On the impossibility of
Traveling to Other Solar Systems

I   
was reading the following piece on the net the other day. It's an important consideration if one believes that traveling to other solar systems is possible and that colonization of the galaxy (in times on the order of fifty million years) is a sure thing. It certainly looks formidable.

An excerpt from ... http://www.siddeutsch.org/essay5.html ... reviews the energy cost of traveling at 1/10 the velocity of light.

"How much fuel do we need to get up to a speed of 18,600 miles per second (and we need not worry about polluting the atmosphere)? I don’t have to answer that, because there is an easier way to look at it: Kinetic Energy. The phrase “kinetic energy” turns UFO people off; the reasoning section of their minds becomes vaporized, and they simply walk away. This is the part they don’t want to hear and/or cannot understand: One of the first and easiest equations in a physics course is that kinetic energy equals one-half mv squared. Plug 200,000 kilograms in for m and 30 million meters per second for v and -- voila -- we get around 1 followed by 20 zeros (watt-seconds). So what does that mean in down-to-earth terms? Well, the total capacity of the United States electrical power system is, very approximately, one trillion (1012) watts. If we could somehow use all of this trillion watts (or its equivalent in one of the propulsion systems of Table 1) to drive the starship, it would take 100 million seconds, or three years, to get up to speed! Negligible, of course, on a 100-year trip."

Pretty Formidable

However, if you look at it another way, there seems to be a problem.

Suppose my Honda Civic undergoes a constant acceleration of 1 meter per second per second. In other words I'm accelerating about as fast as I would normally be, if were trying to get up to expressway speeds. That's about one tenth of the acceleration due to gravity at the earth's surface (9.8 m/sec2). I'm pushed back into the seat with about a tenth of the force that's pushing me down in the seat from gravity. If such and acceleration could be sustained, my Honda would be going at around 1/10 the velocity of light in somewhat less than a year.

30,000,000 seconds = 500,000 minutes = 8333.33 hours = 347 days

I figure that such a constant (24/7) acceleration will cost me no more than 100 gallons of gas per day or 347 x 100 = 34,700 gallons of gas to get me to 1/10c.

My car has a mass of about 1000 kilograms (a little over two thousand pounds). So, in the example given by Mr. Deutsch, I need to accelerate about 200 Honda Civics to 1/10c. Thus, in terms of gasoline, I need 34,700 x 200 = about 7,00,000 gallons of gasoline.

energy released by one gram of gasoline = 5.o x 104 joules
one gallon of gas is 2620 grams ... so, one gallon of gasoline releases about
2620 x 5 x 104 = 1.31 x 108 joules
that times the 7 million gallons equals about 1015 joules (or watt=seconds)

So, from my Honda Civic viewpoint it would take the entire electrical generating capacity of the United States about 3000 seconds to accelerate the 200,000 kilogram ship to 1/10c, i.e. less than an hour (rather than three years). The discrepancy here is on the order of 106 watt-seconds

What's the physics problem here? What am I doing wrong?

Of course you can't accelerate a Honda Civic

... indefinitely ... for two reasons. I can't accelerate 7 million gallons of gas along with my Honda without supplying yet more energy to accelerate that too ... a much bigger engine (very much bigger) ;o) And ... even if I had some sort of light weight nuclear engine to power my vehicle, I'd need to gear it to deliver force to the road in order to make the car go faster and faster. Gears don't work like that. When you put you transmission into a higher gear, it's like a reverse lever. The engine works just as hard (burns as much gas) but only delivers a proportionately smaller force to the ground. Your velocity will still increase with the original engine but at a reduced rate like .05m/s2 for instance, and it will continue to go down as you move into higher and higher gears. If you want to keep up the high rate of velocity increase (1 m/s2) ... you need to get a much more powerful engine which consumes much more gas. So, the Honda acceleration analogy is flawed (it only "feels" like it would work) and we have to accept the enormous energy requirement as given by Mr. Deutsch (and Mr. Newton).

Pulling Down the Square

But the energy requirement doesn't rule out interplanetary space travel. It just makes it very difficult and not something that a planet would undertake this side of a multi-millenium one time (or few times) project.

