Follow-Up: Energy Requirements of Interstellar Travel
Posted by Karl Withakay on May 2, 2010
This is a follow-up to my recent post, Cordial Deconstruction of Stephen Hawking? (Am I So Bold?) where I discussed the likelihood that an alien intelligence would bother crossing the universe or galaxy to plunder the resources of the planter Earth.
In this post, I will discuss the energy requirements of interstellar travel. Before I begin, I want to explain that I’m not going to show the math involved in the numbers, both because many people won’t be interested in the equations, and because this post is going to be long enough without showing all the calculations and equations involved. I’ve also ignored the time dilation factor which would reduce the relative travel time of the journey for the passengers of a spacecraft traveling close to the speed of light, but it only makes a significant difference at speeds that are energetically prohibitive anyway.
First, a discussion of the distances involved when discussing interstellar travel. To quote Douglas Adams’ Hitchhiker’s Guide to the Universe,
“Space is big. You just won’t believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it’s a long way down the road to the drug store, but that’s just peanuts to space.”
A typical galaxy is about 30,000 light years in diameter, the Milky Way being about 100,000 light years across. The distances between galaxies is even more mind bogglingly huge; the typical distance between galaxies is about 3 million light years. The visible universe is about 93 billion light years in diameter. (This is the current, commoving distance, not the distance at the time the light from the furthest visible stars was emitted.) So, to start, lets rule out intergalactic travel and focus on interstellar travel from within the Milky Way galaxy to see how practical that would be.
The nearest star to the sun is Proxima Centauri at a distance of about 4.2 light years, but Proxima Centauri is not a great candidate for habitual planets, for several reason. It’s a red dwarf, and that could pose numerous problems. It’s also variable, which almost closes the door on Proxima Centauri as a candidate for our hostile ET to come from. Moving on, there are 64 known stars within about 16 light years of the Earth, so let’s just say ET is coming from our back yard, say 10 light years away, though the aliens probably wouldn’t be so local unless life is very common in the universe.
So let’s look at how much energy it would take ET to get here from an unspecified plant 10 light years away. If we assume ET doesn’t want to spend 200 or more years making a round trip to Earth, they’re going to need to travel fast, really fast. Even 10% of the speed of light isn’t going to cut it. Let’s shoot for 90% of the speed of light (c). At .90 c, it’s going to take about 11 years to make the trip from ET world to earth, if ET can accelerate and decelerate nearly instantaneously.
So now we have our target speed, but we need to know the mass of ET’s vehicle. An object the size of the space shuttle (~110,000 kg for the orbiter by itself or around 2,000,000 kg for the whole system with boosters and fuel) seems a little physically small for an 11 year journey, so let’s try something a little bigger. A Virginia class submarine is about 8,000,000 kg and is a craft designed for long term endurance travel; let’s assume ET’s craft is the same mass.
The amount of energy needed to accelerate an object of a mass of 8,000,000kg to.90 c is 7.45 9.32 * 10^23 Joules, which is about 180 million megatons of energy. This is the equivalent of 3.6 ~4.5 million Tsar Bombas, the most powerful nuclear weapon ever detonated. It would take more than four five million kg of antimatter annihilating with the same amount of matter to produce this much energy. It’s worse than it looks, because the ETs need to slow down to a relative stop when they get here, which will take the same amount of energy as the acceleration, so we’re talking about 360 ~450 million megatons of energy just for a one way trip. But it’s even worse than that. We are ignoring the mass of the energy source and any propellant used in for ET’s spacecraft, and we are assuming 100% efficiency in the conversion of the energy source into vehicle velocity, which isn’t going to happen in the real universe. All things considered, without going into the increasingly complicated math (which would require us to start using calculus since the mass of the vehicle now decreases as we consume reactant & propellant), we probably need to increase our estimate of the energy requirements by an order of magnitude or so.
So, bottom line, at the end of our rudimentary estimate of the energy requirements to travel at .90 c, we’re talking about an energy requirement in the order of a billion megatons or so.
OK, what if ET is a little more patient and is willing to endure a 200 year round trip at .10 c? The energy requirements drop to ~17,000 ~870,000 Megatons of energy (or 17,000 Tsar Bombas) for a one way trip. (It’s not a linear decrease because we’re talking relativistic mechanics here.)
(For reference, doing a little math, I calculate the Callaway Nuclear Generating Station in Missouri generates about 8 megatons of energy a year.)
So, in summary, the energy requirements are massive for velocities even 10% of the speed of light, and absurdly huge for speeds 90% of c, and even at those speeds, we are limited to about 10 light years of distance for any reasonable length journey. Why would any ET, no matter how conquest driven they were, bother expending such energy resources to plunder the resources of another world, assuming they could even find a suitable planet to plunder in their local stellar neighborhood?
I think we can sleep soundly at night, never having to worry about Stephen Hawking’s ETs ever attacking the Earth ID4 style.
