Tangent Orbital Rendezvous Using Linear Relative Motion with 𝐽₂ Perturbations

Table 1

Solutions of Δ𝑡_tran,𝐹1 and Δ𝑡_tran,𝐹2 and their costs for different Δ𝑡₁.

	Tangent to initial orbit		Tangent to final orbit
Δ𝑡1	Δ𝑡tran,𝐹1	Δ𝑣total	Δ𝑡tran,𝐹2	Δ𝑣total
(Orbit period)	(Orbit period)	(m/s)	(Orbit period)	(m/s)
0	0.704717	0.825201	0.059408	9.837243
0.1	0.502039	0.982136	0.033730	22.20027
0.2	0.004492	158.3517	0.918635	1.034115
	0.260872	1.949606
0.3	0.897311	1.111503	0.561613	1.039989
0.4	0.801650	1.142299	0.342601	1.704567
0.5	0.707957	1.160767	0.193872	3.458322
0.6	0.615953	1.163889	0.097424	8.342175
0.7	0.526142	1.147815	0.034026	28.92826
0.8	0.006292	184.3432	0.875984	1.035060
	0.440795	1.101123
	0.983633	1.313181
0.9	0.022954	51.75954	0.644049	0.655018
	0.370941	0.977307
	0.837305	0.828427