Outer Planets in a Hurry(ish)

In a 2005 paper Craig Williams and crew, from the NASA Glenn Research Center in Cleveland, Ohio, improved on their 1998 fusion propelled Outer Planets vehicle – and dubbed it the “Discovery II”, inspired by the fictional “Discovery” from “2001: A Space Odyssey”. The improved version massed 1,690 tonnes fully loaded with propellant, some 861 tonnes of slush hydrogen propelled to several hundred kilometres per second by fusing 11 tonnes of D-He3. Full throttle and the “Discovery II” promised a trip-time of 118 days to Jupiter and 212 days to Saturn, which is faster than the fictional version.

Intergalactic Travel – Best Way To Andromeda?

If we’re sufficiently patient, M31 is coming towards the Milky Way and should arrive in about 3 billion years or so. Intergalactic Travel is easy, given aeons.

M31, the Great Galaxy in Andromeda, some 2.5 million light-years away.

However, if we’re talking mere megayears, then the trip to M31 and beyond requires boosting the transit speed. If we can accelerate at a continuous acceleration – undergoing so-called “hyperbolic motion” – then the ship-board time can be reduced to arbitrarily low values. With the proviso we can supply sufficient energy and protect ourselves from the high-energy photon/particle bath that cosmic-rays and the Cosmic Microwave Background both become. Aberration – the distortion apparent direction of objects moving towards the observer – means the incoming radiation becomes ever more restriction to dead-ahead, making mitigation somewhat easier.

Slower trips, at constant fractions of the speed of light, require the passengers/payload to remain in some kind of stasis, else the billennia will inexorably erode their viability. Alternatively a World-Ship is sent, sufficiently well provisioned to last several million years. Back in 1987 Burruss & Colwell proposed such a concept, with a vast 1,000 km wide World-Ship, 50 billion passengers, and a cruise speed of 0.4c. The antimatter fuel required would be the equivalent of several days worth of the Sun’s total luminosity, so it would require at least a Kardashev Type II Civilization dedicated to the task to achieve it.

A World-Ship or a whole World? What if we sent an Earth-mass planet, using tricky orbital maneuvering around the 4.2 million solar-mass black-hole in the Milky Way’s Core as our accelerator? A Type III Civilization, with control over the Galaxy’s resources, would surely be able to arrange such a minor rearrangement of masses in the Core, flinging the Intergalactic Planet-Ship outwards at 0.5c. But what would it require to stop in the target Galaxy?

Given the right materials a magnetic-sail might do the job. We can slow an Earth-Ship from 0.5c to 0.005c in about 550,000 years (11% of the trip-time) over a braking distance of about 36,000 light-years. The sail would be 13.4 AU in radius with a super-current of 68 giga-amps and a mass of about 15.4 quadrillion tonnes (if its density is about that of carbon nanotubes.) Thus immensely BIG and probably immensely strong. At the “wire” (1.5 metres in radius) the field strength is 9,240 tesla, which is about 100 times higher than the highest critical magnetic field strength of known super-conductors. Thus not material we presently possess.

Faster Times to Alpha Centauri – II

Now we have somewhere to go…

Ixion, aka Alpha Centauri Bb - the nearest detected exoplanet.

Image courtesy of Steve Bowers, for the Orion’s Arm shared Universe.

Now that we have somewhere to go around Alpha Centauri, with good odds of more clement planets too, then the question of getting there faster becomes more pertinent. In Part 1 I discussed the Mag-Sail equipped Laser-Sail, based on the advanced mission parameters discussed in this paper by Zubrin & Andrews: Use of magnetic sails for advanced exploration missions, from NASA, Lewis Research Center, Vision-21: Space Travel for the Next Millennium; p 202-210.

Suggested Laser-station from Zubrin & Andrews

A limitation not covered by Zubrin & Andrews directly is the Critical Magnetic-Field strength of the superconductor used – using their specific characteristics (density 5,000 kg/m3, current 1.36 MA, mass 950 tonnes, 3,100 km diameter) the magnetic field at the wire is over 100 tesla. Modern High-Temperature Superconductor (HTS) wires struggle to reach 20 T critical field strength. However they did specify a very high critical current of 1011 A/m2, which suggests a high critical field strength.

Zubrin & Andrews discussed two options – deceleration via mag-sail to 0.01c (3,000 km/s) and terminal braking via a fusion rocket, or pure mag-sail braking to 0.00167c (500 km/s) which is sufficiently low to allow pure mag-sail braking in the destination star’s stellar-wind and thus orbital capture. The fusion-rocket option is significantly heavier by 438 tonnes, so let’s look at the pure mag-sail case first. So how well does the pure mag-sail braking do? With a 0.5c cruise speed the trip to Alpha Centauri takes 25.9 years. However the magnetic-braking takes 79% of the total trip-time! Dropping to just 0.25c increases the trip-time to 33.2 years, but reduces the total energy expenditure to just 25% of the 0.5c cruise speed.

