Space Vehicle Guidance, Navigation, Control, and Estimation Operations Technologies
Abstract
Relative orbital elements provide a geometric description of satellite motion referenced to another satellite in close formation flight under two-body circular reference conditions. When the relative motion is adequately characterized by first order theory, the six relative orbital elements describe the location and size of the instantaneous in-the-plane ellipse, the angular position around the ellipse, and the out-of-place amplitude and angular position. These elements are explicitly relatable to the six rectangular position and velocity coordinates. Second order theories become necessary when the close-proximity assumption is violated. Two distinct theories for (quasi) second order relative orbital elements are explored. One theory uses the expanded solution form and introduces several instantaneous ellipses with corresponding element sets totaling twenty-one individual elements. Overall motion is described by a linear combination of the ellipses. Another theory uses the compacted solution form and introduces a single instantaneous ellipse with corresponding element set totaling nine individual elements. In each case, the theory quantifies distortion of the first order relative orbital elements when including second order effects. The new variables are described as quasi elements because they form a non-minimal set of coordinates. Several examples are presented, both analytically and numerically. New periodic conditions, geometric interpretations, and relations to fixed and variable Lissajous curves are also explored.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 29, 2018
- Accession Number
- AD1050955
Entities
People
- Brett Newman
Organizations
- Old Dominion University