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SciFi Round One: Mission of Gravity

Mission of Gravity

Cover of the first print edition of Mission Of Gravity, 1954. The book was originally serialized in Astounding Science Fiction in 1953.
Picture from Doubleday Publishing, via Wikipedia.

Since we are playing Hal Clement’s game, we’ll start by dissecting the world-building behind one of his stories.

Mission of Gravity, its sequel Star Light, and the associated short stories Under and Lecture Demonstration were arguably Clement’s greatest works, and the world-building behind them was the subject of Whirligig World.  The stories are largely set on Mesklin, supposedly a 16 Jupiter-mass planet in orbit around one of the two stars of the 61 Cygni system.  While there were several claimed detections of such a planet between the 1940s and 1970s, we now know that there are no objects more massive than Jupiter around either star.  The initial claims were based on astrometry, measuring the positions of the 61 Cygni stars relative to each other, and the claimed detections were marginal and turned out to be slight systematic biases in the data.  The current limits are from high-precision radial velocity, which provides much better sensitivity except for objects on orbits oriented at almost exactly right angles to the line-of-sight to the stars.  Such orbits aren’t stable around 61 Cygni except very close to each star, because they would be out of the plane of the stars orbit around each other.  This gives us our first problem with Clement’s world-building:

1.   There is no such planet as Mesklin.

But since Clement wrote the original Mission of Gravity in 1952/1953, we should perhaps excuse this one.  At the time, the claimed detections of a similar body were in the literature.  He wrote Star Light and the shorts many years later, but ret-conning the whole setting to put it somewhere else would not have made that much sense.
In order to have a solid surface for the local intelligent species (and visiting humans) to stand on, Clement gave Mesklin a composition similar to what we now know to be the composition of Titan – dominated by ices, water and ammonia, which are rocks at a surface temperature of ~100 K (although the plot of Lecture Demonstration focuses on how water-ammonia mixtures can have a lower melting point than either of the pure chemicals).  Methane was a liquid, and drove a complicated meteorological cycle.  Presumably, there would be some amount of silica as well, but there were only traces of hydrogen and helium.

There are several problems with this, all from Mesklin’s shear mass.  It’s so heavy that it should have accreted huge quantities of hydrogen and helium while it was forming.  There is no method of planet formation that gives such a large object without lots of gas.  More directly, there simply wasn’t that much non-hydrogen non-helium material in the 61 Cygni system when it formed.  Between them, the two stars in the system contain only 12 Jupiter masses of such stuff, and only a small fraction of that amount would have remained outside the stars and been available for planet-building.

2.   A non-gas-giant planet the size of Mesklin cannot normally exist.

This one is much less excusable – Clement knew his astronomy well enough to understand the total amount of material available to build planets, and how little of it is potentially solid material.  And something with 16 times the mass of Jupiter would normally be considered a brown dwarf – it will be fusing deuterium into helium in its interior.

If we grant this impossible planet existing, then we have another problem.  It will be very very hot, because of gravitational energy released when it accreted.  Mesklin would be about the size of Jupiter – the size is determined primarily by electron degeneracy pressure in the interior, rather than by the chemical composition, much like for a white-dwarf star.  But it will have two hundred times the gravitational binding energy of Jupiter.  That is a lot of energy.  When it initially formed, it will be plasma and gas all the way through to the core (although electron degeneracy makes the definition of ‘plasma’ a little strange).  It will cool with time, but cooling models of brown dwarf stars say that even after ten billion years Mesklin would still have an effective temperature of at least 500 K after 10 billion years, depending on the opacity of the atmosphere, and 61 Cygni is only 6 billion years old.  No liquid methane, no solid ice, no liquid water, no surface to speak of – hence ‘effective’ temperature rather than ‘surface’ temperature.

3.   Mesklin cannot have cooled to the point that it would be solid.

This one again is not excusable, given the standards that Clement set himself.

A solid and cold object the size of Mesklin would have very high surface gravity – far too high for any human to endure.  Clement realized this, of course, and came up with a way to decrease the gravity over a portion of the surface.  He gave Mesklin a spin period of ~18 minutes, which gives a much lower gravity at the equator than at the poles – it is just below the spin rate at which material would fly off into space.  Mesklin would then reconfigure into a flattened shape, the exact contours of which depend on the equation of state of the interior – how density changes with pressure.  Clement confessed to an approximation here: he modeled Mesklin as an oblate spheroid, which is not correct (see his 2000 Addendum to Whirligig World), and specified a surface gravity of ~3 g at the equator.  The gravity at the poles worked out to 700 g in Clement’s approximation; values for different equations of state were all >200 g.

