Blake’s 7 Rewatched… Time Distortion Factors and All That

Blakes 7 Logo by Xeno

“Blake’s 7″ was a British dystopian version of “Star Trek” that aired from 1978 to 1981, for four seasons, and ended in a fashion almost as controversial as the end of the original “Neon Genesis Evangelion” TV series. I won’t give away any spoilers as the series is up on “YouTube” and well worth watching. Or rewatching, as I am doing.

The setting is a Future where the ‘Federation’ has become a force against human freedom, some 800 years or so years from now. Roj Blake, the eponymous revolutionary, led the most visible campaign against the Federation some years before the first episode, “The Way Back”, but had been mentally reconditioned and his memories of being a leader had been suppressed. A new resistance/protest movement had recontacted him, hoping to revive his memories… with predictable results. In the first few episodes Blake collects his ‘seven’ – Kerr Avon, computer hacker; Vila Restal, a master thief; Jenna Stannis, a space smuggler/pirate; Oleg Gan, a murderer with an brain-implanted ‘Limiter'; Cally, a telepathic outcast; Zen, a talkative starship computer, and the starship itself, “The Liberator”.


In the first 2 episodes, Blake is sent on an eight month voyage to a prison planet, Cygnus Alpha. The prison ‘barge’ he is transported in is the “London”, which cruises at ‘Time Distort five” through ‘hyperspace’. TV planet names never seem to follow any logical system (real star names are seemingly random to the uninitiated anyway) so suggesting “Cygnus Alpha” is a planet of “Alpha Cygnus[Cygni]” is only a stab in the dark. Alpha Cygni, or Deneb, is a very large, bright star about ~800 parsecs away (2,600 light-years) which implies a cruise speed for the “London” of ~3,900 c. As 5^6 = 3,125, let’s assume that’s how Time Distort factors, as multipliers of lightspeed, are computed and see where that takes us. Thus ‘Cygnus Alpha’ is ~2,100 light-years away, which is within the current distance uncertainty.


The “Liberator” crew talk of ‘speed’ as “Standard speed” with some factor, typically “Standard by 6″ if they’re in a hurry(ish) and “Standard by 12″ (SB 12) when the pedal is to the floor. In Season 2 Episode 1, “Redemption”, the “Liberator” is reclaimed by its Makers, the System, in interceptors able to travel at SB 14.


In one episode, Season 2 Episode 8, “Hostage”, the “Libertor” is pursued by Federation Pursuit Ships, initially at TD 9, but are pushed to do Time Distort 10, at a pinch. They encircle the “Liberator” but the crew fight their way through and pull away at “Standard by 12″, which the Pursuit ship Mutoid crew report as “Time Distort 20″. Interestingly, using TD 20 as (20)^5 = 3,200,000 c = (12.14)^6, thus suggesting the relationship between “TD” and “SB”. Thus TD 10 is SB 6.8, and TD 9 is SB 6.24, which implies Blake’s usual cruising speed of SB 6 is not much slower than the Federation’s nominal top-speed.


In the climactic conclusion to Season 2, “Star One”, the crew have to fly out of the Milky Way to ‘Star One’, the heart of the Federations computer control and its source of power. Blake and crew quickly realise that Star One has been compromised by an extra-galactic enemy, from M31. One might think that the 2.55 million light-years to Andromeda’s Great Spiral Galaxy would be straightforward at Standard by 12, but intergalactic travel is said to take ‘a lifetime’. By the speeds we’ve computed above it’s about 43 years at TD 9, or ~55 years at SB 6. The “Liberator” can’t sustain SB 12 for significant periods of time, without spending days regenerating its powerbanks, suggesting why no one had ever attempted intergalactic travel. Having a ‘power convertor’ blow-out a million light-years from home is a good reason not to push the hyper-drives too hard.

The True Size of M31 in our Sky.
M31 as Big as we’d see it, if bright enough.

