We often forget what Doctors face day-to-day. We should show our support however we can.

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# Crowlspace

## Raw grief

## Deep Future Real Estate

## Extreme Relativistic Rocketry

## More MathJax Testing

## MathJax on Crowlspace

## Mission to Ceres

## Exotic Biochemistries

## Ceres Entices…

## Ceres: Its Origin and Predicted Bulk Chemical Composition

## O’Neill Cylinder from 1931

Nisi cognitio finitas, infinitum sit necesse est ignoratio

We often forget what Doctors face day-to-day. We should show our support however we can.

arXiv Preprint [1503.04376]: Dyson Spheres around White Dwarfs.

Ibrahim Semiz & Salim Ogur, a pair of researchers in Turkey, have posed the possibility of extraterrestrial civilizations building Dyson Spheres around white dwarfs. It’s an astroengineering option for the long-lived civilization that wants a fixer-upper or is looking to renovate their own system after the sun has gone Red Giant.

Consider a white dwarf that has chilled to 1/2500th of the Sun’s luminosity. It’s habitable zone is at 0.02 AU, but to sustain a clement environment, the Shell has to be a bit further out at 0.04 AU, at the desirable thermal equilibrium temperature of ~280 K. More or less. That’s a radius of 6 million kilometres and a surface gravity of 3.75 m/s^{2} for a 1 solar mass white-dwarf. The habitable surface is on the outside. The habitat’s total area would be ~887,000 Earths, so it’s a substantial piece of real estate. To sustain a breathable atmosphere at 1 bar pressure a gas mass of 1.2E+25 kg is required – the mass of Neptune, though in the right mix of gases. While oxygen and carbon are fairly easy to source, the nitrogen might be more difficult, thus a heliox mixture might be required. Some nitrogen is still needed to make protein, but most of the atmosphere would be helium for fire suppression and reduction of oxygen toxicity risk.

Due to the intense gravity of a 1 solar mass white-dwarf star, mass falling onto would release ~27 TJ/kg from gravitational energy alone. By trickling mass on the star, very carefully, its luminosity could be sustained at 0.0004 solar for aeons before it ran into the Chandrasekhar Limit at 1.44 solar masses. Exactly how close one could get to that Limit, without triggering a C/O fusion conflagration and a Type Ia Supernova, is an important bit of astrophysics to learn before building the Sphere.

Such an object would “glow” in the infrared at ~280 K, 9 times the physical size of the Sun, and have a mostly helium spectrum. It’d look like a very odd infrared protostar from afar, compact and opaque to other frequencies.

In Stephen Baxter’s “Xeelee” tales the early days of human starflight (c.3600 AD), before the Squeem Invasion, FTL travel and the Qax Occupation, starships used “GUT-drives”. This presumably uses “Grand Unification Theory” physics to ‘create’ energy from the void, which allows a starship drive to by-pass the need to carry it’s own kinetic energy in its fuel. Charles Sheffield did something similar in his “MacAndrews” yarns (“All the Colors of the Vacuum”) and Arthur C. Clarke dubbed it the “quantum ramjet” in his 1985 novel-length reboot of his novella “The Songs of Distant Earth”.

Granting this possibility, what does this enable a starship to do? First, we need to look at the limitations of a standard rocket.

In Newton’s Universe, energy is ‘massless’ and doesn’t add to the mass carried by a rocket. Thanks to Einstein that changes – the energy of the propellant has a mass too, as spelled out by that famous equation:

$$E=mc^2$$

For chemical propellants the energy comes from chemical potentials and is an almost immeasurably tiny fraction of their mass-energy. Even for nuclear fuels, like uranium or hydrogen, the fraction that can be converted into energy is less than 1%. Such rockets have particle speeds that max out at less than 12% of lightspeed – 36,000 km/s in everyday units. Once we start throwing antimatter into the propellant, then the fraction converted into energy goes up, all the way to 100%.

But… that means the fraction of reaction mass, propellant, that is just inert mass must go down, reaching zero at 100% conversion of mass into energy. The ‘particle velocity’ is lightspeed and a ‘perfect’ matter-antimatter starship is pushing itself with pure ‘light’ (uber energetic gamma-rays.)

For real rockets the particle velocity is always greater than the ‘effective exhaust velocity’ – the equivalent average velocity of the exhaust that is pushing the rocket forward. If a rocket energy converts mass into 100% energy perfectly, but 99% of that energy radiates away in all directions evenly, then the effective exhaust velocity is much less than lightspeed. Most matter-antimatter rockets are almost that ineffectual, with only the charged-pion fraction of the annihilation-reaction’s products producing useful thrust, and then with an efficiency of ~80% or so. Their effective exhaust velocity drops to ~0.33 c or so.