What we have to do is reduce the final velocity of the vehicle to more realistic speeds. If we further reduce that velocity to 1/100 of light velocity we multiply our travel time by ten fold ... but ... we reduce the energy cost by a factor of 100 because of the v2 in the energy equation. Thus, 1/10 squared is 1/100 ... but 1/100 squared is 1/10,000 ... a hundred fold difference. Well, let's go whole hog and run it down to the lowest possible velocity for interplanetary space travel which is about 1/1000 of light velocity. Here, the reduction in energy cost is 1/10,000 that of the original Deutsch estimate ... or ... about 1/10,000 of the three years of US electric generating capacity or less than three hours of that capacity ... a much more realistic cost.

Note: the reason that 1/1000 is the least velocity for space travel to other stars is that stars in the Milky Way Galaxy have relative velocities of that magnitude. So, you can go to another star at ten miles per hour if you want ... but ... it won't stop to let you board and will go whizzing on by ... or ... you can of course crash into it and die.

The philosophy of galactic space exploration ...

... must necessarily be one of "patience". If you are leaving the earth, it stands to reason that you're never coming back. So, to anyone going, the problem isn't the duration of the journey ... it's whether the journey is pleasant and safe as they will experience only part of it anyway.

On the other hand, by the time earth people get around to leaving the solar system, they may no longer be "human" by our present understanding. The may be "sentient robots". That is, we may replace ourselves with robots whose brains are programmed by their "parents", i.e. the couple who "raise" the robot from infancy ... through "assisted auto-programming" ... that is, they teach it right from wrong as they would a human child who basically figures it all out for himself. This is, in fact, the only way to produce a mechanical, sentient being. It can't be done through rote programming as they are trying now. People are too complicated. All that is necessary is to provide the hardware and the teaching (nurturing) environment. The only difference between such a robot and a real human is that it's mind is "downloadable", i.e. you can make a copy so that, in the event of a catastrophe, that person can be re-constituted. Now, such beings could easily travel to another star system at slow speed and still get there instantly by simply switching themselves off and being switched back on by a lower level computer upon reaching the destination star. If this were the case, travel to another star system would be significantly cheaper and less complicated with no life support systems and little support needed upon arrival.

Taking real biological humans to such great distances would require a vast armada of ships strung out in space and time ... far enough apart to guard against catastrophe but close enough to afford transport to other ships to facilitate a more interesting journey. Here's what I would expect if only biological humans go.

Large scale interstellar migration from the earth

For a few thousand more years we will just study the universe and populate the immediate solar system. This will give us plenty of experience and understanding to contemplate the big move. Several candidate planets will have been found but no one will seriously advocate going to them ... until ... they see (by their then advanced observational techniques) that their primary destination of choice has been ... colonized by somebody else ... while they were napping. The rush will be on to go to choice #2 before that gets taken too.

Let's give 'em another 100,000 years to get their shit together, i.e. construct the fleet.

First to go will be the point probes ... faster moving small ships that get here ahead of anything else and scout the path and then the destination. Behind them come the smaller ships, followed by medium ships ... then the big jobs ... followed by more medium ships and bringing up the rear ... lots of small ships. Undoubtedly, there will be several waves such as these over the next few thousands of years following the initial wave. There won't be any trouble at all to get people to do this as there will be plenty of volunteers to do something ... anything ... meaningful with their lives. I see a few hundred thousand individuals going for it, altogether.

This whole process (for other destinations) might be done a number of times over the life of the earth. Our sun goes round the galaxy every 200 million years or so, which presents us with innumerable possibilities to "seed" the galaxy.

As a general rule,

Man will go wherever he can go ... as an exercise of his identity ... as a curious and adventure-seeking sentient being. He won't just sit there and wonder what could have been if he could just get up off the couch and do something instead of just watching. The time required to colonize the entire galaxy by this slow method ... from one initial planet ... is probably on the order of 200 million years instead of the oft quoted 50 million years, i.e. to traverse the galaxy at 1/1000c is something like 100 million years ... then add in the time necessary to get up another wave of colonizers from the new planet (who will have all the knowledge of the initial planet + their own experience).

I concede Mr. Deutsch's point about faster travel being pretty much impossible ... unless new physics is discovered ... and ... it must be remembered that such new physics would have to overthrow Newtonian mechanics. In the history of physics no theory ever overthrows the old ... it just modifies it a bit. We can be completely confident that the laws of motion and the conservations laws will still hold both now and forever. So, even 1/10c is probably out of range for anyone (human or alien) regardless of their scientific sophistication.



Ebtx Home Page