Maneuver Design Using Relative Orbital Elements
- PDF / 1,739,197 Bytes
- 36 Pages / 439.642 x 666.49 pts Page_size
- 38 Downloads / 181 Views
Maneuver Design Using Relative Orbital Elements David A. Spencer1
· Thomas A. Lovell2
© American Astronautical Society 2015
Abstract Relative orbital elements provide a geometric interpretation of the motion of a deputy spacecraft about a chief spacecraft. The formulation yields an intuitive understanding of how the relative motion evolves with time, and by incorporating velocity changes in the local-vertical, local-horizontal component directions, the change in relative motion due to impulsive maneuvers can be evaluated. This paper utilizes a relative orbital element formulation that characterizes relative motion where the chief spacecraft is assumed to be in a circular orbit. Expressions are developed for changes to the relative orbital elements as a function of the impulsive maneuver components in each coordinate direction. A general maneuver strategy is developed for targeting a set of relative orbital elements, and this strategy is applied to scenarios that are relevant for close proximity operations, including establishing a stationary relative orbit, natural motion circumnavigation, and station-keeping in a leading or trailing orbit. Keywords Orbital mechanics · Relative motion · Proximity operations
David A. Spencer
[email protected] 1
Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA
2
Space Vehicles Directorate, Air Force Research Laboratory, Kirtland, NM 87116, USA
J of Astronaut Sci
Nomenclature ar = Az = Er = k= n= P = r= r¯ = r¯ C = s= t= tb = tgt = x= x˙ = xˆ = xr = xq = y= y˙ = yˆ = yr = yq = ys = y˙s = z= z˙ = zˆ = γ = V = V¯ = Vx = Vy = Vz = ρ¯ = ψ= 0=
semimajor axis of the instantaneous relative ellipse amplitude of the motion in the LVLH z-direction relative eccentric anomaly integer multiplier mean motion of the chief’s orbit chief orbit period magnitude of deputy position vector with respect to center of central body deputy position vector with respect to center of central body deputy position vector with respect to center of central body integer number of orbits time maneuver epoch subscript indicating target relative position vector component in LVLH x-direction derivative with respect to time of relative position vector component in LVLH x-direction, taken in LVLH frame LVLH coordinate unit vector in radial direction x-coordinate of instantaneous center of motion x-coordinate of point Q on circle that circumscribes instantaneous relative orbit ellipse relative position vector component in LVLH y-direction derivative with respect to time of relative position vector component in LVLH y-direction, taken in LVLH frame LVLH coordinate unit vector in along-track direction y-coordinate of instantaneous center of motion y-coordinate of point Q on circle that circumscribes instantaneous relative orbit ellipse secular drift in LVLH y-direction secular drift rate in LVLH y-direction relative position vector component in LVLH z-direction derivative with respect to time of relative position vector component in LVLH z-dir
Data Loading...
