Heaven is a Planet 80 Times Bigger than Earth!

Heaven is a planet 80 times bigger than Earth! Or so the late Percy Collett revealed to the world. For years I’ve had a vague memory about a Missionary with a story about a trip to Heaven. Thanks to the wonders of Google I tracked it down – he visited Australia in 1989, on a speaking tour of various Pentecostal Churches. One of which was near my home town and I had managed to catch a radio advert for, thus the memory.

Thanks to his faithful disciples’ transcripts, and notes taken down by sceptical investigators, I gather Dr. Percy told a lurid tale of being carried to Heaven, which is 3 trillion miles away (half a light-year), in just six hours by an Angel, dipping past the Sun and planets on the way. He saw the New Earth, which is being constructed near Heaven, then Heaven itself, which is 2 million miles around. Immense buildings form God’s City, with the Giant Gold Cube City from the Apocalypse included.

Heaven as a Supra-Planet
Heaven is a Supra-Planet?

Such visions are nothing new and Dr. Collett’s visions don’t add much to the canon. The pseudonymous “Enoch” started the Judeo-Christian craze for big visionary journeys, but the Akkadians and Sumerians had their own versions, predating the current crop by a millennium or two. Updated to a post-Copernican Universe, but the message isn’t new or startling. Jesus is still coming back “some time soon” so you’d better be good, for goodness’ sake…

The physics of Heaven is a bit more interesting. A solid planet can’t be 80 times bigger than Earth, as its gravity compresses its atoms into higher and higher densities past a certain mass. At most it would be 3-4 times Earth size. Even made of the lightest element, hydrogen, means planets max-out at just over Jupiter’s size for pure hydrogen planets – thus at most about 15 times as big as Earth. To be 80 times Earth’s size, the planet must be a “Super-mundane” planet – an artificial shell world around a natural object within. To be 80 times bigger than Earth, then by Newton’s gravitational equations, that means it masses (80)^2= 6,400 times Earth’s mass to give Earth gravity on the surface. If we assume a negligible Shell mass, then that’s a 20 Jupiter mass central object – coincidentally (?) a brown dwarf object might lurk in the Oort Cloud at roughly 3 trillion miles with about that mass. Whitmire & Matese, within the constraints computed by Lorenzo Iorio, would put a Super-Jovian out there.

So is Heaven really a vast artificial planet? Once upon a time, it was a solid or aethereal shell directly above our heads and we were like deep-sea fish on this heavier, grosser world. Once the crystal or aethereal spheres were shattered in the 16th & 17th Centuries, Heaven has been looking for a new locale. More modern updates have pushed it into Hyperspace, or totally other space-times or Eternities, but maybe it conceptually lurks just beyond our present day reach, and always will. Alternatively, the Mystics, like Jakob Boehme, place it “next door” to our everyday world, accessible by all who are ready to see it.

Dyson Shells and the Future… Part 2

A comment on Transterrestrial Musings suggested I might be against space development. A quick browse through my earlier blog-posts would quickly correct such a misapprehension. What I was arguing was the race to bust up planets to make cybernetic “Islands of the Lotus-Eaters” might be as much a trap and a dead-end as the Luddite call to “return to the Earth” and thus effectively go extinct.

Spreading into the Cosmos is non-optional for Humanity – Humanity 1.0 or our future upgrades, whatever their architecture. But disassembling the planets isn’t needed – at least, not yet. Take Dvorsky’s “Dyson Shell” plan. For many reasons a Dyson Shell is unlikely as a habitat and Dyson (like Stapledon before him) meant a Cloud or Swarm of habitats to increase habitat size for Life. However a Dyson Shell isn’t non-sensical if we want something else – energy collectors. Wrapping the Sun in “statites” – optically levitated structures – is perfectly reasonable and avoids the issues of the science-fictional Shell Habitat. Such structures, however, have a vulnerability, from in-falling meteoroids and comets. Stuff is always falling into the Sun, or coming very close.

The simplest mitigation effort would be making the individual collectors small enough to manoeuvre out of the way of the in-falling matter. Given sufficient detection time the collector in danger can shift sideways. But that does have one important implication – the collectors need sufficient space between them to do so. Thus coverage of the Sun is likely to be less than 100%, more like 50% or less. This constraint lets us then compute the rough mass of the Dyson Shell.

