4837dbf8-7028-4788-8806-3aed9a7e187f 5 4 5 decimal

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Arenstorf orbit

The Arenstorf orbits are closed trajectories of the restricted three-body problem. Two bodies of masses m and (1-m) moving in a circular rotation, and a third body of negligible mass moving in the same plane (such as a satellite-earth-moon system.)

3 loops: Mass parameter: m = 0.012277471 Coordinates: y1(0) = 0.994 y2(0) = 0 y'1(0) = 0 y'2(0) = -2.0317326295573368357302057924 Period: tper = 11.124340337266085134999734047

t y μ D μp 1 μ - : y1 y 3 el : y2 y 4 el : r1 y 1 el μ + (2^y 2 el 2^+ : r1 r1 r1 sqrt * : r2 y 1 el μp - (2^y 2 el 2^+ : r2 r2 r2 sqrt * : y3 y 1 el 2 y 4 el * + μp r1 / y 1 el μ + (* - μ r2 / y 1 el μp - (* - : y4 y 2 el 1 μp r1 / - μ r2 / - (* 2 y 3 el * - : y1 y2 y3 y4 stack 101 line :

Y 0.994 00 2.00158510637908252240537862224 - 41 mat :

μ 0.012277471 :

t0 0 :

n 200 :

tmax 17.0652165601579625588917206249 :

res Y t0 tmax n t y μ D dn_ExplicitRK45 :

T res 1 col :

Y11 res 2 col :

Y12 res 3 col :

τ t0 n range :

x Y11 t 1 + el : y Y12 t 1 + el : 0.97 0 . 15 blue 1 5 mat t 0 ≡ path x y 1 2 mat : path path x y 1 2 mat stack : if x y . 12 Red 0 0 . 40 blue 2 5 mat 3 1 sys 3 1 line