Planets of Other Stars II

Getting There


Since the development of nuclear power scientists have speculated about the practicalities of travelling between the stars. The energy requirements and time-scales are incredibly larger than anything we have ever known in prior human history.

The ultimate speed limit for matter and energy is the speed of light - 299,792,458 metres per second. Fast enough to reach the Sun in 500 hundred seconds, and Pluto in just 20,000 seconds - a few hours. The Solar System is less than a day-trip for a beam of light. But distances between stars are immensely larger than this. Light travels 63,240 times the distance between the Earth and the Sun [an astronomical unit, or AU] in a year. That's a light year - a unit of length, not time as the popular media seems to think. To the nearest star-system, Alpha Centauri, the distance is 4.4 light years. Which means at 10% the speed of light, roughly 30,000 kilometres per second (30,000 km/s), Alpha Centauri is 44 years away - more like 45 if acceleration time is taken into account.

The best current rocket technology can do is about 30 km/s - a pitiful 0.01% of light speed. That's 10,000 years per light-year in travel time, about the average speed of stars passing each other in the galaxy - you may as well wait a few hundred thousand years for a star to pass near-by!

Extending near-term rocket technology gives a ten-fold boost in speed up to 300 km/s. That's about top exhaust velocity for the VASIMR plasma rocket being developed for future Mars missions, and roughly how fast an advanced solar-sail can go. Faster than the stars a really patient civilisation could expand at this speed and fill the Galaxy in 100 million years - but it's a patience I doubt humans could ever sustain. At their limits VASIMR, ion rockets and solar sails might take 300 years per light-year - 1,320 years to Alpha Centauri. May as well wait until its close approach at 3.3 light years in a few thousand years from now!

When the first thermonuclear weapons were developed several scientists speculated on how to harness the raw power of hydrogen fusion explosions. A bomb tossed out the back of a ship and detonated would not annihilate the space-ship. Instead it would give an immense kick as the blast-wave hit some suitable "pusher plate". With the right shock-absorbers such a ship could carry humans. One such design is called "Orion" and at its ultimate "Orion" has an exhaust speed [Vex] of about 10,000 km/s - 3.3% light-speed. "Orion" at that speed takes 30 years per light-year, putting Alpha Centauri 132 years away.

A rocket needs to carry 1.72 times its own weight in fuel to reach its exhaust speed [Vex] - a mass ratio equal to e [a constant, equal to 2.72 roughly.] To reach twice its Vex the ratio becomes NOT 2e but e x e... 7.39. Three times exhaust speed needs a ratio of e x e x e... that's about 19 times the mass of the ship in just fuel! To slow down from speeds close to light requires reversing a rocket's thrust and reducing velocity - so to reach Vex is only half the velocity change required. "Orion" at take-off weighs roughly ten times its final weight after accelerating and deccelerating.

A way around this is to find another way to slow down. Space is filled with gas, even between the stars, but it is incredibly thin - a few atoms, at most, per cubic centimetre. If a space-craft can generate a powerful magnetic field to create drag against this gas then it can ultimately slow down from interstellar speeds. Such an idea has been extensively researched by engineers Robert Zubrin and Dana Andrews. They call it the magnetic sail, or mag-sail, and it would be an invaluable assistance to any interstellar traveller.

table 1 - getting there

System Velocity (km/s) Velocity (lightspeed = 1.0) years per light-year to Alpha Centauri (years)
Current rockets 30 0.0001 10,000 44,000
VASIMR 300 0.001 1,000 4,400
solar sail MAX 1,000 0.0033 300 1,320
Orion 10,000 0.033 30 132
Orion Ultimate 30,000 0.1 10 44

Using a mag-sail to deccelerate might enable an "Orion" style starship to achieve 10% of lightspeed. Within 20 years of initiating an interstellar program NASA might be able to build such a starship, if they went all out. A couple of hundred people would inhabit a self-contained space-colony mounted on immense fuel spheres of frozen fusion fuel, all of which would be mounted on a massive pusher plate, or perhaps a hemispherical shell protected by magnetic fields that would contain the explosions for higher efficiency. Such a vehicle would weigh tens of thousands of tons - mass ratio of 10 - and would require mining asteroids for fusion fuel rather than thousands of shuttle flights laboriously haulling fuel into orbit. Such a starship would launch for the nearer stars - probably Alpha Centauri - on decades long missions, with the original crew raising a new generation or two en route. Definitely a one way proposition.

