Energy Economics (highlights)
To move something from point A to B at interstellar distances requires velocities close to the speed of light. For example, to get six light-years away, at $1 \over 3$c takes eighteen years.
The minimal energy required to accelerate and slow the load is
- ${mc^2}\over{\sqrt{1-{{v^2}\over{c^2}}}}$ or
- ${mc^2}\over{\sqrt{1-{\%^2}}}$
Some examples:
- Travelling to Alpha Centauri at 10%c will take 40 years and require a minimum of 2% of the cargo mass to be fuel.
- Making the same trip at 33%c will take 12 years and require 22% of the cargo mass to be fuel.
Rocket Equation
Absent a kinetic energy pump like emm drive, or boost drive, the cost to move a payload is further limited by the rocket equation $dv = \ln{M \over m}$, and assuming exchaust velocity is close to the speed of light and dv is expressed in a percentage of light speed.
- A 4 ly trip at 33%c will require about 29% of its mass to be ejected as propellant (which hopefully includes whatever is being burnt for power)
Technology Efficiency
As a tax, there are the theoretical limits to efficiency of certain power technologies : fusion will generate 7 MeV per thousand MeV of hydrogen mass (about 1%), antimatter could potentially be a 100% efficient technology-- but that comes with concerns about safety.
Solar Sails
Per this article, solar sails are limited to an upper velocity of about 0.2% c. A 4 ly trip at this speed will take 200 years.
Reliability of Equipment
You can always trade energy for time, but the upper limit being when enough damage is done by time, radiation, heating and cooling that critical failure is imminent.
Erosion
The density of space is estimated at 1 atom per cubic centimeter. A single hydrogen atom at rest in space being hit by a vessel traveling through interstellar space at 33% c only delivers a few billionth's of a joule in damage, but it adds up over 9,460,800,000,000,000 kilometers per light-year. A throw-away ice shield will undergo meters of erosion in a single trip.
Economic Models
That all being said, what are some economic models that make this work, anyway?
Highway 66
We keep discovering dwarf planets further from the sun. Depending on how flexible we are with this arrangement, it's possible that in a similar way that the American highways were dotted by tiny towns, you might have trade routes that are, individually, a few hundreds of AU between stops. At one gee, a 100 AU trip would take about one week each way, making it a very good fit from a crew and logistics point of view.
Goods and information eventually make it down this highway, with a host of middle loaders and merchants trading hands along the way. Each colony taking enough off the value of material floating through to keep the lights on and the "trucks" running.
Data Economy
Another alternative is a data economy. If you were to built a communications relay of satellites streched 100 AU apart from one another, you'd be able to create an interstellar data trunk for the cost of about 650 relay stations per light-year.
There's a lot more to a data economy than just what is novel on Planet A or Planet B.
In fact, there exists an enormous backlog (just on Earth) of information that has never been properly examined. Examples : bits of ancient pottery, unidentified or untranslated writing, bones, genetic sequences taken of possible new animals, environmental DNA collection searching for new species, mineral surveys, and so on.
The backbone of the interstellar digital economy may be sending large batches of data light-years away where cheap idle minds will work on it and return the most interesting results.
Adding to this backbone could be flashy stuff like novel materials, biotechnology, art, and other innovations.
Science
Our solar system is situated inside a large natural megastructure : a magnetized tube of ions maybe 1,000 light years long. On Earth, a phenomenon called tropospheric ducting allows radio signals to bounce beyond line-of-site and be clearly received nearly on the other side of the Earth.
It's possible, likely even, that there are multiple locations that are very interesting and that particular locations in the large volume of space between stars are the best viewing spots for the phenomenon. Like Mt. Mauna Kea or Greenbank Observatory, these could be remote "off-the-highway" locations that exist exclusively for the purposes of research.
Exotic Material Extraction
There may be a whole other periodic table (or many) in the universe. Some of these materials, such as dibaryons, are predicted to exist in minute concentrations between stars. Shipping vessels, like a paper towel, will accumulate a good deal of this interstellar material during their trip. Sacrificing the hull for exotic material extraction might be a way to recover some of the cost of a trip.
But exotic material need not be as exotic as new atoms. As this person discovered with magnetic locking at room temperature, macrostructures of minerals can do some amazing things. Using the magnetic locking example, imagine a mineral like opal (consisting of tiny equal-sized spheres) that possessed this magnetic characteristic and stably floated in air at certain frequencies.
It's reasonable to expect new minerals made of the same things we're familiar with, but with useful characteristics of their own. Some of these may be industrially worthwhile enough to merit the cost of freight.
Or, a miner could merely find an asteroid with a high concentration of something incredible rare in the solar system (osmium, for example).