Friedwardt Winterberg has suggested that a gamma-ray laser than be created from a matter-antimatter reaction, with an almost perfect effective exhaust velocity of lightspeed. If so we then bump up against the ultimate limit – when the energy mass is the mass doing all the pushing. Being a rocket, the burn-out speed is limited by the Tsiolkovsky Equation:

$$V_f=V_e.ln\left(\frac {M_o}{M_i}\right)$$

However we have to understand, in Einstein’s Relativity, that we’re looking at the rocket’s accelerating reference frame. From the perspective of the wider Universe the rocket’s clocks are moving slower and slower as it approaches lightspeed, c. Thus, in the rocket frame, a constant acceleration is, in the Universe frame, declining as the rocket approaches c.

To convert from one frame to the other also requires a different measurement for speed. On board a rocket an integrating accelerometer adds up measured increments of acceleration per unit time and it’s perfectly fine in the rocket’s frame for such a device to meter a speed faster-than-light. However, in the Universe frame, the speed is always less than c. If we designate the ship’s self-measured speed as \(V’_f\) and the Universe measured version of the same, \(V_f\), then we get the following:

$$V’_f=V_e.ln\left(\frac {M_o}{M_i}\right)$$

[Note: the exhaust velocity, \(V_e\), is measured the same in both frames]

and…

$$V_f=V_e.\left(\frac {\left(\frac {M_o}{M_i}\right)^2-1}{\left(\frac {M_o}{M_i}\right)^2+1}\right)$$

To give the above equations some meaning, let’s throw some numbers in. For a mass-ratio, \(\left(\frac {M_o}{M_i}\right)\) of 10, exhaust velocity of c, the final velocities are \(V’_f\) = 2.3 c and \(V_f\) = 0.98 c. What that means for a rocket with a constant acceleration, in its reference frame, is that it starts with a thrust 10 times higher than what it finishes with. To slow down again, the mass-ratio must be squared – thus it becomes \(10^2=100\). Clearly the numbers rapidly go up as lightspeed is approached ever closer.

A related question is how this translates into time and distances. In Newtonian mechanics constant acceleration (g) over a given displacement (motion from A to B, denoted as S) is related to the total travel time as follows, assuming no periods of coasting at a constant speed, while starting and finishing at zero velocity:

$$S=\frac14 gt^2$$

this can be solved for time quite simply as:

$$t^2=\frac {4S}{g}$$

In the relativistic version of this equation we have to include the ‘time dimension’ of the displacement as well:

$$t^2=\frac {4S}{g}+\left(\frac {S}{c}\right)^2$$

This is from the reference frame of the wider Universe. From the rocket-frame, we’ll use the convention that the total time is \(\tau\), and we get the following:

$$\tau=\left(\frac {2c}{g}\right).arcosh\left(\frac {gS}{2c^2}+1\right)$$

where arcosh(…) is the so-called inverse hyperbolic cosine.

Converting between the two differing time-frames is the Lorentz-factor or gamma, which relates the two time-flows – primed because they’re not the total trip-times used in the equation above, but the ‘instantaneous’ flow of time in the two frames – like so:

$$\gamma=\left(\frac {t’}{\tau’}\right)=\left(\frac {1}{1-\left(\frac {V}{c}\right)^2}\right)$$

For a constant acceleration rocket, its \(gamma\) is related to displacement by:

$$\gamma=\left(\frac {gS}{2c^2}+1\right)$$

For very large \(\gamma\) factors, the rocket-frame total-time \(\tau\) simplifies to:

$$\tau\approx\left(\frac {2S}{c}\right).ln\left(2\gamma\right)$$

The relationship between the Lorentz factor and distance has the interesting approximation that \(\gamma\) increases by ~1 for every light-year travelled at 1 gee. To see the answer why lies in the factors involved – gee = 9.80665 m/s^{2}, light-year = (c) x 31,557,600 seconds (= 1 year), and c = 299,792,458 m/s. If we divide c by a year we get the ‘acceleration’ ~9.5 m/s^{2}, which is very close to 1 gee.

This also highlights the dilemma faced by travellers wanting to decrease their apparent travel time by using relativistic time-contraction – they have to accelerate at bone-crushing gee-levels to do so. For example, if we travel to Alpha Centauri at 1 gee the apparent travel-time in the rocket-frame is 3.5 years. Increasing that acceleration to a punishing 10 gee means a travel-time of 0.75 years, or 39 weeks. Pushing to 20 gee means a 23 week trip, while 50 gee gets it down to 11 weeks. Being crushed by 50 times your own body-weight works for ants, but causes bones to break and internal organs to tear loose in humans and is generally a health-hazard. Yet theoretically much higher accelerations can be endured by equalising the body’s internal environment with an incompressible external environment. Gas is too compressible – instead the body needs to be filled with liquid at high pressure, inside and out, “stiffening” it against its own weight.