For a perfect absorber the ratio between the outward force of sunlight to the inward pull of gravity is 1:1300. That means energy collecting statites need to be very thin. Interestingly, because the sunlight and gravity decline in intensity via the inverse square law, except in very close proximity to the Sun, a statite able to levitate near the Earth will do so at any radial distance from the Sun. The exception is when close to the Sun and instead of being a “point source”, the Sun is a great big wall of light. For materials purposes we’ll assume an operating temperature of 1000 K and 50% conversion efficiency, which puts our collector at about 0.1 AU. Here the sunlight is 100 times stronger than at Earth’s orbit.

To levitate the collector’s areal mass density is 0.00077 kg/m2, which is very thin. A possible design is large reflectors concentrating onto an energy converter, though the exact details we’ll leave for future engineers. What that figure lets us do is estimate the total mass required. At 0.1 AU the total area is 2.81 x 1021 m2, meaning the total mass of our 50% coverage Dyson Shell is 1.08 x 1018 kg. About a quadrillion tonnes. Being so thin each collector can solar-sail its way inwards to its operating position around the Sun. It also means the fraction of Mercury mined, as Mercury masses 3.3 x 1023 kg, is very small.

To transfer the energy collected, solar pumped and energised lasers, presumably solid-state, will be used. With half coverage of the Sun and 50% conversion efficiency, the total energy supplied to the Solar System civilisation is a staggering ~1026 W. Essentially a million tonnes of energy per second is available.

So what do we do with it all? One possibility, which would go a long way towards making a Dyson Swarm, is transferring the power to distant objects and terraforming them. Not just the planets we know, but the potentially thousands of planet-sized objects between the stars, the Nomads of the Galaxy which were recently in the science news. Again, the difficulties of managing so many planetary sized laser streams is an exercise for future engineers, but even with 100,000 Earth-sized worlds illuminated (the Sun’s output is equivalent to 2.2 billion times what Earth receives) the total amount of sky covered by each stream is minute so streams crossing planets will be rare and predictable, thus can be mitigated. Engineered eclipses?

A final thought, for the Worriers, is that power transfer lasers, on planet scale, don’t need to be very intense. Eventually the Earth will need a planetary shell to modify the Sun’s natural input, as its luminosity increases during its Main Sequence climb, but that’s not needed for laser defense just yet. A question worth pondering is just how thick a shell is needed and how high it needs to be, as well as how strong. That’s for a future posting.

Repost: Round-Trip Fusion Rockets Two

A worthwhile predecessor to my present musings is the 1996 efforts by Kelly Starks & the gang at the Lunar Institute of Technology. As you’ll note the “updates” have lagged somewhat, but the Starship Design Study is well worth a look. They went into a lot of detail and their discussion of drive technology, life-support, the trade-off between prepacked supplies and CELSS, and similar minutiae is very handy, if dated slightly.

Some highlights…
Fuel/Sail Class Starships …explains the basics.
Explorer Class Starships …details the “small” design (25,000,000 tons!)
Mission Plan & Manifest for Explorer Class …breakdown of payload and mission plan. Lots of mining of Lithium-6 at destination for journey home.
Bussard Fusor Discussion …for a long time my only reference on Bussard fusor performance available online. Now Askmar.com is the place to go to.

Of course such gigantism is unlikely to ever be very practical. Real crewed starships need something better than mere fusion to get up to decent speeds. I’d bet on Hawking radiation powered Black Hole Starships and/or Reverse Baryogenesis Total Annihilation drives. The ultimate IMO would be the Neutrino Ramjet – basically it uses macroscopic sphaleron fields to annihilate scooped mass, producing a pure collimated neutrino beam. Such a vehicle would be able to launch from planets without melting down continents and have essentially unlimited range. The stuff dreams are made of…

Dyson Shells and the Future… Part I

George Dvorsky recently blogged on the easy way to boot-strap civilisation into Kardashev Type II status. For those new to the Kardashev Civilisation levels, Type I uses the energy received by its planet – humans use and control about 0.01% of that presently. Type II uses and controls the energy output equivalent to its star’s output, about 2.2 billion times more than Type I. A Type III uses the energy output of its Galaxy – roughly 30 billion times the previous level.

A recent paper by Japanese theorists proposed possible ways a Type III civilisation might tap the energy potential of a Galaxy’s Black Hole, essentially creating a tame Quasar. Collectors 1,000 light years from the Active Region would beam energy to any part of the Galaxy requiring it, even to near inter-Galactic distances. To get in the way of such a power-beam would probably rapidly reduce whole planets to rock vapour, so controlling distribution will be quite a challenge.

