Perturbations of a Spacecraft Orbit during a Hyperbolic Flyby

A first-order perturbation theory exists for the flyby problem with the Born approximation as the reference orbit (J. D. Anderson and G. Giampieri 1999, Icarus 138, 309–318, AG thereafter). This theory is applicable when the deflection parameter μ/bv2 (where μ is the product of the gravitational constant by the body’s mass, b the impact parameter, and v the velocity of the flyby) is small. Here we present an analytical theory for the motion of a spacecraft with the hyperbola as the reference orbit. The perturbations consist of the next term after the monopole in the central body’s gravitational exterior potential function, represented by the quadrupole harmonic coefficients C20 and C22. The perturbations of the hyperbolic elements are expressed in closed form, without involving infinite series, as functions of the unperturbed orbital elements. We compare results of the new theory with AG’s theory. We find that AG’s theory can be improved by a simple modification, and by correcting a sign error in the C22 term in the potential function. The effects of the body’s rotation on the perturbations are discussed, and new results pertaining to AG’s approach are given. c © 2001 Academic Press