Dynamics cheat sheet

Algorithm 2 Hohmann rendezvous algorithm, case 1
1: function hohmann rendezvous 1(θ 0 , r a , r b , µ)
π
2: θ 0 := θ 0 180
⊲ convert from degrees to radian
3: a := ra+r b
2
⊲ Hohmann orbit semi-major axes
√
4: TOF := π
5: θ H := π
6: ω a :=
a 3
µ
⊲ time of flight on Hohmann orbit
( ( ) ) 3/2
1 − ra+r b
2r b
√ µ
r 3 a
⊲ required phase angle before starting Hohmann transfer
⊲ angular speed of lower rad/sec
7: ω b := √ µ
⊲ angular speed of higher satellite rad/sec
rb
3
8: if θ 0 ≤ θ H then ⊲ adjust initial angle if needed
9: θ 0 := θ 0 + 2π
10: end if
11: wait time := θ 0−θ H
ω a−ω b
⊲ how long to wait before starting Hohmann transfer
12: wait time := wait time + TOF ⊲ now ready to go, add Hohmann transfer time
13: return wait time
14: end function
An example implementation is below
1 hohmann_rendezvous_1:= proc({
2 theta::numeric:=0,
3 r1::numeric:=0,
4 r2::numeric:=0,
5 mu::numeric:=3.986*10^5})
6 local theta0,thetaH,TOF,a,omega1,omega2,wait_time;
7 theta0 := evalf(theta*Pi/180);
8 a := (r1+r2)/2;
9 TOF := Pi*(sqrt(a^3/mu));
10 omega1 := sqrt(mu/r1^3);
11 omega2 := sqrt(mu/r2^3);
12 thetaH := evalf(Pi*(1-((r1+r2)/(2*r2))^(3/2)));
13 if theta0