TY - GEN

T1 - Solving and analyzing relative Lambert's problem through differential orbital elements

AU - Wen, Chang Xuan

AU - Zhao, Yu Shan

AU - Li, Bao Jun

AU - Shi, Peng

PY - 2012

Y1 - 2012

N2 - A novel approach based on Lagrange's time equation and differential orbital elements is developed to solve the relative Lambert's problem on circular reference orbit. In comparison with the conventional Clohessy-Wiltshire equation, the proposed method can directly obtain the change of orbital elements. This advantage enables us to account for the singularities occurred in relative Lambert's problem. Results reveal that relative velocities depend on five differential orbital elements between the transfer orbit and the reference orbit. Accordingly, singularities can be attributed to any significant change of the semi-major axis, eccentricity or orbital plane. Furthermore, adjusting the initial and final relative positions properly can remove some of the singularities. A numerical simulation based on classic Lambert's formula for a rendezvous mission in closed range demonstrates all the analytical results.

AB - A novel approach based on Lagrange's time equation and differential orbital elements is developed to solve the relative Lambert's problem on circular reference orbit. In comparison with the conventional Clohessy-Wiltshire equation, the proposed method can directly obtain the change of orbital elements. This advantage enables us to account for the singularities occurred in relative Lambert's problem. Results reveal that relative velocities depend on five differential orbital elements between the transfer orbit and the reference orbit. Accordingly, singularities can be attributed to any significant change of the semi-major axis, eccentricity or orbital plane. Furthermore, adjusting the initial and final relative positions properly can remove some of the singularities. A numerical simulation based on classic Lambert's formula for a rendezvous mission in closed range demonstrates all the analytical results.

UR - http://www.scopus.com/inward/record.url?scp=84879327568&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84879327568

SN - 9780877035817

T3 - Advances in the Astronautical Sciences

SP - 2505

EP - 2518

BT - Spaceflight Mechanics 2012 - Advances in the Astronautical Sciences

T2 - 22nd AAS/AIAA Space Flight Mechanics Meeting

Y2 - 2 February 2012 through 2 February 2012

ER -