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 -