Ultimately humans might travel between the stars like so. If we colonise the solar system then much of the human population will live in space colonies built with asteroid materials, and using fusion fuels mined from the same or the gas planets such colonies can fly out to the other stars, perhaps taking centuries to do so. They might decide that planets are not worthwhile sites for a proper human life and instead they will merely use asteroids and comets for raw materials, reproducing their colonies as they grow. In a million or so years they could reach every star in the Galaxy. Other civilisations might have already done so, and some may still exist in the outer reaches of our Solar System.

Getting there Faster

Humans are not a patient species. Decades between stars seems like an excessive waiting time for those of us who want to learn about other life and civilisations. By 2025 NASA hopes to have in orbit, perhaps near Jupiter, a Planet Imager which should provide 100 pixel wide images of terrestrial planets around other stars out to 50 light years, and useful images of planets out to maybe 500 light years. Do we then have to wait up to 5,000 years to go look for ourselves? Even if humans developed immortality such journey times seem excessive. Suspended animation should be possible ultimately, but what if there's a quicker way to get there? Can we get up past 0.1 lightspeed?

Particle accelerators routinely push sub-atomic particles to speeds of 0.9999... times lightspeed. So the issue is not about exhaust speed, it's about energy. Put a particle accelerator on a starship, but the energy in an exhaust beam is proportional to the square of its speed, while the thrust that it gives only rises in proportion to that speed. A higher thrust for a given energy then means a lower exhaust speed. No energy generating process is 100 % efficient - all the power from a fusion reaction doesn't get turned into electrical power to run an accelerator. Theoretically fusion reactors can get up to 95 - 99% efficiency directly converting particle radiations into electricity.

Say your power level for the accelerator is a terawatt - a trillion watts, or a billion horsepower. If its exhaust speed is 0.1 lightspeed then the thrust is about 66,000 newtons (66,000 N.) A fusion reaction produces up to 800 trillion watts per kilogram of fuel - say in this case we get half that. A terawatt of power then needs 2.5 grams of fusion fuel per second. But for the 66,000 N thrust the propellant to fusion fuel ratio is then 2.2 : 2.5 - almost half and half... and even more reactor fuel is required if the accelerator is not 100% efficient! Better to just exhaust the fusion reaction products directly i.e. a plain old rocket system.

Better than fusion?

Are there any power sources better than fusion energy? While the makers of "Star Trek" toss around "antimatter reactions" even they acknowledge the fundamental fact that there is no fuel more abundant than basic fusion fuels like hydrogen, helium, boron and lithium. Antimatter could provide more power, but it has to be made painfully slowly in huge particle accelerators. Perhaps some better means of converting energy to antimatter will ultimately be found but it will still take an immense effort to make the stuff.

Beyond antimatter there is only speculation. The particles that make up matter have unique identities that have normally rigorous conservation laws that preserve them. To change them into energy requires by-passing those laws. This requires unique conditions, perhaps only found in the extreme environment within neutron stars. If humans could duplicate such conditions we might be able to convert matter into energy, but only maybe.

Another possibility is GUT energy, which is energy creation without matter. This doesn't violate thermodynamics because it incorporates the higher physical principles behind the Universe's formation. If we could push some seed-matter to GUT conditions we might be able to tap into the raw power of Creation itself, restarting the Big Bang in minature, but presently such a feat is far beyond us. All these methods currently require new physics that may not even exist.

But what if the power was beamed to the space-craft?

Using high-energy lasers such a system is not as absurd as it sounds. A starship could carry propellant and an accelerator, plus the energy receiver-convertor system. Such a ship might achieve 0.2 lightspeed before certain difficulties arise that make it more efficient to start considering using a stay-at-home thrust system...

Stay-at-home thrust systems

Potentially this is the ultimate way to the stars using physics that we know about in any detail. There are three different approaches to the energy/thrust transmission system - light, particle beams and mass beams. All require immense energy generation/projection systems and extremely accurate guidance systems. Power generation can come from three sources - solar, nuclear fission and nuclear fusion reactors - but the power levels are beyond the Earth's current power needs. If we extrapolated from the current growth levels in power generation hundreds of years will pass before interstellar travel becomes cheap enough to be practical.

