In a science-fiction TV show several years ago, the hero spent the entire 40 min fretting about running out of fuel before he could pilot his spaceship back to base. Time and again the camera cut from his worried face to the blasting rockets, to the trembling fuel gauge, and back to his pained expression as the engines roared and the fuel diminished. What should he have done and why would you say the writers were Aristotelians?

2 answers

Aristotle had the (very wrong) idea that things could move only as long as something was pushing them. This no doubt seemed reasonable in Earth conditions, before quantitative science, when just about everything that moves is pulling against gravity or friction.

In a vacuum, you don't get friction, and far enough away from a large mass, your progress isn't much affected by the gravity of faraway objects either. (Staying conscious that space is not a perfect vacuum, and you are never entirely unaffected by gravity.)

So the hero should probably have turned off his rockets and just coasted back to the vicinity of his base, where he could have turned them on again for the landing.

... but having said that, there do exist orbital scenarios in which a certain amount of fuel is required for the change in velocity needed to intercept a point at speeds that won't leave you at the bottom of a hole in the ground. One such situation, for example, is when your initial velocity relative to your destination is negative - that is, you are already moving away from your base before you turn on the engines. In a case like that, the amount of fuel you have to burn to change your heading may be a critical factor, so the scenario is not impossible.
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