Dynamics cheat sheet

Algorithm 1 Hohmann Walking Rendezvous Orbit, case 1
1: function hohmann walking rendezvous(θ 0 , r, altitude, µ)
2: θ 0 := θ 0
π
180
⊲ convert from degrees to radian
3: r a := r + altitude
4: T := 2π√
r 3 aµ
⊲ period of circular orbit
5: n := 1
6: done:=false
7: while not(done) do
(
8: TOF := N − θ 0
9: a := solve
10: r p := 2a − r a
11: if rp < r then
12: N = N + 1
13: else
14: done:=true
15: end if
16: end while
2π
)
T
(
T OF = 2π
√
17: V befor := µ
h
√
18: V after := µ ( 2
h − 1 )
a
19: ∆V := 2(V after − V before )
20: return (TOF, ∆V )
21: end function
√
An example implementation is below
)
a 3
µ
for a
1 hohmannRendezvousSameOrbit[\[Theta]00_, r_, alt_, mu_] :=
2 Module[{\[Theta]0 = \[Theta]00*Pi/180, n = 1, delT, v1, v2, period, a,
3 rp, ra, done = False, vBefore, vAfter},
4 ra = r + alt;
5 period = 2 Pi Sqrt[ra^3/mu];
6 While[Not[done],
7 delT = (n - \[Theta]0 /(2 Pi)) period ;
8 a = First@Select[a /. NSolve[delT == 2 Pi Sqrt[a^3/mu], a], Element[#, Reals] &];
9 rp = 2 a - ra;
10 If[rp < r,(*we hit the earth, try again*)
11 n = n + 1,
12 done = True
13 ]
14 ];
15 vBefore = Sqrt[mu/h];
16 vAfter = Sqrt[mu (2/h - 1/a)];
17 {delT, 2 (vAfter - vBefore)}
18 ]
And calling the above
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