Dynamics cheat sheet

The input is the following.
1. µ 1 planet one standard gravitational parameter
2. µ 2 planet two standard gravitational parameter
3. µ sun standard gravitational parameter for the sun 1.327 × 10 8 km
4. r 1 planet one radius
5. r 2 planet two radius
6. alt 1 original satellite altitude above planet one. For example, for LEO use 300 km
7. alt 2 satellite altitude above second planet. (since goal is to send satellite for circular orbit around second
planet)
8. R 1 mean distance of center of first planet from the sun. For earth use AU = 1.495978 × 10 8 km
9. R 2 mean distance of center of second planet from the sun. For Mars use 1.524 AU
10. SOI 1 sphere of influence for first planet. For earth use 9.24 × 10 8 km
11. SOI 2 sphere of influence for second planet.
Given the above input, there are the steps to achieve the above maneuver
1. Find the burn out distance of the satellite r bo = r 1 + alt 1
2. Find satellite speed around planet earth (relative to planet) V sat =
√
µ1
r bo
3. Find Hohmann ellipse a = R 1+R 2
2
4. Find speed of satellite at perigee relative to sun V perigee =
√
µ sun
(
2
R 1
− 1 a
)
5. Find speed of earth (first planet) relative to sun V 1 =
√
µsun
R 1
6. Find escape velocity from first planet V ∞,out = V perigee − V 1
7. Find burn out speed at first planet by solving the energy equation V 2
bo
2 − µ 1
r bo
8. Find ∆V 1 needed at planet one ∆V 1 = V bo − V sat
9. Find e the eccentricity of the escape hyperbola e =
√
1 + V 2 ∞V 2
bo r2 bo
µ 2 1
10. Find the angle with the path of planet one velocity vector η = arccos ( − 1 e
11. Find the dusk-line angle θ = 180 0 − η
)
= V 2 ∞,out
2
− µ 1
SOI 1
for V bo
The above completes the first stage, now the satellite is in the Hohmann transfer orbit. Assuming it reached
the orbit of the second planet ahead of it as shown in the diagram above. Now we start the second stage to land
the satellite on a parking orbit around the second planet at altitude alt 2 above the surface of the second planet.
These are the steps needed.
1. Find the apogee speed of the satellite V apogree =
√
µ sun
(
2
R 2
− 1 a
)
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