With the additional fusion rocket, mag-braking to 0.01c and 0.5c cruise speed, the trip-time drops to about 20 years. This might make the fusion rocket worth-while, assuming we can build a fusion rocket light enough that is!

Faster Times to Alpha Centauri – Part I

If fusion, assisted by magnetic sails, gets us to Alpha Centauri in ~50 years, then how do we get there faster? Absent annihilation drives, powered by gamma-ray lasing matter-antimatter reactions or Hawking decaying force-fed mini-black holes, then we need to get the power-supply off the space vehicle and send fuel, momentum and energy to the vehicle as it accelerates. “Centauri Dreams” has covered a number of notable options just recently – the laser-powered ramjet, the laser-powered rocket and, of course, the Bussard ramjet itself.

Then there’s the various light, laser, microwave and momentum sails that have been proposed over time. Jim Benford, twin brother of SF-writer Greg Benford, and high-power microwave expert, has studied in some detail the economics of microwave propelled interstellar sails. The costs are extra-ordinary for all but the most primitive interstellar probes, but such figures are somewhat misleading. A basic assumption is that the energy generating and emitting systems will be installed in much the same way we do things at present – Jim factors in economies of scale, but not revolutions in technique.

Let’s have a look at the raw requirements. We’ll assume a 1,000 tonne payload, 1,000 tonne mag-sail and 400 tonnes of laser-sail. A 5,000 terawatt laser accelerates the sail to 0.5c in about 0.8 years – a total energy expenditure of 1.26E+23 joules. How much power is 5,000 terawatts? Earth receives 174,400 terawatts from the Sun, absorbing 122,200 terawatts of that. Balancing out the heat-flows in Earth’s atmosphere and oceans, equator-wards of the Tropics is a region that gains energy, while pole-wards of the Tropics are regions which lose net energy back into space. Energy flows northwards and southwards via the winds and oceans – the winds carrying about 5,000 terawatts in both directions. Thus our laser-sail needs about 50% of the Earth’s wind-power available.

We can’t power a starship with Earth-based energies, unless we mine heroic amounts of deuterium or boron from the oceans and land. We must turn to what’s available in space – the most abundant source being the Sun. In radiant energy alone, the Sun puts out ~384.7 tera-terawatts (384.7 yottawatts), but also sends forth immense amounts of energy in the Solar Wind. Tapping either is a non-trivial task. In the late 1970s NASA and the US DoE studied Solar Power Satellites (SPS) – one estimate was that a 5 gigawatt SPS would mass ~50,000 tonnes. Thus 5,000 terawatts would require 1 million SPS with a total mass of ~50 billion tonnes. Of course techniques have improved considerably since the 1970s – some ultra-light SPS designs approach ~1,000 tonnes per gigawatt. To go much lighter we need to move them closer to the Sun – if we can operate them at 1,000 K then we can park them just 0.1 AU from the Sun. There our “1 gigawatt” SPS can generate 100 gigawatts. Thus ~5 million tonnes of near-Solar SPS will power the lasers for our starships.

How fast can we get there with 5,000 terawatts of laser-power pushing us? I’ll have some answers in Part II.

Fastest Time to Alpha Centauri – III

a repost from Facebook.

?”Daedalus” had a top speed of ~0.122c, though some variants could hit 0.138c for an extra 10,000 tonnes of fuel or so. This makes for a 36 year trip to Alpha Centauri – but no way of stopping. Equipping “Daedalus” with a magnetic sail and enough propellant to brake downwards from 1500 km/s, when the mag-sail performance drops significantly, lets us contemplate braking to a halt. But, as always for realistic rockets, there’s a trade off between how fast the fuel can be expelled – the mass-flow rate – and the cruise speed. Too high a cruise speed means the time spent accelerating drags out and actually reduces the average speed.

Throwing in the relevant characteristics and model parameters means that I can compute the total flight time for a range of speeds, and then search for the minimum time. I’ve assumed a 1,000 tonne mag-sail which is about equal in mass to the “Daedalus” 2nd Stage with enough propellant for the final brake phase, 1100 tonnes. The mag-sail is 800 km in radius and carries a super-current of several hundred kiloamps. The maximum magnetic field in the wire is about 16 tesla, which is high, but not as high as the critical field of some present day SCs.

What results is a minimum flight time of 45 years – not much more than the bare minimum. The cruise speed is a higher 0.1388c, while the initial mass is 181,480 tonnes. In the original “Daedalus” plan mining 50,000 tonnes of propellant from Jupiter would take 20 years. To mine the extra 130,000 tonnes needed for a faster probe could require ~60 years. However going a bit slower means a 50 year flight needing only 66,040 tonnes initial mass.

Fastest Time to Alpha Centauri – Two-Stage Mag-Sail Scenario

After rearranging the mass-models, just for the sake of the exercise (Eric Storm’s suggestion), I’ve computed the fastest time to Alpha Centauri via a Mag-Sail equipped Two-Stage “Daedalus”. In this case both stages will be use to reach the cruise speed, then the mag-sail will be deployed at the appropriate point in the voyage. The minimum trip-time is when the cruise-speed is 0.13488c, the mission time 45.82 years and an initial mass of 181,480 tonnes. So, yes, Alpha Centauri can be reached in under 50 years by “Daedalus”. Interestingly exactly 50 years needs a mass of 66,040 tonnes (this includes the 1,000 tonne mag-sail.)

