Interstellar Comparisons

By 2025 Elon Musk believes SpaceX can get us to Mars – a journey of about 500 million kilometres, needing a speed of over 100,000 km/h. By comparison travelling to the stars within a human lifetime via the known laws of physics requires energies millions of times more potent than that budget-price trip to Mars. In our energy hungry modern world the prospect seems fanciful, yet we are surrounded by energies and forces of comparable scale. By taming those forces we will be able to launch forth towards the stars, save our civilization and extend the reach of our biosphere.

How so? Consider the sunlight received every second by planet Earth, from the Sun. About 1.4 kilowatts of energy for every square metre directly facing the Sun – all 128 trillion of them – means a total power supply of 175,000 trillion watts (175 petawatts.) That’s 8,750 times more than the mere 20 terawatts human beings presently use. Earth itself receives a tiny fraction of the total available – the Sun radiates about 2.2 billion times more, a colossal 385 trillion trillion watts (385 yottawatts).

Just how much does a starship need?

Project Daedalus proposed a fusion propelled star-probe able to fly to nearby stars in 50 years. To do so it would fuse 50,000 tonnes of deuterium and helium-3, expelling them as a rocket exhaust with an effective jet speed of 10,000 km/s. A total useful energy of 2500 million trillion joules (2.5 zettajoules) – the actual fusion energy available in the fuel was about 10 times this, due to the inefficiency of the fusion rocket motor. However that gives us a useful benchmark. This is dwarfed by the energy from the Sun. A full Daedalus fuel-tank is equivalent to about 4 hours of Sunlight received by planet Earth.

Another design, the laser-sail, masses 2,500 metric tons and requires a laser power of 5 petawatts, which accelerates the laser-sail starship 1 gee for 190 days to achieve a cruise speed of half light-speed or 150,000 km/s. A laser-power equal to what Earth intercepts from the Sun, 175 petawatts, could launch ~67 laser-sail starships per year. Total energy required per sail is 8.24 yottajoules, equal to 5.45 days of Earth-sunlight.

What else could we do with power that can launch starships? Power on the scale of Worlds (i.e. 175 petawatts) allows the remaking of Worlds. Terraforming is the shaping of the dead worlds of the Solar System into more life-friendly environments. Mars, for example, is considered to be the most life-friendly nearby planet other than Earth, yet it lacks an oxygen atmosphere, a significant magnetic field, and is colder than Antarctica. To release Earth-levels of oxygen from its rocks, power an artificial magnetosphere to deflect away the potentially harmful solar-wind, add nitrogen to reduce the fire risk, and keep the planet warm, the energies required are similar to those required to launch starships.

Releasing oxygen from Martian rocks requires melting the rock, usually composed of about 30% oxygen, and breaking the chemical bonds. What results is a melt of mixed metals, like iron, and semi-metals, like silicon, and oxygen gas, plus hardy compounds like aluminum oxide. For every kilogram of oxygen released, about 30 megajoules of energy are needed. Earth-normal oxygen levels require a partial pressure of 20 kilopascals (20 kPa), which means a mass of 5.4 tons of oxygen for every square metre of Martian surface – 775 trillion tons in total. The total energy required is 10 yottajoules. Adding 80 kPa of nitrogen, like Earth’s atmosphere, requires mining the frozen nitrogen of Neptune’s moon Triton, doubling the total energy required. Pluto’s vast plains of convecting nitrogen ice is another possible source, though without the handy proximity of a big planet’s gravity well for getting a boost towards the Sun it might prove uneconomical in energy terms. Shipping it from Saturn’s moon, Titan, as Kim Stanley Robinson imagines in his “Mars Trilogy”, requires 8 times the energy of using Triton as a source, due Saturn’s less favourable gravity conditions. Warming Mars to Earth-like levels, via collecting more solar energy with a vast solar mirror array, means collecting and directing about 50 petawatts of solar energy (equal to about 10 laser-sail starships). Before we use that energy to gently warm Mars, it can be concentrated via a “lens” into a solar-torch able to burn oxygen out of Mars’s rocks. With 50 petawatts of useful energy the lens can liberate sufficient oxygen for breathing in a bit over 6 years.

