Launching trash into space

[Stranger_On_A_Train]

@heavyarms553

Could someone crunch the numbers to determine the mass of propellant needed to accelerate a theoretical vehicle with a total mass of 10000 kg to a velocity of 30 km/s assuming a specific impulse of 30,000 s (the reported maximum specific impulse of VASIMR). Would the mass of propellant be less than the total mass of the vehicle? If the required mass is more than the mass of the vehicle then it is impossible without further improvements to technology. I’d do it myself, but I have no head for physics.

Although it isn’t really this simple, you can apply the Tsiolkovsky rocket equation. With the exhaust velocity being 30,000 s * 9.81 m/s[sup]2[/sup], and the delta-V being 30,000 m/s, easily simplifies to being m[sub]p[/sub] = 1 - e[sup]-1/9.81[/sup], giving a result that approximately 9.6% of the initial mass is propellant. However, this ignores a couple of significant realities. One is that like all ion propulsion systems, VASMIR is seriously energy inefficient and thus will require some kind of huge internal or external power source. (Although I see the Wikipedia article claims something like 58% efficiency, I find this highly unlikely and does not account for inherent thermodynamic inefficiency in producing power via any thermal cycle, or PV inefficiency in solar-derived power.) Another is that the VASMIR has not shown specific impulse anywhere close to the supposed 30,000 s, although scaling it up will probably result in proportional increases in I[sub]sp[/sub]. This still doesn’t address the amount of energy needed to raise such waste from the Earth’s surface to outside the Earth’s SOI, nor the hazard involved in doing so.

Stranger

[The_Controvert]

@Bone

Am I correct in thinking that if our theoretical garbage pile was much larger, it would be easier to hit the sun? Like say, 1/2 the size of the sun?

If your garbage pile were 1/2 the size of the sun, you wouldn’t need to incinerate it. It would collapse into a fusion star all on its own.

[heavyarms553]

Provided it had sufficient density and was composed primarily of materials capable of undergoing fusion reactions at that theoretical pressure and temperature. Otherwise it would just compress into a large planet.

[JoelUpchurch]

@Lemur866

The biggest problem with materials mined in space is getting them back to Earth’s surface. Even if we’re cheaply producing megatons of iron and aluminum in space, the primary use for those materials will have to be in space, rather than on Earth. I guess if we’ve got some space elevators running we’ll want to send the same amount of mass down to Earth as we send up from Earth. So unless we’re sending megatons of something into space we aren’t going to be sending megatons of processed material back to Earth.

This is assuming we don’t just drop the stuff and recover the metals from the crater. A lot of beautiful sunsets in our future if we go that route.

You don’t need a space elevator to do this. I saw one scheme that took advantage of the fact that it takes a lot less energy to get to orbital height than it does to orbital velocity. You put a linear accelerator in low earth orbit and the vehicles enter the accelerator to be boosted to orbital velocity. The vehicles returning to earth enter the other end to be decelerated and renter without ablation shields. We could be talking about some vehicle like SpaceShipTwo that is designed to reach 110 kilometers.

[Chronos]

Hm, that’s an interesting idea. You’d want to make sure that the mass going up balances the mass going down pretty well, though, or the accelerator is going to get dragged down. It probably wouldn’t hurt, either, to make the mass of the accelerator complex much greater than that of any of the payloads, as a sort of ballast.

[Tim_T-Bonham.net]

@Chronos

Hm, that’s an interesting idea. You’d want to make sure that the mass going up balances the mass going down pretty well,

Sure, just like is done in regular building elevators.