Once that biomedical wonder is achieved – and it has been for axolotls bred in centrifuges – we run up against the propulsion issue. A perfect matter-antimatter rocket might achieve a 1 gee flight to Alpha Centauri starts with a mass-ratio of 41.

How does a GUT-drive change that picture? As the energy of the propellant is no longer coming from the propellant mass itself, the propellant can provide much more “specific impulse”, \(I_{sp}\), which can be greater than c. Specific Impulse is a rocketry concept – it’s the impulse (momentum x time) a unit mass of the propellant can produce. The units can be in seconds or in metres per second, depending on choice of conversion factors. For rockets carrying their own energy it’s equivalent to the effective exhaust velocity, but when the energy is piped in or ‘made fresh’ via GUT-physics, then the Specific Impulse can be significantly different. For example, if we expel the propellant carried at 0.995 c, relative to the rocket, then the Specific Impulse is ~10 c.

$$I_{sp}=\gamma_e.V_e=c.\sqrt{\gamma_e^2-1}$$

…where \(\gamma_e\) and \(V_e\) are the propellant gamma-factor and its effective exhaust velocity respectively.

This modifies the Rocket Equation to:

$$V’_f=I_{sp}.ln\left(\frac {M_o}{M_i}\right)$$

Remember this is in the rocket’s frame of reference, where the speed can be measured, by internal integrating accelerometers, as greater than c. Stationary observers will see neither the rocket or its exhaust exceeding the speed of light.

To see what this means for a high-gee flight to Alpha Centauri, we need a way of converting between the displacement and the ship’s self-measured speed. We already have that in the equation:

$$\tau=\left(\frac {2c}{g}\right).arcosh\left(\frac {gS}{2c^2}+1\right)$$

which becomes:

$$\frac {g\tau}{2c}=arcosh\left(\frac {gS}{2c^2}+1\right)$$

As \(V’_f=\left(\frac {g\tau}{2c}\right)\) and \(\left(\frac {gS}{2c^2}+1\right)=\gamma\), then we have

$$V’_f=I_{sp}.ln\left(\frac {M_o}{M_i}\right)=arcosh\left(\gamma\right)$$

For the 4.37 light year trip to Alpha Centauri at 50 gee and an I_{sp} of 10 c, then the mass-ratio is ~3. To travel the 2.5 million light years to Andromeda’s M31 Galaxy, the mass-ratio is just 42 for an I_{sp} of 10c.

Of course the trick is creating energy via GUT physics…

This one uses a Javascript to load MathJax direct. Seems easier than the plug-in.

In equation 1, we find the value of an

interesting integral:

$$\int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}$$

or this:

\(\int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}\)

or this:

$$\mathcal{\int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}}$$

I’ve just downloaded the MathJax Plugin for WordPress and this is a test equation:

\(E=mc^2\)So what do you think?

Ceres is in the news, thanks to the marvellous “Dawn” mission, which has seen a plucky little solar-powered ion-drive achieve orbit around two heavenly bodies on one tank of propellant. However the low power-to-mass ratio of the ion-drive means a multi-year journey, which is punishing for human crew and would-be colonists. A more reasonable design was proposed by James Longuski and his team at Purdue:

Abstract

A low-thrust trajectory design study is performed for a mission to send humans to Ceres and back. The flight times are constrained to 270 days for each leg, and a grid search is performed over propulsion system power, ranging from 6 to 14 MW, and departure V?V?, ranging from 0 to 3 km/s. A propulsion system specific mass of 5 kg/kW is assumed. Each mission delivers a 75 Mg payload to Ceres, not including propulsion system mass. An elliptical spiral method for transferring from low Earth orbit to an interplanetary trajectory is described and used for the mission design. A mission with a power of 11.7 MW and departure V?V? of 3 km/s is found to offer a minimum initial mass in low Earth orbit of 289 Mg. A preliminary supply mission delivering 80 Mg of supplies to Ceres is also designed with an initial mass in low Earth orbit of 127 Mg. Based on these results, it appears that a human mission to Ceres is not significantly more difficult than current plans to send humans to Mars.

