Shouldn’t the gravity of the planet force the craft to expend fuel to escape the gravity?
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You’re 100% correct… except for one thing, and that’s the motion of the planet. If the planet’s coming towards you, you can steal some of its motion by passing behind it. Think of it like falling on a trampoline… if a bowling ball smashes at +20m/s into a stationary trampoline, best case scenario, it rebounds at -20m/s. Now if bowling ball is traveling at +20 m/s and the trampoline is moving towards it at -5 m/s… that’s as if the bowling ball is traveling at +25 m/s (relative to the trampoline) and responds with a speed of -25 m/s (relative to the trampoline, which actually adds up to be -30 m/s!).
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