764}
}

• I. Michael Ross, Sang-Young Park, S. Porter
• Published 1 September 2001
• Geology, Physics
• Journal of Spacecraft and Rockets

Analyses incorporating the gravitational effects of Earth to calculate optimal impulses for dee ecting Earthcrossing asteroids are presented. The patched conic method is used to formulate the constrained optimization problem. Geocentric constraints are mapped to heliocentric variables by the use of the impact parameter. The result is a unie ed nonlinear programming problem in the sense that no distinctions are made for short or long warning times. Numerical solutions indicate that the D V requirements are considerably more than those of the previously published two-body analysisthat excludedthird-body effects. Generally speaking, theincrementsin the minimumD V dueto the gravitational effects of the Earth are large (by as much as 60% )for near-Earth asteroids, and the errors diminish for orbits with large eccentricities (e>0:7). Some interesting results for short warning times are also discussed. Nomenclature F;G = Lagrange coefe cients for position Ft;Gt = Lagrange coefe cients for velocity J = objective function for nonlinear programming problem R; R = radius vector from Earth to Earth-crossing asteroid (ECA), its magnitude Rb = impact radius and its generalization Rcritical = proposed miss distance between Earth and ECA RSOI = radius of Earth’ s sphere of ine uence R© = radius of Earth r 0 = initial heliocentric position vector of ECA tb = time when R.t/D Rb t f = time of closest approach between Earth and asteroid after application of 1V t1V = time of application of 1V t1 = time when an ECA impacts Earth V 0 a = initial inertial velocity of ECA V1 = hyperbolic excess velocity V©;Va = inertial velocities of Earth and asteroid, respectively 1V = impulsive velocity increment imparted to an ECA k1Vk = magnitude of 1V π© = gravitational constant of Earth