meetings - Space Flight Mechanics Committee

A detailed comparison will be made between the planned method for inserting the Orbiting
Carbon Observatory 2 (OCO-2) into the A-train and the one that would have been used had
OCO-1 successfully achieved its Injection Orbit. Ma-jor differences arise from the fact that
OCO-1 was launched on a Taurus XL with a target 65 km below the A-Train while OCO-2
will be launched on a Delta II with a likely target only 15 km below the A-Train.
Comparisons will include the designs to handle nominal, off-nominal, and contingency
cases.
9:20 AAS Lyapunov-Floquet Transformation of Satellite Relative Motion in Elliptic
13-466 Orbits
Ryan Sherrill, Auburn University; Andrew Sinclair, Auburn University; Thomas
Lovell, Air Force Research Laboratory
9:40 Break
The relative motion between chief and deputy satellites in close proximity with orbits of
arbitrary eccentricity can be described by linearized time-varying equations of motion. The
linear time-invariant Hill-Clohessy-Wiltshire equations are typically derived from these
equations by assuming the chief satellite is in a circular orbit. A Lyapunov-Floquet
transformation has been determined which relates the linearized equations of relative
motion to the Hill-Clohessy-Wiltshire equations through a periodic coordinate
transformation. This transformation allows the Hill-Clohessy-Wiltshire equations to
describe the relative motion for any elliptic orbit.
10:05 AAS Calibration of Linearized Solutions for Satellite Relative Motion
13-467 Andrew Sinclair, Auburn University; Ryan Sherrill, Auburn University; Thomas
Lovell, Air Force Research Laboratory
The motion of a deputy satellite relative to a chief satellite can be described with either
Cartesian coordinates or orbital-element differences. For close proximity, both descriptions
can be linearized. An underappreciated fact is that the linearized descriptions are equivalent:
the linearized transformation between the two solves the linearized dynamics. This suggests
a calibrated initial condition for linearized Cartesian propagation that is related to the
orbital-element differences by the linearized transformation. This calibration greatly
increases the domain of validity of the linearized approximation, and provides far greater
accuracy in matching the nonlinear solution over a larger range of separations.
10:25 AAS Mission Design for NASA’s Van Allen Probes Mission
13-454 Fazle Siddique, The Johns Hopkins University Applied Physics Laboratory; Gene
Heyler, The Johns Hopkins University Applied Physics Laboratory
The Van Allen Probes mission, part of NASA’s Living With a Star Program, successfully
launched on August 30th, 2012 from Cape Canaveral. The two year mission consists of
two spin stabilized spacecraft in highly eccentric Earth orbits that cause one spacecraft to
lap the other approximately four times per year and provide insight into the dynamics of
Earth’s radiation belts. The observatories were designed, built, and operated by the Johns
23 rd AAS / AIAA Space Flight Mechanics Meeting Page 101