Resources of the Solar System: Beyond Our Inner System


Some of the major objects within 100 AU of the Sun are omitted from the above – four major moons of Jupiter, one of Saturn and one of Neptune – all of which are much larger than the “dwarf planets” highlighted above. Several major asteroid populations are subsumed into “the Asteroid Belt” and the “Kuiper Belt Objects”. Jupiter and Neptune have large populations of asteroids sharing their orbits in the leading and trailing Lagrange points, the so-called Trojans. Also the Centaurs range between Jupiter and the Kuiper Belt, grading into the so-called “Jupiter Family Comets”, some of which are sourced from the Kuiper Belt, Neptune Trojans & Centaurs, while the rest are from the Oort Cloud.

The Trans-Neptunian region, beyond the Kuiper Belt, is little known. Several largish objects are known in that region, like Sedna, and their dynamics suggests the existence of one or two Mars to Super-Earth sized planets just beyond them, at perhaps 200 to 250 AU. We’ve discussed such objects here before, so let’s move a bit further out, into the Inner and Outer Oort Cloud. We see comets come falling towards the Sun from somewhere this side of ~22,000 AU. Based on the best orbital data, the quasi-spherical Oort Cloud that the comets must fall from extends out to about ~2/3 of a light-year. Doesn’t sound like much when said like that, but that translates into 44,000 AU – forty-four thousand times the distance between the Earth and the Sun. Our “Inner System” – the spherical volume ringed by the Classical Kuiper Belt at ~44 AU radius – occupies just 1 billionth of the volume. How many comets might it have? How could we even know?

Actually we do have a pretty good idea. Firstly, the Oort Cloud comets give us some statistical meat to chew on, producing estimates between 100 billion and 10 trillion comets. An average comet is somewhere between 1-10 km across and at ~1,000 kg/m3 density, that’s a mass between several times the mass of Earth to several Jupiters. How did it get there? Currently the comets are believed to have been ejected mostly by Jupiter and Saturn as they changed orbits during the early days of the Solar System via interacting gravitationally with billions of “planetesimals”, the leftovers of planet formation which became the comets.

While a trillion comets seems an immense resource, they’re spread very thinly – that 44,000 AU radius volume means each comet has, on average, about ~400 cubic AU to itself. Even more widely spread will be the estimated ~1,000 or so Pluto-to-Earth-Moon-sized “planetary embryos” that different planet formation theorists have postulated. These too would’ve been flung from the Inner System by the migrating Gas Giants. At the upper end of the mass scale there might be Mars-to-Earth sized objects. If such objects have significant geophysical heat sources and captured a H2/He envelope from the proto-Sun’s Nebula, then they might retain sufficient heat to have liquid water oceans. Alternatively they might have water-ice crusts and buried oceans, if stripped of their proto-atmospheres.

Could a planet-sized world be cold enough for more exotic oceans, like hydrogen? I have discussed the possibility before, but hadn’t closely examined the requirements of such a state of affairs. Large masses of rock are “warm” compared to cold stuff like liquid hydrogen (~20.3 K), let alone frozen hydrogen (13.8 K) or even liquid helium (~5 K under pressure.) If we assume the usual heat-source suspects, the radioactive decay of Uranium, Thorium and Potassium-40, then planets with significant fractions of rock (which contains U, Th & K naturally) are unlikely to ever get cold enough. Earth, which is 2/3 rock, has an equilibrium temperature of 34.4 K – and no amount of pressure can keep hydrogen liquid at that temperature, as its critical point is 33 K at 13 bar. Outcroppings of colder rock might allow pools of the stuff, but never oceans. Even if Earth’s geothermal output came from just radioactive decay (rather than ~50%) and the heat of formation had dissipated, the equilibrium temperature is still 28.8 K.

If we reduce the rock fraction, then we might be able to get closer to liquid hydrogen conditions. Using the mass-radius relations for different materials, derived by Sara Seager and her team, I’ve computed the equilibrium temperature for different planets. Of course we might posit planets with NO silicates, but no such planet (dwarf or otherwise) is observed in our solar system, and even comets have some fraction of “grit”.

