- #1

BitWiz

Gold Member

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Generically, work = m * d^2 / t ^2 (mass, displacement, time)

If to a 1kg mass at rest in space I attach a small rocket that fires with a force of one newton for one second, at the end of that period the mass will have traveled 0.5 meters, and the rocket will have done the work of 0.5 joules. (I think I've got this right(?))

Now if I do the same thing with a 1kg mass that is

*already*traveling at 100,000 meters per second, this same rocket applies a newton over a displacement of about 100,000 meters. From an observer's frame, has the rocket now done 100,000 joules of work? If so, how are joules as quantifying *anything* useful in space travel?

Ultimately, I'm trying to resolve this assertion, seen in several locations: "Accelerating [1000 kg] to 10% of the speed of light requires 450 picojoules of work." The author used this huge number to substantiate his claim that even traveling to the middle of the Oort cloud is beyond human endurance and even physics.

I understand the arithmetic from which this number was (apparently) derived:

W = mc^2 / SQRT(1 - 10%^2) - mc^2

But I wonder about the relevance of using "work" to describe what a rocket engine does. If I'm trying to get to 10% of the speed of light, why do I care about the distance travelled during the effort except in the increments required to quantify velocity? Shouldn't I care only about newtons and seconds (impulse)? Is this 450 PJ number just smoke and mirrors?

Thanks,

Bit