Surviving Doomsday

Red Giant Sun

How to Survive Doomsday

The online science magazine Nautilus recently published this piece, which is based on the work of Ken Caldeira and James Kasting (Caldeira, K. & Kasting, J.F. Nature 360, 721-723 (1992)), which predicted a biospheric doomsday some 500 million years from now, due to the decline in CO2 as the Sun inexorably brightens at 10% per aeon. The Nautilus author discusses some of the astroengineering options for moving the Earth outwards from the Sun – asteroid flybys, solar-sail gravity tractors. Alternatively there’s the (presently unproven) option of uploading into robotic/cyborg forms adapted to the heat.

In my view, the real problem is that the Earth isn’t reflective enough because it spins too quick. Based on advanced Global Circulation Models, the surprise result is that slow rotating “Water Worlds” can survive higher insolations (sunlight intensity) by reflecting more light/heat back into space. A thick, permanent cloud mass forms beneath the sub-solar point – the noon position – and this mass reflects so much light/heat that the planet retains its water up to more than twice the Earth’s present insolation. Could we slow the Earth sufficiently? A sol (the time from sunrise to sunrise) that’s more than 240 hours long seems to result in this cloud bank forming. Thus if the Earth were slower rotating, it might prove habitable for longer. At least in part. The equatorial zone could be too torrid for advanced plant life, but land plants aren’t the main source of oxygen for animal life, so this may not be as big an issue as imagined.

As our technology and biology become more interrelated we may find that uploading/cyborgization are quaint concepts from a bygone age. Techno-Adaptation, for all terrestrial life, may become the way the Biosphere adapts to the brightening Sun. Thus Life’s tenure is expanded all the way to the Red Giant stage, but what then?

Most popular discussions of the Sun’s Red Giant stage give the impression that it’s a sudden change in the Sun. Certainly all the TV depictions imply that (e.g. Star Trek & Doctor Who) but it’s actually a protracted process. When the Sun is about 10 billion years old it will leave the Main Sequence, when its core supply of hydrogen fuel is exhausted, and over the next ~2.2 billion years become a Red Giant. For the first billion years not much happens. The Sun is a bit brighter (rising slowly from 2.2 to 2.7 times the present day) and becomes a bit cooler and bigger (cooler stars are bigger for the same amount of light output.)

Two main sources of data inform my discussion of the Sun’s Red Giant phase. First is a classic paper by Boothroyd, Sackmann & Kraemer (1993) and a revision of that work by Schroeder & Smith (2008). There is some uncertainty as since both papers came out, there’s been some scholarly arguing over new data about the abundance of ‘metals’ in the Sun. Astrophysically speaking, metals are all the other elements other than hydrogen and helium. Just how much of those other elements is in a range between 1.5% and 2%, roughly speaking. What that difference means for the Red Giant Sun is, as yet, unclear.

BSK - 1993 - Table 2Main Points of Solar Evolution from BSK 1993

BSK - 1993 - Table 3Evolutionary Stages of the Sun from BSK 1993

Distant future of Sun and Earth - tableRevised version of the Stages from Schroeder & Smith 2008

The very pinnacle of the Red Giant process lasts about a million years and the Sun bloats to over 200 times its present size and is over 2,000 times brighter. While it’s bloating, the Sun is blowing itself away in an enhanced Solar-Wind, with ~1/3 of its mass blown into space by the end of the Red Giant phase. If nothing impeded them, the inner planets would expand in their orbits and escape the expanding Sun – except Mercury, though its orbit is sufficiently chaotic that it might no longer be there anyway. However there will be tidal drag – the tides raised in the Sun by the planets Venus and Earth will cause them to spiral into their fiery doom. All this happens in the last, crowded half million years of the 2.2 billion years of the Sun’s Red Giant “Life Change”.

Distant future of Sun and Earth - Fig2Note how the Sun doubles in size in about 1.5 million years. The doted line is Earth and its fatal plunge

And Life? Migration away from the Sun seems a sensible option, yet maybe there’s a way to tweak the Sun into behaving in a more Life Friendly way. We’ve discussed that here before.

