Closed Cluster Solution 8 There exist free orbits that cause a S/c to follow a closed and periodic motion with respect to the Hills frame as well as other S/c of the same period x= Acos(nt +a) y=-2Asin(nt +a)+ Z Bcos(nt+β) 8 the s/c must follow a two-by-one ellipse in the Hills frames zenith- velocity plane transverse displacement is independent and oscillatory 8 The parameters A, B, a,B, and y can be selected for each spacecraft in the cluster based upon the projection of some ground track motion to allow natural orbital dynamics to most uniquely sweep out aperture baselines to make the array appear rigid from some perspectiveClosed Cluster Solution Closed Cluster Solution F There exist free orbits that cause a S/C to follow a closed and periodic motion with respect to the Hill’s frame as well as other S/C of the same period. F the S/C must follow a two-by-one ellipse in the Hill’s frame’s zenith￾velocity plane. — transverse dis placement is independent and oscillatory. F The parameters A, B, α, β, and y o can be selected for each spacecraft in the cluster. — based upon the projection of some ground track motion. — to allow natural orbit al dynamics to most uniquely sweep out aperture baselines. — to make the array appear “rigid” from some perspective. x = Acos(nt + α ) y = − 2 Asin(nt + α ) + y o z = Bcos(nt + β )