Here’s a summary table for different compositions – a “Mercury-like” planet that’s just 32.5% silicate (i.e. half Earth’s); a pure Silicate planet, and an icy planet that is only 22% silicate. Mass and Radius are in “Earths”, while ‘T(eq)’, is the Equilibrium Temperature in K.

Equilibrium Temperatures

A very Icy planet, as you can see, could easily support liquid hydrogen on the surface, as could the smaller Mercury and Silicate planets. Even an Earth composition would come close. But there’s a complication. Hydrogen is a greenhouse gas and significant amounts of it as gas will quickly raise the surface temperature, holding in the heat from the rocks. Depending on how much you have, it might be warm enough for nitrogen oceans (~63 K) or ammonia (196 K) or even liquid water (~273 K).

A Deeper Future View

UPDATE Centauri Dreams has published this essay here: A View of the Deepest Future

The long-term fate of Life in this Universe is rarely contemplated. A few landmark studies, by Freeman Dyson, then Fred Adams, Peter Bodenheimer & Greg Laughlin, have looked into Deepest Time, long after Matter itself fails and the Void becomes unstable. How far can biological Life extend into the Long Dark? A study by Robin Spivey extends Life’s tenure, in neutrino-annihilation warmed Ocean Planets, to 1025 years – and Beyond. That’s 100 times longer than the 1023 years we’ve reported here previously and some 1,000 trillion times longer than the time the Universe has presently existed. If the current Age of the Universe was a clock tick – a second -, then those 1025 years would be 20 million years.

Spivey discusses his new finding here: Planetary Heating by Neutrinos: Long-Term Habitats for Aquatic Life if Dark Energy Decays Favourably [Open Access article]
Outer-shell electrons of 56Fe (iron) inside the cores of Ocean-Planets become ‘catalyzers’ of Inverse Photo-Neutrino Process (IPP) reactions, annihilating neutrinos and creating a steady heat-flow sufficient to warm the planet at ~0.1 W/m2. This Figure illustrates the flow:

Neutrino-Heated Ocean Planet - Large

Perhaps coincidentally, the inexorable processing of stellar materials in Type Ia Supernovae leads to a chemical mixture which makes Earth-like planets. Each Type Ia Supernova masses about 1.4 Solar Masses, or about half a million Earths, with the ejecta debris being mostly iron, then oxygen and silicon. Earth-stuff. Thus the ‘ashes’ of stars can produce a multitude of Ocean Planets.

To quote Spivey:

Observations have determined that the ejecta of a typical SNIa are, by mass, 18% oxygen, 15% silicon, 13% iron, and 49% nickel (almost all in the unstable form 56Ni which decays radioactively to 56Fe), along with smaller amounts of carbon, calcium, sulphur and magnesium. Elements emerge from SNIa in strata, with the lightest occupying the outermost layers. This provides the oxygen-rich outermost shell with the best opportunities for reacting with hydrogen in the interstellar medium, resulting in the formation of water molecules. On cooling to temperatures found in deep space, ice XI is obtained, whose ferroelectric self-aggregation may be relevant to comet formation [38-40]. The bombardment of protoplanets with comets would be important to the formation of oceanic planets, deferring the delivery of water to their surfaces.

Notice that the iron component is 62% by mass, thus the very large core in the illustration. Quoting Spivey again:

Based on the composition of type Ia supernova ejecta, a hypothetical oceanic planet of one Earth-mass is projected to consist of a large iron core of radius ~4240 km surrounded by a silicate mantle of thickness ~1300 km through which heat would be transported by advection. External to this inner mantle would be an outer mantle of ice consisting of strongly convective ice VI and VII phases of combined depth ~320 km. A liquid ocean ~50 km in depth covered by a solid crust of ice Ih upwards of 50 m in thickness would overlie the hot ice mantles.

