Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010cemda.107..319z&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 107, Issue 3, pp.319-336
Astronomy and Astrophysics
Astronomy
1
Relative Motion, State Transition, Eccentric Orbit, J2 Perturbations, Rendezvous
Scientific paper
A new second-order solution to the two-point boundary value problem for relative motion about orbital rendezvous in one orbit period is proposed. First, nonlinear differential equations to describe the relative motion between a chaser and a target are presented considering the second-order terms in the gravity. Then, by regarding the second-order terms as external accelerations, we establish second-order state transition equations. Moreover, the J2 perturbations effects can also be considered in the state transition equations. Last, the initial relative velocity to fulfill a rendezvous is determined by solving the state transition equations. Numerical simulations show that the new second-order state transition equations are accurate. The second-order solution to the two-point boundary value problem on eccentric orbits is valid even if the relative range is farther than 500 km.
Zhang Gang
Zhou Di
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