THE PHYSICS OF SPACE TRAVEL (AS WE UNDERSTAND IT)
Here we will deal with the possibility of interstellar travel, as limited by the known laws of physics. Unless you are willing to take thousands of years to get anywhere, travel will have to be done at speeds where the effects of special relativity apply.
For a spacecraft accelerating at a rate a, the velocity v reached and distance x traveled in a given interval of time t is:
Just for quick reference, let's see what the round-trip duration and range for a trip with acceleration and deceleration to the target at 1 g (one earth gravity = 9.8 m/s2) and, and a similar trip back to Earth. Due to time dilation on the ship, the duration for the crew is shorter than for those left on Earth:
| Crew Duration (years) | Earth Duration (years) | Range (pc) |
| 1 | 1 | 0.02 |
| 10 | 24 | 3 |
| 20 | 270 | 42 |
| 40 | 36,000 | 5,400 |
Thus, accelerating a 1 g will get you to the nearest stars and back in 20 years ship time (centuries pass on Earth) and half way to the center of the Galaxy in 40 years ship time (over 30 millenia on Earth).
Cost of Interstellar Travel
It's easy to do this in science fiction. Just make up some bogus name (warp drive, for example), and assume it will do the job. No questions asked. In the real world, however, we know of no such mechanism. And unless there is a major revolution in our understanding of the laws of nature, such a drive is not possible. If we are limited to known physics, we will have to use rockets.
Rocket engines work most efficiently when the rocket reaches the speed of the engine exhaust. So a good rocket will start out at zero velocity, and if possible, accelerate up to a velocity equal to the exhaust speed (going faster reduces efficiency). Furthermore, all rockets must accelerate not only their payload, but all the fuel they carry!
For a final velocity Vf a ratio of initial mass (payload plus fuel) to final mass (ditto) M, and exhaust velocity W, then:
For Vf< 0.1c, then M="e"=2.7182…..
For a round trip, where 4 legs of the trip each require a factor of M:
Suppose we took a round trip to a star 5 pc away:
| Via Chemical Rocket | Via Nuclear Rocket |
| Vf / c ~ 10-5 | Vf / c ~ 10-1 |
| MRT=55 (=e4) | MRT=55 |
| t=3 million years | t=300 years |
The cost of making the fuel can also be estimated. Suppose we had a payload of 1000 tons. This requires 55,000 tons of fuel. An efficient and abundant fuel to use would be hydrogen, perhaps mined from one of the moons of Saturn. For 55,000 tons of H you need 440,000 tons of ice, requiring 1016 Joules of energy to dissociate the H from the O.
This is approximately 1000 times the entire yearly electrical energy consumption of the US! Who is going to pay for this?!
Matter/Antimatter Rockets
Since we want to go fast (presumably) and the fastest speed we can go is light-speed, for an efficient rocket, the exhaust must also be light-speed. Light travels at the speed of light (duh!) so we need a fuel that produces light as the exhaust. If you bring matter and antimatter together they will annihilate, and a major product is gamma-ray photons. So let is use matter-antimatter annihilation, and set W=c:
where a is the acceleration, x is the distance covered by the time Vf is reached, and ln="e"log10.
Just for the point of illustration, let's forget about having to take round trips. How far and fast can one go with just flat-out acceleration? (No stopping, drifting, or return).
| Vf / c = 0.1 | Vf / c = 0.98 | Vf / c = 0.1 | Vf / c=0.98 |
| a=0.01 g | a=0.01 g | a=1 g | a=1 g |
| M=1.1 | M=9.95 | M=1.1 | M=9.95 |
| Tcrew=9.7 | Tcrew=230 y | Tcrew=0.1 y | Tcrew=2.3 y |
| Tearth=39 | tearth=2000 y | tearth=0.4 y | tearth=20 y |
The fuel supply needed to reach Vf / c=0.98 for a round-trip (MRT=M4=9,800):
A "tiny" 10-ton payload requires 100,000 tons of matter/antimatter:
which is approximately 1 million times the present yearly electrical energy consumpOttion of the US. This is EXPENSIVE!
Other "interesting" ideas that have been tossed around:
Thermonuclear Rockets (Project Orion - you may have seen this resurrected for the motion picture Deep Impact)
Here, one sets off nuclear bombs behind a "reaction plate" (shock absorber). Might be more efficient than chemical rockets, but falls short of matter/antimatter. Also violates current ban on nuclear devices in space.