Spivey’s new paper focuses on how the supply of neutrinos can be maintained at the right density to keep planets warm for the maximum amount of time. He posits several, as yet, unobserved processes – the decay of dark energy into neutrinos in less than ~70 billion years and the accelerated decay of black holes, also preferably into neutrinos. Other researchers have posited the existence of ‘sterile’ neutrinos, which Spivey shows improves the characteristics of the neutrino halo surrounding a Galaxy cluster, enabling planets to be warmed in a life-friendly manner in a sphere of 400 thousand light-years radius.

The existence of Dark Matter itself has been called into question by physicists, such as Mordechai Milgrom, who think the evidence for invisible Dark Matter can be equally well explained by modifying Newtonian Gravity to have a minimum gravitational acceleration. This Modification of Newtonian Dynamics (MOND) theory neatly explains the structure of galaxies, but hasn’t been as successful on a cosmological scale. Intriguingly if Galactic haloes are made of sterile neutrinos, then MOND and Dark Matter physics are equivalent in outcomes: Reconciliation of MOND and Dark Matter theory with giant ‘Neutrino Stars’ forming around each large Galaxy. Spivey suggests that a key research priority is determining the properties of neutrinos, to confirm the IPP heating mechanism. Such neutrino studies are important for refining the Standard Model of particle physics – and possibly discovering new physics, such as the masses of the various neutrinos, something not predicted by the Standard Model.

Spivey’s most audacious suggestion is the strategy that Life should adopt in the next few aeons to extend its lifespan. Unfortunately for Life in this Galaxy, our local Group of Galaxies is insufficiently massive to form a large enough neutrino ‘star’ before Dark Energy spreads galaxies too far apart. To survive, Life in our Local Group needs to emigrate to the Virgo Super-Cluster. Although our Milky Way is heading towards Virgo at ~200 km/s, cosmic acceleration, from Dark Energy, is presently pushing us away from Virgo at ~1,000 km/s. Thus we need to launch towards Virgo faster than the Dark Energy pushing us away. Yet the reward is 10 trillion trillion years of Habitable planetary environments, which may well be worth intergalactic migration.

Spivey suggests using antimatter rockets to launch modest payloads. Essentially small Life-seeds, like those proposed by Michael Mautner to seed Life in our own Galaxy, but launched on intergalactic journeys of a hundred or more billennia. Whether the cosmic-ray flux between the Galaxies can be endured for geological epochs is presently unknown and while I wouldn’t rule it out, it seems unlikely at best. A good reference, available online, is still Martyn Fogg’s “The Feasibility of Intergalactic Colonisation and its Relevance to SETI”, which suggests how a mere 5 million year intergalactic voyage might be survived by a bio-nanotech seed-ship.

But we’ve discussed other options in these pages previously. In theory a tight white-dwarf/planet pair can be flung out of the Galactic Core at ~0.05c, which would mean a 2 billion year journey across every 100 million light-years. A white-dwarf habitable zone is good for 8 billion years or so, enough to cross ~400 million light-years. It’d be a ‘starship’ in truth on the Grandest Scale. Perhaps other Intelligences have begun their preparations earlier than us and we should look for very high-velocity stars leaving the Milky Way and Andromeda’s M31. Over the next aeon we might observe many, many stars flinging towards Virgo from the nearby Galactic Core black-holes.

The Verse as an Engineered System


Years ago, when the 1970s “Battlestar Galactica” was the pinnacle of TV Sci-Fi in a 10 year old’s imagination, I wondered at the nature of the 12 Colonies of Man, which all seemed to be in the same star system. The old BSG was a bit confused about “star systems” vs “galaxies” so much so that the interstellar nature of the Colonies and their systems had to wait for the 2004 reboot to be made explicit. Yet the idea stuck with me – could a system have 12 habitable planets? I knew about binary and trinary star systems as well as the possibility of Gas Giant moons being habitable (something I imagined as a child, only to have confirmed by the discovery of habitable zone Gas Giants over the last 19 years.)