Whatever Happened to Black Holes as Star-drives?

Black Hole Hawking Radiation Power & Thrust
Black Hole Hawking Radiation Power & Thrust

Back in 1979 Robert Freitas, in his massive now-classic study “Xenology” first discussed Black Holes and their Hawking radiation as a possible propulsion system for interstellar flight (section 17.3.5.) Since then the concept has remained relatively ignored, since black holes are hard to make and hard to handle. By the late 2000’s, as our confidence in the existence of Hawking radiation had grown, the idea was revisited by Louis Crane, with his colleague Shawn Westmoreland, in a 2009 preprint.

In the above Table I’ve set out black-holes of various masses and have computed their self-thrust, with results similar to Freitas’s. Since the holes mass millions of tonnes, any associated starship should likewise mass similar amounts, so the acceleration can be ~halved. The very smallest black holes might prove difficult to feed at the indicated rates, since they’re smaller than protons, so Crane & Westmoreland suggested using the black hole as a “battery” – a finite store of energy – and letting it push self and payload until just before its final explosive last few seconds. One problem is that the hole becomes very energetic indeed as it loses mass, so just when the appropriate time to EJECT is an interesting question. For every 10-fold decrease in mass, the self-acceleration increases 1000-fold, so a crewed starship would need either acceleration mitigation or would need to eject once the black-hole was under one million tonnes.

For some background, several good introductions to Hawking radiation exist – Andrew Hamilton’s and the Think Quest discussions are the ones I’ve found most helpful. And, of course, there’s the paper by Crane & Westmoreland.

Since then, however, further exploration of the concept has been pursued by Jeff Lee, under the resonant name Black Hole Kugelblitz – though with less than interstellar results: Acceleration of a Schwarzschild Kugelblitz Starship The main problem is that the known particle spectrum of the Standard Model of particle physics causes much lower purely energy outputs, producing mostly a spray of near useless short-lived particles. Worse, the gamma radiation also produced is near impossible to redirect and can only be partially absorbed by a huge hemisphere of titanium (a good gamma absorber), thus making a poor Photon Rocket, which uses just a fraction of its power to produce directional thrust.

In conclusion the concept needs considerable work before it can be considered an interstellar drive option. The radiation intensities that need to be handled boggle the mind. However coupling our particle theories to black holes is not without problems – quantum gravity may well alter the intensity once the hole is small enough and we have no clear idea of the fate of the multitudinous particles produced. Does a super dense ball of quagma result, “stuck” to the ball by gluons dragged out of the vacuum of space? The related idea, of quark matter, might present the option of embedding a Kugelblitz inside a quark nugget. A more developed understanding of the quantum chromodynamic (QCD) vacuum and quantum gravity needs developing.

For now, like the original Photon Rocket, this idea goes back on the shelf, until our physics catches up.

Journey to Planet 9: Part III

If Planet 9 is a mini Gas Giant, rather than an Ice Giant or Super Earth, then it’ll be similar to Jupiter and Saturn in size, even if it’s much lighter. Jupiter’s gravity compresses hydrogen into its dense metallic phase, thus causing that planet to be much smaller than it would be if it was just a gas ball.

With a mass of 10 Earths and a radius of 8, the ‘surface’ gravity will be just 10/64 times Earth’s, or about Lunar gravity. Because I’m assuming a silicate core of just 1 Earth mass, it means the heat-flow from radioactive decay is diluted by all that extra area to radiate it from. Instead of ~38 K effective temperature, for an Earth mass of silicate, it’ll be ~13 K, below the Triple point of hydrogen, which is 13.84 K at 0.0704 bar pressure. At the Triple point the gas, liquid and solid phases co-exist. Colder than that and only ice and gas co-exist. Light from the Sun will achieve an equilibrium temperature of 9 K, so there’s no warmth from that source. Only radioactivity and residual formation heat are likely to stir the atmosphere.