However, such a rapid spin rate cannot be maintained, or originate in the first place.  During planetary and stellar accretion, objects spin down to well below breakup speed.  Angular momentum is transferred from the material that accretes onto the star or planet to material that escapes, by gravitational tides.  For large objects, particularly stars, the object and the innermost part of the accretion disc are both ionized, and something called magnetorotational instability also transfers angular momentum outward, giving a relatively slow-spinning object.  Clement can be excused from not understanding this, since the theory for it has only been developed over the last twenty years or so.

But Mesklin would have some elongation.  This means that tidal interactions between it, the two stars in the system, and the moons that Clement specified Mesklin to have would act to rapidly de-spin it.  The masses of Mesklin’s moons were not specified, but they would have very rapidly evolved outward to very distant orbits or to escape Mesklin entirely.

4.   Mesklin cannot retain its rapid spin, or any satellites in close orbits.

While magnetorotational instability is a recent development, the theory of tidal damping isn’t.  So Clement missed this one as well.

Edit: Mesklin’s inner moon was supposed to have a semi-major axis of 90,000 miles.  But Mesklin’s Roche Limit would be ~300,000 miles.  Any satellites within that distance would be shredded to pieces by tides.  Clement should have caught that too.

There is one final error, which I noticed even the first time I read Mission of Gravity.  The plot of the book is that humans have landed a special research rocket at the north pole, but it broke and was unable to launch again (how to build a rocket able to accelerate at 700 g was never addressed, nor was it adequately explained what science they hoped to learn).  Since the book was written before computers became as ubiquitous and capable as they are now, the solution was to land humans at the equator, have them make contact with a group of the local intelligent species, and trade weather reports, satellite recon, and radio communications for retrieval of the rocket’s payload.  The trader captain they make contact with, Barlennan, is 18 inches long and 2 high and looks like an armor-plated centipede, but he’s shrewd at negotiating and goes along with the plan.  The adventure story of his crew’s travel across the planet, first accompanied by one of the humans and then with only radio links as they get to higher-gravity regions, is the bulk of the book and lets Clement show off his world.
But near the end of the book, they get to near the landing site and find their way blocked by a cliff one hundred meters high.  That’s the problem.  Under 700 gravities, the pressure on the ice underneath the cliff will be ~7 mega-Pascals for each meter of height.  The yield strength of ice at 90 K is about 70 mega-Pascals (it is weaker still at higher temperatures, which is why we don’t have 7 km high ice cliffs on Earth).  That means that Mesklin can’t have cliffs higher than ~10 m at its pole.  The material would promptly collapse (and be turned into steam from the energy release).  So those few chapters of the book don’t work; nor does much of the plot of Under , where Barlennan and several of his crew are washed into methane-eroded caves under the cliff-face.  Neither the cliff nor the caves could exist.

5.   There cannot be tall cliffs or caves at Mesklin’s pole.

In the 1950s, nobody had measured the yield strength of cryogenic ice, but scaling from values at warmer temperatures would say that the cliffs and caves were impossible.  Clement should probably have figured this one out as well.

There is an additional complication: at a temperature of ~90 K and a depth of 20-30 m under 700 gees, ice transitions from ice Ih or Ic to ice IX or ice II.  That increase in density and change in mechanical properties would do something odd to the geology.  This hasn’t been investigated in detail, because on real objects with much lower gravity, the phase transitions happen at much greater depths with much greater temperatures, giving a sub-surface liquid water layer and then a transition to Ice V, VI, or VII.
So, unfortunately, there are at least five ways that Mission of Gravity is impossible, and Clement should have seen four of them.  Perhaps he did, and ignored them for the sake of his story.  And least you think that I’m beating up Clement in particular: when we dissect other works, you’ll see that Clement’s errors are relatively subtle in comparison to most.  And, as the name implies, hard sci-fi is difficult to do correctly.  Clement played the game very very well, although he didn’t play it perfectly.

Are there any problems with Mission of Gravity that I’ve missed?  I haven’t touched on the problems of biology based on liquid methane as a solvent – biology able to produce plant fibers can can be woven into few-hundred-meter-long cords with twice the tensile strength of Kevlar.