Then along came “Firefly” and its Verse, which is in a multiple planet, multiple star, yet single system. Dozens of planets! Could that be possible?

Planet-formation Guru, Sean Raymond, has wondered the same thing and has now posted a series of blog-posts which have made the imagining more concretely physics based.

The discussion begins here: Build a better Solar System, a post in which Raymond ponders how our Solar System could be improved by rearranging the known bodies – he concludes we could have 7 habitable ‘planets’ though several would orbit a more Sunwards Jupiter.

Leaving our Solar System behind, he ponders the “Ultimate Solar System”, which squeezes the maximum number of planets into orbit around the best kind of star (an M0-M1 star at about 0.5 Solar Masses probably.)

Ultimate Solar System, Prelude: Building the ultimate Solar System

Ultimate Solar System, Part 1: Building the ultimate Solar System part 1: choosing the right star

As mentioned the right star is an M star, but not one that is too small, as smaller stars mean planets are subject to much higher tidal forces. For example, the strength of tides varies with the inverse cube power of the orbital radius, while the luminosity of stars varies with the 4th-3rd powers. For a 0.5 Solar mass star, the luminosity is about (0.5)^4 = 0.0625 times the Sun, so the habitable radius is at about 0.25 AU, but the tidal forces are ~(0.5)*(1/0.25)^4 times what Earth experiences from the Sun i.e. 32 times stronger. Meaning instead of half metre tides, the planet might get 16 metre tides, though it’d also be rotating slower due to more tidal-braking.

Ultimate Solar System, Part 2: Building the ultimate Solar System part 2: choosing the right planets

Naturally enough, since we’ve picked a long-living star, we want long-living planets – not too small, else they’ll lose their atmospheres. However, since we’re engineering things, selecting a low-EUV activity star will aid in keeping the atmosphere. Another concern is the inexorable decline in geological activity. Bigger planets last longer.

Ultimate Solar System, Part 3: Building the ultimate Solar System part 3: choosing the planets’ orbits

Raymond discusses habitable zone orbits and orbital stability – spaced properly and the system is stable against mutual perturbations for aeons, at least.

Ultimate Solar System, Part 4: Building the ultimate Solar System part 4: two ninja moves — moons and co-orbital planets

This is where the real innovation appears – firstly, twin planets – equal mass planets orbitting each other; then two pairs sharing an orbit 60 degrees apart. This allows 24 planets to be squeezed in, on six mutually stable orbits. Alternatively there could be four Gas Giants in 3/2 resonance orbits, each with five habitable moons, and each Gas Giant with two Trojan pairs in the L4/5 positions, thus 9 habitable planets per orbit for a total of 36.

Ultimate Solar System, Part 5: Building the ultimate Solar System part 5: putting the pieces together

Finally the Ultimate System is a Binary – one with the double Trojan Pairs in six orbits (24 total) and the other with Gas Giants and their retinues of Trojans and Moons – for a Grand Total of 60 habitable planets. The binary stars are at least 100 AU apart, to avoid exciting each other’s systems into too much Chaos. Of course we know of widely separated stellar systems with higher multiplicity. We could have two 100-AU apart binaries, themselves orbitting another binary at a distance of ~2,000 AU. Now that’d be a setting for some cool SF!

Lockstep Empire


Karl Schroeder’s imaginary “Lockstep” Civilization or Empire is a group of thousands of human-inhabited planets which periodically go into synchronous suspended animation for 30 years at a time, then revive for a month – a ratio of 360:1. This conserves resources and allows them to travel ‘quickly’ (from a subjective point-of-view) between worlds. Intriguing the planets are those possibly thousands which are sprinkled through the dark void between every star. The suggested number is ~hundreds of thousands of Pluto-to-Moon sized objects and thousands of Earth-sized objects for every star in the sky. A vast territory, all within a few light-years at most.