Could Planet 9 be a Hydrogen Ice Planet, wrapped in thick gaseous helium? No. Too hot, even at -260 K. It’s possible that hydrogen has condensed into ice clouds in the outer fringes, but lower down condensed oceans of hydrogen resting on compressed molecular hydrogen might be possible. Really depends on the efficiency with which heat is convected through the H2/He mix. The outer reaches, if hydrogen is confined to the depths, will be enriched in helium, which makes the task of atmosphere mining much easier.

Just how easy? Presently we have no data on its rotation rate. If it was rigidly solid, then the maximum spin rate is 10 hours – at that point its surface gravity would equal the centrifugal force created by its spin, thus it would fly apart. Long before it reached that point, because on planetary scales all matter behaves like a fluid object, it would distort into an oblate spheroid, which would decrease the effective gravity at the equator significantly.

OblateSpheroidhttps://commons.wikimedia.org/wiki/File:OblateSpheroid.PNG

The relationship between the spin and the flattening of the planet gets complicated because it depends heavily on how the mass of the planet is distributed – mostly in a dense core or spread evenly? Gas planets, because gases compress significantly as the pressure rises, are especially centrally condensed. For our hypothetical planet the flattening becomes significant even if the day is 20 hours, but not enough to disrupt the planet. Modelling the planet as a Maclaurin Spheroid, this would mean an ellipticity of 0.362, an eccentricity of 0.77, and a difference between the rotational and orbital speeds of just over 3 km/s. This would make the planet *incredibly* easy to mine via gas scoop.

But it would also mean aerobraking a madly careening e-sail flying at ~143 km/s would be significantly easier, due to the lower density gradient in the lower gravity atmosphere. The surface gravity is about 1/8th Earth, and 1/20th Jupiter, so even though it’s significantly colder – 10 times colder than Jupiter – the slower rate at which it gets denser with depth means more room to brake in.

Journey to Planet 9: Part II – Faster Trips

Worlds of IF 1962

Conventional propulsion, even using gas-core nuclear reactors to power a Dual-Stage 4-Grid ion drive, struggles to reach Planet 9 at 700 AU. What are the alternatives?

We can contemplate a fast flyby using either solar or electric sails that start from close to the Sun. The scientific return from such a flyby is debatable – New Horizons has returned a treasure trove of data from distant Pluto, but would take centuries to reach Planet 9 at “New Horizons” current speed of ~3 AU/year. Upping the speed to 30 AU/year means a much faster flyby. That might suffice, since Planet 9 is *much* bigger than Pluto.

What if we want to go into orbit? Many years ago Fritz Leiber wrote, in “The Snowbank Orbit”, of a rather desperate plan to slow down in the atmosphere of Uranus from a speed of 100 miles/second by solar-powered spacecraft with empty tanks. Leiber hand-waved the difficulty, with the ships experiencing a peak acceleration of almost 90 gee and hull temperatures over 900 K. The crew survived, barely, by use of some sort of force-field reinforcing in their spacesuit harnesses. The fastest re-entry ever endured by a probe was by “Galileo’s” descent probe, which entered the atmosphere of Jupiter at 48 km/s. But 30 AU/year is 143 km/s, which would sorely tax our ingenuity.

Of course until we know how big Planet 9 we can’t be too sure of how much atmosphere we have to work with. If Planet 9 is mostly hydrogen/helium around a small core, then it might have a very extended atmospheric envelope indeed. Many of the exoplanets seen in silhouette by the Kepler and K-2 missions have low masses and large radii, leading researchers to discuss the case for low-mass Gas Giants, rather than Ice Giants or Super Earths.

Mass-Radius Relationships for Very Low Mass Gaseous Planets

Such planets might have solid cores of a few Earth masses, but the majority of their mass in a puffy H2/He atmosphere. If the core masses 1 Earth mass and the envelope is 9 Earth masses, then it’s close to 8 Earth radii in size – for comparison, Jupiter’s average size (69,911 km) is only 11 Earth radii. Such a planet presents some interesting possibilities, which we’ll discuss in Part 3.