I believe the basis for the above paper is the 2011 Student Project Vision here:

…which has this rather elaborate Crew Transfer Vehicle doing the heavy-lifting of carrying a crew to Ceres:

…which requires a bit of explanation:

Getting to Ceres is not easy. The major delta-vee budget is due to the plane change (Ceres is inclined to the ecliptic by 10.6 degrees) and the lack of high energy capture orbits, aerocapture or aerobraking at such a small object. Yet it’s not much more difficult than getting to Mars in some respects – if you include the landing delta-vee budget. The major enticement is the chance of abundant water ice and, perhaps, some sort of easy access to liquid water from cryovolcanic vents. “Dawn” has given us the mysterious White Spot, which is at least a kilometre above the crater floor it is in the middle of. Could it be a protusion of the water ice from below the asphalt black crust? Or something more exotic – an icy fumerole? There’s water vapour around Ceres, which hopefully “Dawn” will study in more detail.

The real crying need for such missions is multi-megawatt space-power supplies. Until that’s developed, such missions will remain paper studies.

Check out Paul Gilster’s discussion of azotosome-based life in the methane lakes of Titan

[Ref: “Membrane alternatives in worlds without oxygen: Creation of an azotosome” Science Advances Vol. 1, No. 1 (27 February 2015), e1400067.]

His essay prompted this quick discussion.

In 1961 Isaac Asimov, who was a research Chemist as well as uber-writing machine, wrote a highly influential essay (for “Fantasy & Science-Fiction” magazine) on exotic biochemistries. For those who want to read what the Good Doctor had to say it was reprinted in the old “Cosmic Search” newsletter and is available online here:

Not as We Know it – The Chemistry of Life

Asimov suggested the following options, in order of decreasing temperature:

There, then, is my list of life chemistries, spanning the temperature range from near red heat down to near absolute zero:

1. fluorosilicone in fluorosilicone

2. fluorocarbon in sulfur

3.*nucleic acid/protein (O) in water

4. nucleic acid/protein (N) in ammonia

5. lipid in methane

6. lipid in hydrogenOf this half dozen, the third only is life-as-we-know-it. Lest you miss it, I’ve marked it with an asterisk.

I originally read about Asimov’s typology in “Man and the Stars”, the collection of discussions on Extraterrestrial contact by the ASTRA group in Scotland published by Duncan Lunan.

A more recent discussion of exotic biochemistry, which inspired Stephen Baxter’s recent depiction of Titanian life in his novel “Ultima”, is found in William Bains’ essay here:

Many Chemistries Could Be Used

to Build Living Systems

[Ref: ASTROBIOLOGY Volume 4, Number 2, 2004 ]

In turn Bains’ work led to a collaboration with Sara Seager which provocatively argues for a hydrogen-based photosynthetic life:

Photosynthesis in Hydrogen-Dominated Atmospheres [Open Accesss]

[Ref: Life 2014, 4(4), 716-744; doi:10.3390/life4040716]

…the full implications of which are yet to be explored – the essay was published late last year. One irritating conclusion is that such H2 based biospheres might be very hard to detect remotely.

Another exotic option is the possibility of chlorinic photosynthesis, making chlorine based compounds instead of oxygen as a by-product:

The potential feasibility of chlorinic photosynthesis on exoplanets

[Ref: Astrobiology. 2010 Nov;10(9):953-63. doi: 10.1089/ast.2009.0364]

…though chlorine compounds do tend to be very opaque and may make the surface too dark to sustain life. In his “Manifold” trilogy, book 2 “Space”, Stephen Baxter imagined a world poisoned by the deliberate seeding of its oceans with chlorine producing organisms. If such a photosynthetic pathway is possible, then its spontaneous evolution in our own oceans is a possibility that we might’ve be lucky enough to avoid thus far. Other worlds, maybe not.

Dawn Mission: Multimedia >Ceres Awaits Dawn.

The Bright Spots of Ceres entice with their “sudden” appearance in sunlight and their delayed fade as they cross the terminator. Is it some bright projection of salty-ice, freshly exuding into a crater floor, or something more dramatic like a salt diapir that has pushed through from below?

Ceres: Its Origin and Predicted Bulk Chemical Composition.

Andrew Prentice’s Modern Laplacian Theory (MLT) has made definite predictions, with a reasonable success rate, for the bodies of the Solar System for the last ~40 years. The latest new body in view of our probes is Ceres, which the MLT predicts is a metal/silicate core wrapped in water ice and salt.

Note Prentice’s statement:

Perhaps Dawn will find the surface of Ceres to be very flat, though roughened through aeons of impacts, with fresh craters having bright floors and ejecta.

…in light of this enigma:

Buck Rogers adventure *in* Eros.

In its early days, the “Buck Rogers” comic-strip kept an eye on new developments in astronomy and tried for scientific plausibility based on the (admittedly shaky) facts of the day. The asteroid Eros was discovered in 1931 and appeared in a story that same year. A particularly prescient tale it featured a cylindrical habitat 20 miles long and 5 wide, with gravity produced by centrifugal force.