In regards to the energy requirements of some mythological faster than light propulsion system, who can really say what those would be? I can speculate that they would be much greater than those of traveling at velocities at “significant” percentages of the speed of light, and someone else can say that as long as we are speculating about faster than light travel, why can’t we speculate about some relatively low energy process to achieve those speeds? It’s all wild speculation if not outright fantasy at that point, so there’s really no numbers to talk about.
Cordial Deconstruction 
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astrowright said
Only one reason an ET might expend that much energy to plunder our planetary system comes to mind, which is survival. From that, I can only really imagine three cases:
The first, that an advanced society is suffering from the effects of a dying or erratic parent star (Krypton Effect?) and chooses to leave the star system to colonize elsewhere. (As you say, the energy requirements for such an expedition are so great that a society able to undertake one would be able to manage mere planetary-scale catastrophes.)
The second scenario is quite similar, in that an advanced society is suffering from some sort of galactic catastrophe (nearby supernova – Romulus Effect?) and chooses to escape destruction and colonize elsewhere.
The third is less logical but perhaps more likely, if our own society is any indicator – and that relates to the very sort of “locust”-style imperialism Hawking fears. It was not energy efficient at all for settlers to cross the Atlantic Ocean or for prospectors to travel to the Yukon, but they were compelled anyway for space to call their own. We can’t discount the possibility that a sufficiently advanced species won’t have limited their population growth and will simply choose to spread out.
Two cents.
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speising said
So what about ram-jet like ships? probably quite useless (to vulnerable) as carriers for an invasion force, but they do not have the problem of carrying all that fuel with them.
also, of course, If we assume ET doesn’t want to spend 200 or more years making a round trip to Earth… doesn’t necessarily apply for ET’s with, eg., longer life spans than ours.
Karl Withakay said
Thanks for the comment, see my reply here: https://blog.cordialdeconstruction.com/2010/08/22/reply-to-a-comment-on-interstellar-travel/
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Mike H. said
Well all this of course assuming that interstellar travel can only be that way. And also assuming that a society so advanced to use those amounts of energy would consider that technology as we do. What do I mean. Well imagine you are in the middle ages and someone tells you that to take a certain quantity of people across the Atlantic in a flying machine to do X or y kind of things you would need z amounts of energy. Well that kinds of energy at that time would of course be only imagined by the impressive force one thousand horses or more pulling that thing. However now, we have technology at our reach that easily give’s us that amounts of energy and even more in the every day life and we don’t consider it a waste of time. So maybe an advanced culture is so ahead of our current level of technology that they consider the amounts of interstellar travelling in their every day calculations.
Karl Withakay said
Actually, the energy requirements to travel across the Atlantic by jet wouldn’t be beyond the imagination of someone in the middle ages; it’s the technology that would be beyond them. If you explained the energy requirements to them in terms of firewood, coal, lamp oil, or alcohol, they would not only be able to understand the energy requirements, they would be able to produce that much energy, though not necessarily in the form a jet plane could use. Per your analogy, a king or local ruler would also be able to put together the required number of horses and feed for the same amount of energy.
There’s really no greater energy density than matter-antimatter annihilation, pretty much by definition- the result is 100% conversion of mass into energy, so 4 million tons of antimatter & 4 million tons of matter isn’t going to be replaced by anything more manageable.
To stay within the spirit of your analogy, let’s say that a middle age explorer believed there were 100 ounces of gold (and nothing else) on an island in the middle of the Atlantic, and that it will cost him 100,000 ounces of gold to retrieve it. Why would he bother doing so?
davidjwbailey said
Loved this. every school needs to teach it to 16 year olds. the whole human race needs to adjust to the ‘long clock’ and slow accumualtion of massive energy and physical resources required to deliver solar system wide and galactic expansion of the human race (and we *must* leave this blue marble, or we will certainly perish from one of the Universes little ‘jokes’).
It is also clear that no reasonable biological systems could survive the radiation load of 200 years in space, nor could any reasonable shielding prevent the catastrophic impact with dust or particles at interstellar speeds. Oh, and magnetic fields transected at 0.9c, I don’t fancy that much either! Any protection from the risks would require both more mass and more energy.
The simple physics also push forward the necessary discussion of “what if you only need to send 0.1kg?”. It is a logical step to examine small, hardened, non-biological sentiences with some advanced replication ability. They could be the ‘locust swarm’ that we send out. It won’t be ‘meatbag human’, but it will represent us. And, it might even become ‘us’ when re-incorporated on habitable planets if we include a DNA based payload and the chemical and biological tools to recreate life.
So, no, I don’t fear that giant alien ships will appear in our sky, like ‘V’.
I do fear that anyone who learns we are here will send a few kg of antimatter towards our planet at .99c. Why? Because total annihilation is the only logical reaction they might have to discovering another civilisation capable of sending ‘locust replicators’ (as we are). Their fear of us is that they might not deliver their payload before we begin to seed the galaxy with smart dust…