Journey to Planet 9

Planet-9-Art-NEWS-WEB

Power, Distance and Time are inextricably linked in rocketry. When leaving the Earth’s surface this is not so obvious, since all the sound and fury happens for a few minutes, and silence descends once the rocket enters orbit, free-falling indefinitely, at least until drag brings it back down. For slow journeys to the Moon, Near Earth Asteroids, Mars, Venus etc. the coasting Hohmann Transfer orbits and similar low-energy orbits, are all typically “sudden impulse” trajectories, where the engines fire for a few minutes to put a spacecraft on a months long trajectory.

For trips further afield – or faster journeys to the nearer planets – the acceleration time expands to a significant fraction of the total journey time. Ion-drives and solar-sails accelerate slowly for months on end, allowing missions like “Dawn” which has successfully orbited two Main Belt objects, Ceres and Vesta, all on one tank of propellant. Given more power an electrical propulsion system can propel vehicles to Mars in 2-3 months, Jupiter in a year and Saturn in under 2. Exactly how good the performance has to be is the subject of this post.

Firstly, an important concept is the Power-to-Mass ratio or specific power – units being kilowatts per kilogram (kW/kg). Any power source produces raw energy, which is then transformed into the work performed by the rocket jet. Between the two are several efficiency factors – the efficiency of converting raw heat into electricity, then electricity into jet-power, which includes the ionization efficiency, the nozzle efficiency, the magnetic field efficiency and so on. A solar array converts raw sunlight into electricity with an efficiency of between 20-25%, but advanced cells exist which might push this towards 40-50%.

Let’s assume a perfect power source and a perfect rocket engine. What’s the minimum performance required for a given mission? The basic minimum is:

Power/Mass is proportional to (S^2/T^3)

That is the Power-to-Mass ratio required is proportional to the displacement (distance) squared, and inversely proportional to the mission time cubed. For example, a 1 year mission to Jupiter requires 1,000 times the specific power of a 10 year mission.

The minimum acceleration case is when acceleration/deceleration is sustained over the whole mission time. When acceleration is constant, it means a maximum cruise speed (i.e. actual speed of vehicle) of 2 times the average speed (defined as total displacement divided by total mission time).

Another result, from a mathematical analysis I won’t go into here, is that the minimum specific power mission requires a cruise speed that is 1.5 times the average speed and an acceleration+deceleration time, t, that is 2/3 the total mission time T.

Remember that kinetic energy is 1/2.M.V^2, thus specific kinetic energy per unit mass is 1/2.V^2.

The power required – which is work done per unit time – is a trade off between acceleration time and mission time. Say the mission time is 10 years. If all the acceleration is done in 1 year, then the cruise speed required is 1/0.95 times the average speed, but power is proportional to the speed squared divided by the acceleration time: P = (1/2).V^2/t = (1/2).(1/0.95)^2/1 ~ 0.55, whereas in the case of constant acceleration, the average specific power is (1/2).(2)^2/10 = 0.2. For the case of minimum power it’s (1/2)*(3/2)^2/(2/3*10) = 0.16875 – just 84.375% the constant acceleration case and ~31% the 1 year thrust time.

So what does it take to get to Planet 9? If we use the distance of 700 AU to Planet 9, and a total trip time of 10 years, that means an average speed of 70 AU per year. To convert AU/yr to km/s, just multiply by 4.74 km/s, thus 331.8 km/s is needed. Cruise speed is then 497.7 km/s and the specific jet-power is 1.177 kW/kg, if we’re slowing down to go into orbit. Presently there are only conceptual designs for power sources that can achieve that sort of specific power. If we take 20 years to get there, the specific power is 0.147 kW/kg, which is a bit closer to possible.

Vapor Core Reactor Schematic

Space reactor designs typically boast a specific electrical power output of 50 W/kg to 100 W/kg. Gas-core nuclear reactors could go higher, putting out 2,000 – 500 W/kg, but our applied knowledge of gas-core reactors is limited. Designs exist, but no working prototypes have ever flown. In theory it would use uranium tetrafluoride (UF4) gas as the reacting core, which would run at ~4000 K or so and convert heat to electricity via a magnetohydrodynamic (MHD) generator. Huge radiators would be required and the overall efficiency of the power source would be ~22%. In fact there’s a theorem that any thermal power source in space has its highest specific power when the Carnot efficiency is just 25%, thanks to the need to minimise radiator area by maximising radiator temperature.

