So you’re sitting in your car at a red light. It turns green and you stomp on the gas. 0 to 60 in what, 9 seconds for an average car? Probably so. But that acceleration doesn’t stay constant forever. Air resistance and engine inefficiency eventually brings you to a maximum speed no matter how long you keep the pedal floored. But let’s pretend you’re in the vacuum of space and able to keep up that initial acceleration for however long you want.
That’s how long it will take you to go a distance x, as almost all of you probably know. The fact that x is under a square root sign means x can get pretty large without t growing at the same rate. Plug in your average close approach distance from Earth to Mars and you’ll get… just over 2 days. Be sure to allot some time for braking, but that’s really not much extra. So why did it take 9 months for the new Phoenix lander to reach Mars? Again as you all know, because there’s no way in the world to keep a spacecraft engine burning at full throttle for 2 days. It’s simply not possible to get that much fuel into orbit. Fuel is heavy and rockets are expensive.
Further complicating the issue is the fact that even if you get a lot of fuel into space, you still have to accelerate a spaceship full of heavy fuel. This is much worse. If you have 1 ton of spaceship and 100 tons of fuel, this is only a factor of 2 improvement in final velocity over a 1 ton spaceship with 10 tons of fuel. Further multiplication by 10 yields even worse returns.
You and I will probably never vacation in the rings of Saturn. But there are some cool possibilities in the pipeline. If the space elevator turns out to be a workable concept, it’s possible you and I will at least be lunar tourists at some point. I don’t know about you, but I’d blow my retirement money on that in a heartbeat. In fact I’d go to low earth orbit on the shuttle tomorrow if they offered it, 2% chance of death and all. Call me a romantic, but space travel is one of the most amazing things humanity has done, and I’d love to be there in person one day. I’d be no less delighted even if it were as a tourist on a perfectly routine sightseeing trip. But I’m one of those guys who still is amazed by looking out of an airplane window.
1 response so far ↓
1 CCPhysicist // Jun 4, 2008 at 8:14 pm
About 9 to 11 covers a lot of “average” cars.
When I mention this sort of thing in class, I usually mention “super” sports cars being in the 3 to 4 second range, then say “but if you are really serious, you’re looking for 0 to 60 mph in about 0.5 seconds.”
That gets the attention of the car nuts, who usually know about drag racing but don’t know that a top fuel car has an average acceleration of about 5 g’s off the line, hence 0 to 60 in 0.55 s. They are close to 100 mph when they cross the 60′ timing line.
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