TY - GEN

T1 - Approximate time-dependent solutions of the two-body problem

AU - Benavides, Julio César

AU - Spencer, David B.

PY - 2010

Y1 - 2010

N2 - The N-body problem is defined and its equations of motion are introduced along with the equations of motion for the two-body problem. Time dependent series solutions of the two-body problem are discussed. A new time transformation based on these series solutions is introduced and used to develop a time-dependent, analytic, first-order solution of the two-body problem. A process of deriving higher-order, time-dependent, analytic solutions of the two-body problem is also introduced. These analytic solutions are shown to be capable of describing complete, two-body trajectories with good accuracy and with far fewer function evaluations than are required by numerical integration.

AB - The N-body problem is defined and its equations of motion are introduced along with the equations of motion for the two-body problem. Time dependent series solutions of the two-body problem are discussed. A new time transformation based on these series solutions is introduced and used to develop a time-dependent, analytic, first-order solution of the two-body problem. A process of deriving higher-order, time-dependent, analytic solutions of the two-body problem is also introduced. These analytic solutions are shown to be capable of describing complete, two-body trajectories with good accuracy and with far fewer function evaluations than are required by numerical integration.

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M3 - Conference contribution

AN - SCOPUS:80053409709

SN - 9780877035602

T3 - Advances in the Astronautical Sciences

SP - 1239

EP - 1256

BT - Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences

T2 - AAS/AIAA Space Flight Mechanics Meeting

Y2 - 14 February 2010 through 17 February 2010

ER -