More MathJax Testing

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:

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

Mission to Ceres


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:


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:

Project Vision

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

Crew-Tranfer Vehicle for Ceres

…which requires a bit of explanation:

Crew-Tranfer Vehicle for Ceres 2

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.

Exotic Biochemistries


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 hydrogen

Of 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.

Ceres: Its Origin and Predicted Bulk Chemical Composition

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:


O’Neill Cylinder from 1931

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.