This will change if large scale power generation becomes common-place in a solar system based economy. A large nuclear power reactor is essentially a rocket motor with some sort of generator coupled to it, drawing energy off the exhaust directly - set up on an asteroid the system would be environmentally insignificant since the Sun produces far more radiation than anything humans can build.

Large-scale solar generation would only be feasible if Self-Replicating Solar-Power Systems [SRSPS] can be developed - a robotic system that converts asteroidal material into solar-panels and new SRSPS that then reproduce and so forth... thanks to exponential growth this is generating enough power for large-scale interstellar travel within a couple of decades, and could beam power to solar-system projects via the same beams it uses to push starships.

The Kinds of Starship Propulsion are as follows:

An LPLS is essentially a solar sail propelled by a massive laser or maser [the microwave version of a laser] system. Using a careful choice of sail material the LPLS can be more efficient than a simple reflective solar sail. To deccelerate at the target star system the LPLS uses a magsail, or else a system of stage sails - a large sail acts as a back reflector to slow down a smaller decceleration sail. LPLS need massive Fresnel lenses to sufficiently focus the laser beam across interstellar distances, or else must accelerate very rapidly within the Solar System.

PBPMS use a magsail in place of a light-sail and are pushed by banks of particle beams, providing a hard wind to sail rapidly to interstellar speeds. The magsail then deccelerates the starship at the target system. The magsails required can be much lighter than a similar LPLS since the magnetic field acting as the sail has no mass. Accelerations required by a PBPMS are very high, as particle beams disperse rapidly. Several hundred gee acceleration might seem to preclude human crews, but if humans are suspended in oxygenated fluid this is not impossible. Salamanders have lived for years in high gravity centifruges suspended in water.

Mass Beam Propulsion uses large particles instead of ions to do the accelerating. The difficulty is much higher because the catchment on the starship is much smaller - metres rather than kilometres of magnetic field or light-sail. Nanotechnology could endow the accelerator particles with primitive self-guidance and course-correction enabling this very promising technology. Mass Beams could allow starships to accelerate to very close to the speed of light.

table 2: getting there faster

Propulsion Velocity MAX (lightspeed=1.0) Range Acceleration
LPLS 0.5 Light-years? 100s - 1/10 gee
PBPMS 0.3? AU 100s gee
MBP 0.9999... Light-years variable

Decceleration for an exploration vessel would require a magnetic sail, but once a base was established a suitable acceleration/decceleration system can be set up for two-way traffic. With the right system, energy drawn off a slowing vehicle can be used to accelerate another, ultimately reducing the energy requirements dramatically. A "rapid transit" network might then be set up across the galaxy - it might well already exist if other intelligent species have expanded across the Galaxy before us.

However even with ultimate mass beams the stars are still decades or more away. Einstein's relativity says time slows down as the speed of light is approached, but there's a catch. Here's why... at 0.87 lightspeed time slows down to 1/2 its Earth-pace, at 0.94 it is down to 1/3, at 0.98 it's 1/5, and at 0.995 it is 1/10. But to accelerate to those speeds takes time.

From Earth's point of view the time needed is the final velocity divided by the time reduction factor times the acceleration... so 0.995 lightspeed takes 9.65 earth years to reach at one gee. On ship the time distortion reduces that to 2.9 years - still quite a while. At ten gees the time taken is 0.29 years on ship, and just 0.965 years on Earth. But who wants to float in a tank of fluid for months to reach high time distortion factors?

For quicker journeys two questions arise...

Planets of Other Stars I

Planets of Other Stars III: Getting There Quickly

Arthur C. Clarke Tribute Page

Appendix: Time distortion factors...

Ship time, t (tau), is related to Earth time, t, by the reduction factor calculated as follows...

t/t = sqrt[1 - v^2/c^2] where v is the ship's speed, while c is the speed of light. If c = 1.0 then it's a whole lot simpler, since v is always less than 1...

Call this reduction factor 1 / g ...

To accelerate to v then takes an earth time, t1, equal to...

t1 =[ v *g ] / a where a is the acceleration [but in this case use v in metres a second and a in metres per second per second. If you want to use v as a decimal fraction of lightspeed, time in years and acceleration in gee, then the constant is 0.9687]

The ship time is more complicated. Call the inverse of the time reduction factor, g (gamma). Then the ship time to accelerate to v is t1...

t1 = [c / a] * [ln ( g + sqrt( g^2 -1)] ... which for large values [> 10] of g is the natural logarithm of roughly 2g times the speed of light divided by the acceleration.

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