More exotic options would be the Fusion-Driven Rocket or a space-going stellarator or some such fusion reactor design with a high specific power. In that case it’d be operated more as a pure rocket than powering an electrical rocket. Of course there’s the old Orion option – the External Nuclear Pulse Rocket – but no one wants to put *potential* nuclear warheads into orbit, just yet.

Planet IX?

Planet-9-Art-NEWS-WEB

https://www.caltech.edu/news/caltech-researchers-find-evidence-real-ninth-planet-49523

Presently the details are sketchy. A Neptune-ish size orb out past Neptune – semi-major axis about x20 Neptune, perihelion about 200 AU, and a period of roughly 10,000 years. The discovery paper is here: EVIDENCE FOR A DISTANT GIANT PLANET IN THE SOLAR SYSTEM

What would it be like? Odds are, if it’s one of Uranus or Neptune’s kin, then it’s not a ‘Super-Earth’. Instead it’ll be whatever concoction they are – several theoretical options are available, one of which is that they formed from mostly carbon monoxide ice. The CO then reacted with primordial H2 to make H2O and CH4 – the observed ‘ices’ in both. This could explain their depleted D/H ratios as compared to their supposed cometary building blocks. Some planet formation simulations do throw a fifth ‘Gas Giant’ into the Outer Dark, so it’s a live option.

Alternatively, it is a Super-Earth. If it was formed further out than the other Terrestrials, then it might’ve retained its primordial H2/He atmosphere. Too much of that and there’s no chance of liquid water, but if the surface pressure is under ~200 bar, then the hydrogen greenhouse effect will allow *liquid* water. An Ocean Planet is a real possibility. Perhaps the name ‘Poseidon’ should be considered. The ocean would be Stygian in its darkness, so maybe ‘Tartarus’ would be more apt.

Happy Birthday, Roy Batty

from here http://au.ign.com/articles/2016/01/08/happy-birthday-roy-batty

[from here]

“Blade Runner” was Ridley Scott’s reworking of Phil Dick’s “Do Androids Dream of Electric Sheep”. The original tale, published in 1968, was set in the futuristic date of 1992. By 1981 this seemed much too close in time, so Scott pushed it back to 2019…

Now 2019 seems not so futuristic – though we might have working “Spinners” by then. Just no “Off-World Colonies” nor “Replicants”. Not sure that’s a bad thing.

Stuhlinger Mars Ship Paper

Disney’s 1957 TV program “Mars and Beyond” introduced the world to a spacecraft design like nothing ever before seen – the “Umbrella Ship”.

Disney Tomorrowland episode “Mars and Beyond”

Disney Mars Fleet - Nyrath Redux

The ion-drive Atomic Umbrella Spaceship, so called for obvious reasons. The umbrella is a vast radiator surface for dissipating the heat from the reactor at the end of the long boom.

Disney Mars Fleet - Ignition

The original source was this paper: ELECTRICAL PROPULSION SYSTEM FOR SPACE SHIPS WITH NUCLEAR POWER SOURCE by Ernst Stuhlinger.

Most of the details are available elsewhere, largely due to Ron Miller’s “Dream Machines” compendium of fictional spacecraft. From the paper itself we get the following data:

Stuhlinger Mars Ship Specs

The asterisk denotes quantities I’ve derived. The payload, which includes the landing vehicle and crew habitat, is 20.5% of the launch mass, which is quite impressive. However the acceleration is very low, albeit optimized for the trajectory chosen. These days we wouldn’t want a crewed vehicle spending weeks crawling through the Van Allen Belts, but back when Stuhlinger computed his trajectory and even when the design aired, the Belts were utterly unknown. Now we’d have to throw in a solar radiation “storm shelter” and I’d feel rather uncomfortable making astronauts spend two years soaking up cosmic-rays in interplanetary space. Even so, the elegance of the design, as compared with the gargantuan Von Braun “Der Mars Projekt” for example, is a testament to Stuhlinger’s advocacy of electric propulsion.