The Lockstep Empire is a reasonable solution to the problem of interstellar travel & communications – if we can’t develop warp-drive. It’s also a good exposition of the inter-stellar (“between the stars”) territory that civilizations could access and populate. Schroeder has rightly noted that many thousands of large objects probably exist between the stars, though maybe not so many Neptune to Jupiter sized ones, however, as WISE has demonstrated there seem to be fewer brown-dwarfs and super-Jovians Out There.

Here’s a short-story set in the Lockstep universe, from Tor: Jubilee, by Karl Schroeder

The kind of materials captured by the small denizens of inter-stellar space depends on how they formed. Two main options: via direct collapse out of protostellar nebulas or via scattering from forming planetary systems. In either scenario they might capture large amounts of the primordial nebula’s hydrogen/helium gas, along with ices, silicates and metals. One could have a large population of “micro-Neptunes” – Mars-to-Earth mass objects with gas-planet atmospheres. Internal geothermal heat will make it very hard for such objects to condense their helium atmospheres, but hydrogen might cool sufficiently to form oceans and ice-caps. Imagine such dark, eerie oceans of ultra-cold liquid, lit by stars twinkling through helium atmospheres…


Marshall Eubanks notes in the the comments:

In a short submission to Nature in 1999 (, David Stevenson pointed out that an Earth-like nomadic planet in deep space, with an Earth-like amount of radioactive heating, could have a thick hydrogen-helium atmosphere and a surface temperature high enough to support liquid water on the surface, even though there was no Sun and the planet would appear to have a temperature (as seen from the outside) of only 35 K. So, there might be “dark, eerie oceans” of regular old water on some dark Earths, oceans we might conceivably be able to sail without much protection, although we would need some sort of breathing apparatus.

Stevenson’s paper is available here, slightly longer than the “Nature” edit, on the author’s web-site: Interstellar Planets

Helium Planet?

Somewhere between 100-200 times Astronomical Units (AU) from the Sun, planets get COLD enough for hydrogen to begin condensing, as the surface temperature drops below the hydrogen critical point (~33.2 K, 13 atm) and then triple point (~20.6 K, 0.07 atm). Raw hydrogen is unlikely to be present without helium – both were ~99% of the mass of the Solar Nebula that the planets formed out of. Helium, in the form of its stable isotopes helium-4 and helium-3, doesn’t condense until much, much further from the Sun and inside the Galaxy might be too hot for it to condense at all.

The recent study, blogged here, which computed primordial H2/He atmospheres would resist being eroded from Super-Earths by their stars’ early high levels of soft x-rays (“XUV”), also computed significant H2/He atmospheres would be captured by planets from Mars-size and upwards. If such an object was driven out of the Inner System, or from near the Gas Giants, then it might’ve retained its primordial atmosphere and found orbital stability in the region beyond Neptune. Several such objects may exist, for there’s reason to think the Gas Giants formed from Mars-size “planetary embryos”, but such would be undetectable by astronomers due to their slow orbits and dimness… all, except the inner-most, which may explain the curious orbits of objects like Sedna and 2012 VP133, as reported recently:

Solar System’s edge redefined

Dwarf planet ‘Biden’ identified in an unlikely region of our solar system

Of course, being Crowlspace, our take is the implications of a planet with a condense hydrogen surface (oceans?) and an atmosphere of high-purity helium. Helium-3 is an advanced fusion fuel and, once we have reactors up to the task, highly desirable. With a solar abundance of 4E-4 (i.e. 1/2500) relative to Helium-4, that might sound a bit scarce, but it’s immensely more than what we can scrape together here on Earth. A “Super-Mars” (~0.5 Earth masses) with a primordial atmosphere might have captured anything from 4.7 bars to 772 bars of atmosphere according to this reference:

Origin and Loss of nebula-captured hydrogen envelopes from “sub”- to “super-Earths” in the habitable zone of Sun-like stars