How far can it reach in under 100 years? About Tau Ceti’s distance – 11.9 ly. To reach GJ 581c requires ~152 years and about 540,000 tonnes initial mass, minimum. For the same mass as the minimum time to Alpha Centauri, the trip to GJ 581c takes 164 years. Patience is required, it seems.

Fastest Time to Alpha Centauri – Errata Nipped in the Bud

Blogging helps collect one’s thoughts. After the previous post I revisited my presentation and mass-models, only to discover a significant mistake in a key cell reference in Excel. Yikes! Re-writing my equations’s references I managed to shave a significant number of years off the minimum voyage time to Alpha Centauri via a mag-sail equipped “Daedalus” 2nd Stage. And update the affected slide being presented by my friend Pat Galea (thanks again, Pat!)

Now I am really interested in what a two-stage “Daedalus”+Mag-Sail can do. More importantly, how far can we send it in 100 years? As fascinating as Alpha Centauri A & B (and Proxima) might be, the known exoplanets are all much further away. The nearest (arguably) habitable exoplanet is Gliese 581g at a distance of 20.3 light-years. Can we get there in under 100 years using fusion and mag-sails? Or do we need something different?

Fastest Time to Alpha Centauri – Errata

Something about my mass model of “Daedalus” didn’t sit right with me, so I recomputed the tankage from first principles. The percentages were more like 5%, thus meaning a slightly slower fastest time – 71.58 years with an initial mass of 281,181 tonnes.

While “Daedalus” can cruise at 0.12-0.14c, meaning speedy trips to Alpha Centauri, compared to the above, the problem is that there’s no way of stopping at such speeds – finite tank mass means an infinite mass of propellant would be required.

I went on to compute the performance of a magnetic sail equipped vehicle and got quite an encouraging result – which I’ll post here after the Symposium presentation itself, which is in a matter of days. Traveling to Alpha Centauri via fusion rocket in sub-50 years will be an immense engineering challenge, so one hopes better options will arise. Jonathan Vos Post has a paper online which is a good example of the extreme performance required for very rapid flybys – a perfectly efficient fusion motor, a five stage vehicle, and a mass-ratio of ~100,000 means a flight in ~9 years or so. Wildly unrealistic, but illustrative of the effort needed.

To do better will need something better than rockets, but not necessarily more powerful than fusion energy.

Fastest Time to Alpha Centauri

Currently I am working on a paper & presentation for the 100 YSS Symposium in Houston, to be presented by an Icarus colleague. I am examining the effectiveness of using a magnetic-sail to brake to low-speeds in the target system, but part of that is a comparison with a pure fusion rocket. As it is still the most detailed design for an interstellar fusion rocket I am using the performance characteristics of the “Project Daedalus” star-probe. The most economical use of propellant for pure-fusion is to boost up to cruise speed using the 1st Stage, drop the spent stage, then brake using the 2nd Stage after a period of cruising. “Daedalus”, due to its ignition system and the tricky physics of implosion ignited fusion, had two different exhaust velocities for the stages – 1st Stage was 10,600 km/s and 2nd Stage was 9,210 km/s.

A limiting variable on the possible mass-ratio was the mass of the cryogenic tankage required to keep helium-3/deuterium fuel at a chilly 3 K storage temperature. For the 1st Stage the tankage was 2.85% of the fuel mass stored and 4% for the 2nd Stage. As a critical mass-ratio is approached the required mass of propellant goes asymptotic – runs off to infinity. Thus there’s a maximum cruise speed for a single stage using “Daedalus” style storage systems. It works out as 0.1c for the 2nd Stage engine. To achieve that speed requires infinite propellant mass, so it’s not really practical.

A more practical question is the fastest trip to a given destination. Rockets are limited in how quickly they can burn their fuel – Stage 1 burns it at 0.72 kg/s and Stage 2 burns it at 0.0711 kg/s. To achieve higher speeds requires burn-times that are asymptotically rising, when the critical mass-ratio is factored in.

Alpha Centauri is 4.36 light-years away. A two-stage “Daedalus” vehicle can travel there in 68 years at a maximum speed of 0.075c and then brake to a halt at the destination. However the amount of fuel required is about 300,000 tonnes. Going a bit slower – arriving in 71 years – can reduce the fuel required to just 140,000 tonnes. “Daedalus” carried an immense payload by modern standards – 450 tonnes, the equivalent of the International Space Station. The recent paper on boot-strapping a robotic economy on the Moon only required delivery of 41 tonnes to kick-start things. A large exo-solar industrial base could be sent to other star systems in a decent time frame to build, in advance of human arrival, large laser or mass-beam facilities to decelerate a human-carrying star-ship. Such would allow much faster trip-times.