Solar Sailing
The ship uses a sail to turn the momentum of sunlight and the solar wind into a means of propulsion. Since the solar wind never exceed about 1000 km/s in speed, the ship cannot either (unless you can tack this sort of stuff effectively), so its speed will be limited to about 0.003 c if it used the solar wind alone. Luckily, sunlight helps.
Suppose we start at 1 AU from the Sun (i.e. Earth's orbit), a sail area A and a payload (plus sail mass) M. Then
Let's start with a "tiny" 10-ton payload, and a sail 1000 km x 1000 km in size. Then the terminal speed (reached after an "infinite" time) is 0.04 c. Not very fast, for our purposes, since the average separation of stars in the Galaxy is about 1 pc (a little over 3 light-years). It would take roughly 3/0.04 = 75 years to get anywhere (let is ignore the deceleration and stop at the end, for now).
But wait! A 1000 km x 1000 km sail has mass, too! We also need to include it! Gold, although it is dense, can be made in very thin films, and is highly reflective. A sail 1 atom thick (a real sail would have to be much thicker) would have a mass of 170 tons, much larger than the payload (it effectively becomes the payload), and so the top speed is 0.009 c. Now it is over 300 years to get anywhere!
So when someone in a science fiction story sails from star to star in a day or two 1/300th of a year), this is impossible by a factor of 300 x 300 = 90,000 times! 5 orders of magnitude!!
Such trips are, therefore, unrealistic fantasy.
Yet other "Possibilities" for Interstellar Flight
Ships pushed by X-ray lasers A rear reflector plays the same role to a powerful planet-based light source as the solar sail did to sunlight. Interstellar Ramjets This uses interstellar gas as fuel. You no longer need to carry it with you. Avoid low-density regions? How do you get the fuel into the engine? |
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FTL (Faster-Than-Light)
Warp drives, etc. Contrary to all known physics. Sorry.
Proxy
Send machines that are sentient, can build copies of themselves ("von Neumann Machines", named after one of the pioneers in electronic computing), and spread exponentially throughout the Galaxy to do the exploring for us at a leisurely pace. What happens if the programming goes wrong has been the subject of more than one Star Trek episode (TV series and motion picture - they plagiarized themselves).
Unless there is a major revolution in our understanding of the laws of nature, space travel is likely to be confined to the solar system, unless someone wants to launch "generation ships" that only their distant descendents will see arrive somewhere. (Again, many stories on this theme).
My Personal Thoughts
IF interstellar travel were to become, but still limited to relatively slow travel, all trips will be 1-way. For M="e", M1way=M2=7.4, while MRT=M4=55.
Also, why return? Everyone you know back on Earth will be dead. You will be an anachronism (how would your great-great-great-great grandparents fit into today's society?), or worse, a specimen in a zoo.
DANGER-HAZARD
A 1-mm grain (mass of 0.012 grams) hit by a spacecraft travelling 0.1 c hits with an energy (E=1/2 mv2) of 5.4x109 J. This is the same energy as a 1-ton object hitting at Mach 9.5 (7,000 mi/hr)!!!!
Past "Attempts" at Physical Contact
The Pioneer 10 spacecraft, now exiting the solar system, carries a plaque with information etched on it that gives anyone who finds it some idea of where it came from, if they can decipher it.
The Voyager 1 and 2 spacecraft each carries a gold record (and stylus for "playing") with images and sounds of Planet Earth.
Neither of these are targeted at any specific star. Their trajectories were constrained by their science missions to the jovian planets.
What are the chances of a spacecraft on a random trajectory actually "hitting" a planetary system? Let us suppose it has to come within 1 AU of a star to be accidentally discovered. The average distance required to travel before you "hit" something is what physicists call the "mean free path" x=1/(s n), where n is the number of systems per pc3, and s is the "target area" to be hit. For a circle, the target area is "pi" times the radius (here 1 AU), which we will express in pc2 to get the units we need. As for n, we can get this by dividing the number of stars in the Galaxy N by its volume, p R2h, where R is its radius and h is its thickness.
For R=15,000 pc, h=100 pc,
Now if
then
So, in order to "hit" a planetary system before exiting the Galaxy (say, after 104 pc) requires N > 1017, far more than the number of stars in the Galaxy (roughly 109). Looking at it another way, the chances are 1 in 100 million (109/1017=10-8)! Increasing the "target size" to the size of Neptune's orbit increases the odds, to about 1 chance in 100,000.
Anyone want to bet?