Let’s assume a neat 100 bars. A 0.5 Earth-mass planet, of Earth composition, would have a radius of (0.5)^0.3 ~ 0.81 times Earth and thus a surface gravity of (0.5)^0.4 ~ 0.76 times Earth, with a column mass of ~1,350 tonnes, of which 75% is hydrogen. Thus 336.4 tonnes of helium for every square metre of planet and ~100 kg of that would be helium-3. Total supply would be ~3.8E+16 kg. Interestingly the primordial deuterium/hydrogen ratio is 1/40,000, meaning that the condensed hydrogen would supply 50 kg/square metre of deuterium. A stoichometric mixture of D/He3 for fusion would be 50/75 or 125 kg/square metre of planet – 4.2E+16 kg or 42 trillion tonnes. One could fuel up 840 million “Daedalus” class starships. For the same fuel mass, 50,000 tonnes per ship, one could send 50,000 tonnes of payload (a small space-colony) to the stars at 0.012 c and slow it down at the destination. With a mass allotment of ~50 tonnes per person, the total travelling population would be ~840 billion people…

Wonder Material, Part 3 – By Macron Beam to the Stars!

We’ve discussed the potential boost that quarter-wave sails made of Carbon Nano-Tubes (CNTs) might achieve from being pushed by the Sun. Dropping to 0.019 AU, the final velocity is 0.056c – dropping to 0.00465 AU (skimming the photosphere) would allow a speed of over 0.11c, but the material might not be up to the beating. Crewed vehicles would not endure the extreme acceleration – 84,000 gee at peak – so the speeds that might be achieved by solar-sailing star-travellers would be limited to 1,000 year flights to Alpha Centauri, with just 17 gee peak acceleration (as described in papers by Matloff).

Yet there is another option. Given a supply of small sails, carefully aimed or with some guidance, then why not use them as the momentum transfer system for a crewed starship? Greg Matloff explored the “macron beam” option in his discussion of non-nuclear starship propulsion in the early 1980s, but AFAIK didn’t suggest using mini-sails to accelerate larger starships. Jordin Kare proposed micro-sails pushed by laser to use as a momentum beam, but what I am suggesting is using very rugged solar-sails for boosting manned vehicles to higher speeds than their ‘natural’ acceleration limits would allow.

If CNT quarter-wave sails prove as agile as Christensen, Zubrin & Spieth have described, able to accelerate at 18 m/s2 at Earth’s orbit, thus having a thrust/mass ratio of ~3,000, then they could form the basis of a naturally energised “Sail-Beam” or “Macron Beam”. The most energy efficient ratio of macron-particle to space-vehicle velocity is 2:1, which allows a macron beam total mass of 1/2 the space-vehicle to be used. If the peak speed is limited to 0.056 c, then the most efficient starship speed is 0.028 c. But we can go faster if we have plenty of sails, approaching the macron beam speed asymptotically. In theory a Macron Beam of mini-sails could push an Icarus Probe, with a payload of 150 tonnes, to the preferred mission speed of ~0.045 c.


I’ve derived a proof of the most efficient ratio, using an equation originally derived by Matloff – the proof is available here: Maximum Mass-Beam Efficiency

The basic equation is:

dV/V = 2.e.(Mp/Ms)/[1 + 2.e.(Mp/Ms)]

…where dV is the velocity change, V the macron beam speed, e the momentum transfer efficiency, Mp the total particle mass, and Ms the vehicle mass. If we rearrange it to find the ratio Mp/Ms, we get:

Mp/Ms = (dV/V)/[2.e.(1-dV/V)]

If we assume a perfect reflection (e = 1), then double the mass of the vehicle in Macron Beam mini-sails is needed to get to 0.045 c, with a Macron Beam speed of 0.056 c. As the mini-sail approaches the ship it’s zapped by a laser tuned to a frequency at which it absorbs strongly, quickly blasting it into plasma. Alternatively it is heated by smashing into the vehicle’s magnetic field at a high relative speed. Then the plasma is reflected from a magnetic mirror arrangement on the starship. Some will stream forward at the centre of the magnetic mirror, reducing the reflection efficiency slightly.