The final task, creating an artificial magnetosphere, is puny by comparison. A superconducting magnetic loop, wrapped around the Martian equator, can be used, powered up to a magnetic field energy of ~620,000 trillion joules (620 petajoules), by about 12.4 seconds of energy from the solar-mirrors. This is sufficient to create a magnetosphere about 8 times the size of Mars, much like Earth’s.

Total one-time energy budget is 20 yottajoules – 8,000 “Daedalus” starprobes, or 243 laser-sail starships equivalent. The ongoing power-supply of 50 petawatts is enough to propel 10 laser-sail starships at a time.

To terraform the other suitable planets and moons of the Solar System requires similar energy and power levels. For example, if we used a solar-torch to break up the surface ice of Jupiter’s moon, Europa, into hydrogen and oxygen, then used it to ‘encourage’ the excess hydrogen to escape into space, the total energy would be about 8 yottajoules, surprisingly similar to what Mars requires. The nitrogen delivery cost is about 6 yottajoules, again similar to Mars. Ongoing energy supply would be 10 petawatts – two starships worth.

A less exotic location to terraform would be the Moon. One advantage, as well as proximity to Earth, is that it requires no extra input of energy from the Sun to stay warm. However, unlike Europa or Mars, water as well as atmosphere would need to be delivered, multiplying the energy required. If shallow seas are sufficient – an average of 100 metres of water over the whole surface – the energy to deliver ice and nitrogen from Triton, then make oxygen from lunar rocks, is 27 yottajoules.

The only solid planet with close to Earth gravity is Venus. To remake Venus is a vastly more challenging task, as it has three main features that make it un-Earthly: too much atmosphere, too much day-time and not enough water. Take away the atmosphere and the planet would cool rapidly, so while it is often likened to Hell, the comparison is temporary. The energy required to remove 1 kilogram from Venus to infinity is 53.7 megajoules. Venus has over a thousand tons of atmosphere for every square metre of surface – some 467,000 trillion tons of which is carbon dioxide. To remove it all requires 25,600 yottajoules, thus removal is far from being an economical option, even in a future age when yottajoule energy budgets are commonplace.

One option is to freeze the atmosphere by shading the planet totally. To do so would require placing a vast shade in an orbit between Venus and the Sun, about a million kilometres closer. In this position, the gravity of the Sun and Venus are balanced, thus allowing the shade to stay fixed in the sky of Venus. With a diameter about twice Venus’s 12,100 kilometres, the shade would allow Venus to cool down over a period of decades. Eventually the carbon dioxide would rain, then snow, covering the planet in dry-ice. Some form of insulation (foamed rock?) would then be spread over the carbon dioxide to keep it from bursting forth as gas again. Alternatively it might be pumped into natural cavities, once the sub-surface of Venus is better mapped. The energy cost of assembling such a vast shade, which would mass thousands of tonnes at least, would be far less than the cost of removing the carbon dioxide. So close to the Sun, the shade would intercept the equivalent of 8 times what Earth receives from the Sun – 1,400 petawatts in total, sufficient to propel 280 laser-sail starships, or power the terraforming of the other planets. Or both.

The next desirable for Venus is the addition of water. If 100 metres depth is required the total energy to ship it from Triton is 144 yottajoules. Using 50 petawatts of power, the time to export the water is about 122 years, with a 30 year travel time for ice falling Sunwards from Neptune. The total energy of creating an artificial magnetosphere similar in size to Earth’s would be 6 exajoules (6 million trillion joules) – a tiny fraction of the energy budget.

Further afield than the Inner System and the Outer Planets (including IX, X, XI…) is the Oort Cloud, a spherical swarm of comets thousand to ten thousand times the Earth-Sun distance. According to current planet formation theories there were once thousands of objects, ranging in size from Pluto to Earth’s Moon, which formed out of the primordial disk of gas and dust surrounding the infant Sun. Most coalesced via collisions to form the cores of the big planets, but a significant fraction were slung outwards by gravitational interactions with their bigger siblings, into orbits far from the Sun. One estimate by astronomer Louis Strigari and colleagues hints at 100,000 such objects for every star.

