A First-Order Analytical Theory for Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptical Coplanar Orbits

Table 2

Final state variables.

Final state variables
	Analytical theory				Numerical solution
	Secular solution		Complete solution
𝑡𝑓−𝑡0=1000	500	1000	500	1000	500	1000
𝐹^	2.0000	2.0000	1.9967	1.9973	1.9968	1.9973
𝑢=√2E𝑡	0.2500	0.2500	0.2475	0.2480	0.2476	0.2480
𝑎^𝑎^0=1−2𝑢𝑣0cos𝑘^0+𝑢𝑣0^2^−1𝑢,(5.1)𝑣0=sin√2𝜓sin(√2𝜓+𝑘0),(5.2)	0.0000	0.0000	𝑣0=𝜇/𝑎^0	𝑘0	𝑣𝑢0=⎷1−2𝑎^0𝑎^cos√2𝜓+𝑎^0𝑎^.(5.3)	𝐽=E𝑡
𝐽=𝑣^202𝑡[1−2𝑎^0𝑎^cos√2𝜓+𝑎^0𝑎^].(5.4)	𝑡0=0	(𝑎^,𝜙,𝜔^)	(𝑎^0,𝜙0,𝜔^0)	𝜏	𝜓	𝛼=𝑎^/𝑎^0