Energy required to travel a distance in a Vacuum?

Post Reply New Topic

Hi, I am working on a hard science fiction novel and I am using a great amount of maths to figure out various physical requirements for my civilization's setting. Though the book does involve faster than light travel via Lorentz symmetry violation for faster than light travel, otherwise it stays in the realm of general relativity and standard quantum physics.

I have a physics question that I have been trying to figure out for over an hour by searching online on Wikipedia, Google and various academic websites and I was wondering if anyone here could help me with it; here it is: Let us say that there is a 1 gigatonne body in a vacuum that has been accelerated to 100,000,000 metres per second. It is now moving at a constant speed and it needs to travel 100,000 kilometres, let us say. How many joules are required to send it the 100,000 kilometres?

Now, I know how to calculate the energy required to accelerate the body to 100 million metres per second yet I am not sure what the formula is for a body of a certain mass to travel a certain distance at a certain speed (if it matters?) Or does travel at a constant speed in a vacuum simply not require any energy due to the conservation of momentum or some other basic law of physics?

Thank you for your help!

Your are asking the wrong question. What FORCE will accelerate a body from rest to 100 million meters per second. And in a vacuum -any- no zero force will do that. The smaller the force the longer it takes to reach the desired velocity.

Free advice: Learn the basic units and definitions of classical physics before writing your science fiction.

In a vacuum a body with no forces acting on it will proceed in a straight line at whatever velocity it was going. No force means that the momentum of the body does not change over time. Force equals the rate of change of momentum.

ruveyn

Even ignoring ruveyn's excellent advice the answer to this is already clear: zero. All you need to do is wait.

Wouldn't the length of the power cord be limiting?

That makes sense now, thank you. I now realize (correct me if I am wrong) that the formula for force means the energy required to accelerate a mass, not to propel the mass at a constant speed.

I don't know what formula for force you are talking about. But the formula for work is W=Fd where W is work, F is force, and D is distance. Alternatively you could work out the kinetic energy imparted to the system as E=(mv^2)/2 where m is mass and v is speed. However, there is always inefficiency when accelerating something (conservation of momentum means you have to also be accelerating something backwards, which also takes energy). In the case of rockets this makes some of the energy calculations a real pain because the velocity of the rocket is constantly changing so the energy carried away by the exhaust will also keep changing. If you want to get that accurate you'll need calculus I think (I've never looked closely at this stuff, so I don't know exactly what level of math will be involved).

I should also ask, what sort of vacuum is this thing travelling through? If it's within a gravitational field that will slow the object down, meaning more energy will be needed to get it where you want in the amount of time you want (and if you don't give it enough energy it won't get there at all). If it were withing a vacuum tube below the Earth (I'm assuming it's not because then it would be circumnavigating the Earth several times) then you'd probably need to take into account energy lost due to friction--I don't think even Maglev is 100% efficient. And remember, no system is entirely efficient. In fact, there are fundamental limits on efficiency depending on what sort of system you're using. In a heat engine the maximum efficiency is that of a Carnot engine--you can find it on Wikipedia. I don't know what sort of system you'd be using or what sorts of other systems the Carnot cycle can be applied to. I can't imagine very many. Maybe someone with a better understanding of thermodynamics can answer that.

Ruveyn is right, you really need to get a firm grasp of basic physics. I first year university text book would have this sort of information in it (of course, it would be expensive, so maybe you should check out Wikibooks or Wikiversity to see if they have a free equivalent).

I am traveling through the vacuum of interstellar space, by the way. And the formula I am using for energy is as follows: 1 kJ=(1 t·1 m^2)/s^2.

Of course all energy have inefficiencies in them. I also had heard of the Carnot Cycle (and the Rankine Cycle.) And I did know of the loss due to friction and a gravitational field.

Okay, the formula you're using isn't actually a formula but a definition of a unit. It shouldn't be used here.

In interstellar space there are basically no energy losses. Unless you are going REALLY fast in which case you'll lose energy from drag with the interstellar medium.

What is the interstellar medium. There is no aether so what is it?

ruveyn

no space has absolute vacuum, particles might be in the dozens per kubik kilometer but even those particles will slow you down.
this might be the "interstellar medium", not that i would know of course.

To OP:

Please look up Newton's first law of motion.

ruveyn

I think ruveyn and AstroGeek are fair in their statement that I do need to learn more about physics, which I will do largely because I love learning and precision. I will go to Wikibooks and read about physics to better understand it.

That is correct. I think the density is about 1 atom per cubic meter (or maybe that's the intergalactic density--I forget). It would be slightly more in star-forming regions, planetary nebulae, cold gas clouds etc. It's tiny, but if your ship is going at a decent fraction of the speed of light then the drag would be noticeable. But the bigger problem is that these atoms would start behaving like cosmic rays, so you'd need some shielding. In Arthur C. Clarke's Songs of a Distant Earth a ship with some sort of fictional quantum engine capable of reaching some huge portion of light speed actually had to stop at a planet known to be covered with oceans part way through it's trip to get more ice to act as its radiation shield.

Even at a significant fraction of lightspeed, for any reasonably-sized vessel the effect of drag from the interstellar medium can be ignored, particularly over a mere 100,000 km (in which space it's unlikely to encounter more than a few atoms overall, assuming it's not going to hit an asteroid or something). The only reason a Bussard ramjet is limited to about 12% of lightspeed is because the scoop needed (usually assumed to be a directed magnetic field, perhaps with a delicate "web" of metal to help direct and contain it) must cover at least several hundred square miles, in order to even have a prayer of catching enough interstellar hydrogen to fuel itself.

Now, if you're looking to coast over interstellar distances, you might need to take the galactic magnetic field into account...

Well, I think that Arthur C. Clarke's ship was pretty massive, and it was going at a VERY large percentage of light speed. But yeah, a 100 000 km is very small indeed (I hadn't looked closely at the number--that's only like 1/4 of the distance from the Earth to the moon!), so it wouldn't be important here unless the ship was travelling almost at light speed. Which there is really no need to.

Read these two wiki articles:

Impulse

and

Specific Impulse

They're both about the classical version of the mechanics (no general relativity applied), but they're both the best place for you to start.