If the starship accelerates at 1 m/s2 then it’ll need a final mass-flow of ~0.03 kg/s to push a 200 tonne starship. This doesn’t seem onerous. To reach 0.045 c will need 13,500,000 seconds – just over 156 days. The real trick is keeping the sails on course over ~600 AU when the acceleration finishes.

Water-rich gem points to vast ‘oceans’ beneath the Earth

Water-rich gem points to vast ‘oceans’ beneath the Earth.

A fortuitous sample from the Transition Zone in the Mantle has demonstrated the long suspected presence of Ringwoodite and its water-rich properties, confirming the idea of buried oceans deep within the Earth. Crustal slabs are believed to carry water into the mantle as they subduct. Such water returns to the crust as water-enabled melts like the granite ‘balloons’ (batholiths) which float up through ‘solid’ rock and lift up the terrain. This new evidence confirms that there’s water down there already, possibly several oceans worth.

The “Nature” paper is: Hydrous mantle transition zone indicated by ringwoodite included within diamond

The SF implications of all that water have not remained unexplored – Stephen Baxter flooded the Earth with mantle water in his tale “Flood” (one-word titles are a favourite of Baxter’s). Of course, Flood-believers posit that at least some of the waters of the Noachic Flood came from the mantle and then returned, but – unlike SF-writers – they’re obliged to explain the mechanism aside from a wave of God’s magic-wand.

At least one Super-Earth around every M dwarf


Every red dwarf star has at least one planet

The news is that every M dwarf probably has at least 1 planet, if not more, which is good news when looking for cosmic real estate. The bad news – as blogged here previously – is that exoplanets bigger than Earth, or even Earth-sized and unlucky, are unable to rid themselves of the primordial H/He atmosphere they capture while forming. Too big means the planet becomes a mini-Neptune.

The relevant preprint is here: Bayesian search for low-mass planets around nearby M dwarfs: Estimates for occurrence rate based on global detectability statistics

One of the systems identified is a two-planet system around the star GJ 682. The planets are Super-Earths, though the uncertainty range goes as low as 2 Earth-masses for the habitable zone planet. Being radial velocity measurements, the odds are it’s a Sub-Neptune massing ~4 Earths. Intriguingly GJ 682 is only 16.6 ly away, so we should probably add the planet to the list of “Nearby Habitable Zone Planets” even if it is a sub-Neptune.

An atmosphere of H/He can be an asset for an anoxic (oxygen-less) biosphere for planets further out from their stars, though too much primordial atmosphere means a very large greenhouse effect trapping geothermal heat in. For example, Earth emits ~0.08 W per square metre, on average. Thus, with no stellar input, its equilibrium temperature is ~34.5 K. With an adiabatic atmosphere holding the heat in, and a photospheric temperature of 34.5 K, then the critical point of water (647.3 K) is exceeded at a surface pressure of ~5742 bar. A convenient measure of total H/He is “Earth Ocean Equivalents (Hydrogen)” (EOEH) – in Earth’s case there’s 1.5E+20 kg of hydrogen in our oceans, the equivalent of 29.4 bar surface pressure. Thus >200 EOEHs would mean no liquid water is possible. Bigger planets would have higher radiogenic and cosmogonic heat-fluxes, roughly increasing with the 1/2 root of the mass. A 10 Earth-mass planet would have a photospheric temperature of ~46 K, but it’d also have a higher gravity, but a higher surface area to spread a given mass of atmosphere over too. For Super-Earths the surface pressure produced by a given atmosphere mass at the surface of the solid core decreases slowly with planet mass (a ~-0.1 power, roughly). So >90 EOEHs would broil a 10 Earth-mass Super-Earth.

Sounds like a lot, but even 200 EOEHs is only 0.5% the mass of the Earth. Not a lot of hydrogen, by proportion, will mean death for an otherwise Earth-like planet.