Knowledge Zone · Card 10 of 13
The Moon flyby
A flyby steals nothing from the Moon that the Moon can feel, and gives the ship something it could not have bought. Relative to the Moon the pass is a hyperbola and is perfectly symmetric: the ship leaves at exactly the speed it arrived with, only pointing somewhere else. Add the Moon's own orbital velocity back in and that change of direction has become a change of speed in Earth's frame — free, from geometry.
How much depends on how hard the Moon can bend the path, and it bends slow ships hardest. The turn angle is δ = 2 asin(1/e), so a ship crawling past at 1 km/s a thousand kilometres up turns 80°, while a ship already on its way to Mars at 3.4 km/s turns only 21° even skimming at 100 km. The game flies the second case, inside a sphere of influence 66 194 km across.
Here is the honest part. The route really does add about 100 m/s to your heliocentric arc, and that is exactly what the checkbox says: it adds, it does not save. The model spends the assist rather than banking it, so what you get is a longer arc, not a cheaper one. Nor is it quite free — at the default burn those extra metres cost about 27 m/s out of the tanks, because speed bought this high above Earth is cheap. And if a longer arc is not what you wanted, you can hand it straight back on the departure slider, which is where the +1 500 points turn into a bargain.