The technology to send a laser beam to a starship accelerating to half light-speed over thousands of Earth-Sun distances opens up that vast new territory we’re only just beginning to discover. A laser able to send 5 petawatts to a laser-sail at 1,000 times the Earth-Sun distance, would be able to warm a Pluto-sized planet to Earth-like temperatures at a distance of a light-year. Powering starships will thus anable the spread of the Earth’s biosphere to thousands of worlds which would otherwise remain lifeless. Life on Earth spread out in abundance, aeons ago, once it learnt the trick of harnessing the Sun’s energy via photosynthesis to make food from lifeless chemicals. Humankind can do the same, on a vastly greater scale – it’s the natural thing to do.

Planet Nine, Ten, Eleven…

new-planets

Recently the regular press has been abuzz with the possibility of more Planets than the putative ‘Planet Nine’ posited by Mike Brown & Konstantin Batygin.

Finding Planet Nine: a Monte Carlo approach

Ref: de la Fuente Marcos, C. & de la Fuente Marcos, R. 2016, Monthly Notices of the Royal Astronomical Society

Dynamical impact of the Planet Nine scenario: N-body experiments

Ref: de la Fuente Marcos, Carlos, de la Fuente Marcos, Raúl, & Aarseth, Sverre J. 2016, Monthly Notices of the Royal Astronomical Society

Commensurabilities between ETNOs: a Monte Carlo survey

Ref: de la Fuente Marcos, C. & de la Fuente Marcos, R. 2016, Monthly Notices of the Royal Astronomical Society

In the 3rd paper we find these interesting hints:

The average value of the barycentric semimajor axis of (90377) Sedna and 2007 TG422 is 504 au. On the other hand, the equivalent mean value for 2004 VN112, 2010 GB174 and 2013 RF98 is 332 au. These five objects are part of the set of six singled out by Batygin & Brown (2016). The associated period ratio for these two sets of ETNOs is 1.87. In the main asteroid belt, this ratio is obtained for objects trapped in the 5:3 mean motion resonance with Jupiter and those in the 3:1, that is one of the main resonances in the outer belt (Holman & Murray 1996). Making a dynamical analogy between the two situations and decomposing Eqn. 1 in two we have: (ap/504)3/2 = 5/3 and (332/ap)3/2 = 1/3. The average of the two values of ap is ~700 au which is the favoured value for the semimajor axis of Planet Nine in Batygin & Brown (2016). The 1.8 commensurability has a statistical significance of 239σ for heliocentric orbits, the 1.89 commensurability has 51σ for barycentric orbits (see Fig. 3). This is unlikely to be mere coincidence.

…thus the orbits of the Extreme Trans-Neptunian Objects (ETNOs) very strongly suggest they’re in commensurate orbits with Planet Nine. But what of the other ETNOs?

Another example of the potential implications of our findings arises when we focus on 2003 HB57, 2015 SO20, 2005 RH52, (445473) 2010 VZ98 and 2013 GP136, the first two could be in a 3:2 resonance with a hypothetical planet at a = 213 au, with the other three in a 5:3 resonance with the same planet. In this framework, the pair 2003 HB57 and 2015 SO20 would be in a 10:9 accidental resonance with the other three ETNOs. A ratio of periods ~1.1 is present in both the main asteroid belt and the trans-Neptunian belt.

The 1.1 commensurability has a statistical significance of 76σ for heliocentric orbits and 61σ for barycentric orbits (see Fig. 3). On the other hand, the 1.65 commensurability is present for both heliocentric (192σ) and barycentric (131σ) orbits; a similar analysis focusing on 2003 HB57, 2013 GP136, (82158) 2001 FP185 and 2002 GB32 is compatible with a hypothetical planet at a = 329 au considering resonances (3/1)(5/9)=5/3~1.66. With the currently available data, degenerate solutions are possible, but they still hint at a multiplanet scenario.

Thus by the same reasoning for Planet Nine at 700 AU, the data is hinting at two more worlds at 213 and 329 AU. What will they be like? Patryk Lykawka suggested back in 2008 that a Mars-to-Earth mass object (or objects) sculpted the inner Kuiper Belt – the suggested Planets 10 & 11 could well be such. Another study by Laskar et al posited a 0.15 Earth mass object caused Uranus to roll over in its orbit, so it’s another candidate.

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.