Category: Carnival

The Unknown Solar System

Kuiper-Belt

Just beyond Neptune is the Kuiper Belt, a torus of comet-like objects, which includes a few dwarf-planets like the Pluto-Charon dual-planet system. Despite being lumped together under one monicker, the Belt is composed of several different families of objects, which have quite different orbital properties. Some are locked in place by the gravity of the big planets, mostly Neptune, while others are destined to head in towards the Sun, while some show signs of being scattered into the vastness beyond. Patryk Lykawka is a one researcher who has puzzled over this dark, lonely region, and has tried to model exactly how it has become the way it is today. Over the last two decades there has been a slow revolution in our understanding of how the Big Planets, the Gas Giants, formed. They almost certainly did not begin life in their present orbits – instead they migrated outwards from a formation region closer to the Sun. To do so millions of planetoids on near-misses with the Gas Giants tugged them gently outwards over millions of years. We know what happened to the Gas Giants, but what of the planetoids? A fraction today form the Kuiper Belt and the Oort Cloud beyond it (how many Plutos exist out there?) But a mystery remains, which Lykawka convincingly solves in his latest monograph via an additional “Super-Planetoid”, a planet between 0.3-0.7 Earth masses, now orbiting somewhere just beyond the Belt.

Noaa_ganymede

Such an object would be a sample of the objects that formed the Gas Giants, a so-called “Planetary Embryo”. Based on the ice and silicate mix present in the moons of the Gas Giants, the object would probably be half ice, half silicates/metals, like a giant version of Ganymede. However such an object would also have gained a significant atmosphere, unlike smaller bodies, and being cast so far from the Sun, it would have retained it even if it was composed of the primordial hydrogen/helium mix of the Gas Giants themselves. This has two potentially very interesting consequences. David Stephenson, in 1998, speculated on interstellar planets with thick hydrogen atmospheres able to keep a liquid-water ocean warm from geophysical heat-sources alone. Work by Eric Gaidos and Raymond Pierrehumbert suggests hydrogen greenhouse planets are a viable option in any system once past about ~2.0 AU. A precondition that obtains for Lykawka’s hypothetical Super Trans-Neptunian Object.

So instead of a giant Ganymede the object is more like Kainui, from Hal Clement’s last novel, “Noise”. Kainui is a “hot Ganymede”, a water planet with sufficiently low gravity that the global ocean hasn’t been compressed into Ice VII in its very depths. Kainui’s ocean is in a continual state of violent agitation, lethal to humans without special noise-proof suits, but Lykawka’s Super-TNO would probably be wet beneath its dense atmosphere, warmed by a trickle of heat from its core and the distant Sun.

NOISE

Gravitational perturbation studies of planetary orbits by Lorenzo Iorio constrain the orbital distance of such a body to roughly where Lykawka suggests it should be. A Mars-mass object (0.1 Earth-masses) would exist between 150-250 AU, while a 0.7 Earth-mass body would be between 250-450 AU. If we place it at ~300 AU, then its equilibrium temperature, based on sunlight alone, would be somewhere below 16 K. That’s close to the triple-point of hydrogen (13.84 K @ 0.0704 bar), suggesting a frozen planet would result. However geophysical heat, from radioactive decay of potassium, uranium and thorium, could elevate the equilibrium temperature to over ~20.4 K, hydrogen’s boiling point at 1 atm pressure. Thus a thick hydrogen atmosphere should stay gaseous.

To keep liquid water warm enough (~273 K) at the surface, the surface pressure will need to be ~1,000 bar, the equivalent of the bottom of Earth’s oceans. An ammonia-water eutectic mixture would be liquid at ~100 bars and 176 K. With a higher rock fraction and higher radioactive isotope levels (as seen in comets, for example), liquid water might be possible at ~300 bars. Such a warm ocean would seem enticingly accessible since a variety of submarines and ROVs operate in the ocean at such pressures regularly. While the prospects for life seem dim, the variety of chemosynthetic life-styles amongst bacteria suggest we shouldn’t be too hasty about dismissing the possibility.

A primordial atmosphere also invites thoughts of mining the helium for that rare isotope, helium-3. At 0.3 Earth masses and 1:3 ratio of ice to rock, such a body has 75% Earth’s radius and just 40% the gravitational potential at its surface – even less at the top of the atmosphere. Such a planet would be incredibly straight-forward to mine and condensing helium-3 out of the mix would be made even easier by the ~30-40 K temperature at the 1 bar pressure level. There’s no simple relationship between the size of a planet and its spin rate, but assuming Earth’s early spin rate of 12 hours, then the synchronous orbital radius is just 2 Earth radii above the operating altitude of a mining platform. A space-elevator system would be straight-forward to implement, unlike the Gas Giants or even Earth.