Similarly Dvorsky envisages surrounding the Sun in energy collectors built from materials extracted from the planet Mercury, even going so far as to disassemble the planet. Then the rest of the planets might follow, to be converted into “computronium”, which is essentially smart materials for building virtual environments for virtual life-forms to live in. Alternatively large real habitats might be constructed, though these rapidly run into materials strength issues as they grow in size.

Such wholesale consumption of star systems seems kind of short-sighted to me. Enthusiasts argue that because natural planets are essentially random arrangements of elements, crafted by simple “generator codes” then simulated planets made the same way will do just as well. Perhaps. But I find the prospect of ripping apart planets without first studying them in detail kind of artless. Regardless of how elaborate our simulations, the Universe is vastly more detailed and thus escapes the necessary simplifications of our copying/mimicking of its processes. What would we miss by artless consuming it all willy-nilly?

In the long-term I am not against converting the available inert matter into living material, biological or otherwise. To be against that is anti-Life and ultimately futile. But once we reach the post-biological stage must we then hasten our pace of consuming the cosmos? The available mass-energy is only being trickled out by the stars. At most they fuse and radiate away 0.9% of what’s available. There are many trillions of years of the Age of Stars before us, as Post-Biologicals once we have our First Singularity. Why trash the planets in a few centuries?

Super-Earths and Red-Dwarfs

Super Earth in GJ667 Trinary System
From Physics Today

The European Southern Observatory (ESO) has reported, after studying nearby red-dwarfs, that ~40% (range 28%-95%) have Super-Earth planets in their habitable zones, which is quite remarkable considering how small a red-dwarf’s habitable zone is (from 0.25 AU and smaller.) That means 80% of the stars in our Galaxy – at least our bit of it – have large planets in their habitable zones. By “Habitable Zone” the ESO researchers use the “Recent Venus-Early Mars” limits – in other words from an insolation of ~1.7 – 0.4 times Earth. For really “Earth-like” the Zone is much more restricted, from 1.1 – 0.9 Earth insolation. In that case the numbers crash to <10%, but the sample size is still pretty small, so more observations are needed.

The original ESO release is here: Many Billions of Rocky Planets in the Habitable Zones around Red Dwarfs in the Milky Way

The research is part of a series of papers publishing findings from the ESO’s HARPS instrument. The series is:

The HARPS search for southern extra-solar planets
In particular…
XXXI. The M-dwarf sample
XXXV.Super-Earths around the M-dwarf neighbors Gl 433 and Gl 667C

So the figures are 9 Super-Earths found around 102 Red-dwarfs via the radial velocity method, 2 of which are in the (broad) habitable zone. Once all the probabilities are worked out, plus the odds of transit, the ~41% of red-dwarfs figure is produced. How Earth-like are “Super-Earths?” is the relevant question. Being more massive, their gravity is higher, but not overly so. A 4.5 Earth mass super-Earth has 2 gee surface gravity, if it has Earth-like internal structure. If it’s an Ocean Planet – thus very Un-Earth-like – then the gravity is even lower, about 1.26 gee. The Broad Habitable Zone is from Venus-like (up until it lost its ocean c. 1 Gya) to Early Mars (when it still had an ocean – still a maybe.) Alternatively a Desert planet can remain stable to 1.77 Earth insolation, while a Hydrogen planet (with water oceans) can be stable to 0.01 or less.

A more meaningful way of understanding “habitable” is “biocompatible” – usually phrased as “can liquid water exist on its surface?” A broad range of environments are compatible with this, but most aren’t Earth-like. Truly Earth-like restricts the range to a much narrower span of orbit, reducing the Earth-like planets to a small fraction of the “Biocompatible Planets”. Instead of ~40%, the Earth-like worlds are more like ~4% or less.

By necessity a red-dwarf habitable zone planet has been significantly braked by tidal forces. If it’s too close and it formed with significant eccentricity, then the planet is probably inhospitable from the energy released by tidal braking. The usual end-state is for one face of the planet to always face its star, and the other to have eternal night. However neither Mercury or Venus ended up so, and exhibit other possible final states after significant tidal evolution. Mercury orbits 3 times for every 2 Solar days (its sidereal day is 2/3 its orbital period), while Venus rotates backwards compared to its orbital motion, which results in a Solar day that is significantly shorter than its sidereal day (116.7 vs 243.1 Earth days.) The actual final spin-state of a red-dwarf planet might be something like one of those, thus precluding the Endless Day/Endless Night dichotomy beloved by SF fans.