Travelling to 300 AU is a non-trivial task, ten-times the distance to Neptune. A minimum-energy Hohmann trajectory would take 923 years, while a parabolic orbit would do the trip in 390 years. Voyager’s 15 km/s interstellar cruise speed would mean a trip of 95 years. A nuclear saltwater rocket, with an exhaust velocity of 4,725 km/s, could be used to accelerate to 3,000 km/s, then flip and brake at the destination. The trip would take six months, which is speedy by comparison.

Speed Kills?

Father & Son team, William and Arthur Edelstein discuss one of the dangers of near lightspeed travel in their paper published just last month: Speed kills: Highly relativistic spaceflight would be fatal for passengers and instruments [citation: Edelstein, W. and Edelstein, A. (2012) Speed kills: Highly relativistic spaceflight would be fatal for passengers and instruments. Natural Science, 4, 749-754.doi: 10.4236/ns.2012.410099.] They highlight the lethality of the high-energy proton head-wind that the Interstellar Medium (ISM) becomes when moving at near light-speed, which they define as above about ~0.9c.

I hadn’t realised the Edelsteins finally published their work until a Facebook friend, Jay Real, sent me a link. Of course these issues have been discussed in the literature for years so their discussion is nothing new – but welcome nonetheless as an explicit statement of the problem. High relativistic speeds are difficult to achieve, so most vehicles would probably stay below ~0.9c unless something exotic appeared, like an easy way of making one of Sonny’s warp-drive fields for rapid sub-light travel. In our part of the Galaxy the proton flux is much lower than the 1.8 protons/cc assumed by the Edelsteins. Some hot bubbles in the Local ISM go down to ~0.01-0.05 protons/cc and the local clouds are ~0.1-0.2/cc. This doesn’t change the results very much, but does lessen the local applicability.

Their analysis focuses chiefly on mass-shielding – big enough chunks of material to absorb the incoming flux. Magnetic shielding is mentioned dismissively, but I think that’s premature. Workable designs using known materials exist which can deflect 10 GeV cosmic rays, the equivalent of flying at 0.995c. Advanced superconductors, which will be needed for antimatter containment, plasma nozzles, magnetic-sails, will allow even higher protection levels. Thus I submit the Edelsteins’ negativity is premature.

The energy flux of interstellar matter hitting the ship can cause a lot of heating. If the ISM is just 100,000 atoms per cubic meter the flux is equivalent to 536 K temperature at 0.866 c. Peak temperature during re-entry is 2700 K for a moonflight – that level is reached at about 0.997c. Of course a starship wouldn’t just absorb that heat on its forward surfaces. A magnetic deflector would channel most of it away- but deflecting particles makes them lose momentum as high energy photons (x-rays) which would need to be shielded against. And the shield would get HOT! Fast starships would need to be long and narrow to minimise the energy absorbed. An x-ray reflective diamond coating could be used, but will need to be keep highly reflective while operating. Maintenance will be tricky!

As an example of the kinds of particle energies we can handle the Large Hadron Collider regularly bends a high energy stream of particles into a circle – the protons in the beam have a speed of 0.99999999c when it’s at full power. Cosmic-rays can reach much higher energies and need protection against. However the very highest energy cosmic rays are very rare, so only lower energy particles need deflecting in a crew habitat. The ones of biological concern, due to their numbers, are in the 1-10 GeV range. If we can deflect 10 GeV protons coming at us from our motion through space, then cosmic rays aren’t an issue.

Aberration comes into play at such high-speeds – the direction of origin of incoming particles and photons starts piling up directly in front of the starship. I would suggest the best protection at very high speed might be a “diffuser” – a high intensity magnet held far forward of the starship’s main hull which deflects the charged particles and creates a “shadow cone” behind it. The faster we go, for the same magnetic intensity, the further forward we put the diffuser. We fly, in safety, in its shadow thanks to aberration concentrating all the radiation to directly in front of us.

If we can deflect particles up to LHC energies, then how far can we accelerate at 1 gee? The acceleration distance required to increment the time-distortion/gamma factor (call it the TDF) by 1 is about 1 light year at 1 gee. At 0.99 c the TDF is about 7. So it takes about 6 light-years (because we start with TDF = 1) to get to 0.99c. To reach 0.9999c (TDF = 70) takes about 69 light years. Thanks to the time distortion, on ship the trip-time is much less. Remember a light-year is a distance, but as we’re flying so close to light-speed the ship is seen to take about 70 years to travel 69 light-years. A speed of 0.999999c (TDF = 700) takes 700 years Earth-time and 699 light-years of distance, but on the ship only just over 7 years have passed. If we decide to stop, then another 7 years ship time, 700 Earth-time, and 699 light years is needed – meaning we’ve flown 1398 light years in 14 years ship-time. But let’s push on. We’re pushing to TDF = 7,000 (0.99999999c) so the distance is 6,999 light-years, 7,000 years Earth-time, about 9.5 years onboard ship. Thus we could travel 13,998 light years and stop, in 19 years of our time, if can protect against proton energies equal to the LHC.

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?