A critical look at the physics in 'The Wandering Earth' by Liu Cixin

 

As a young and as yet unpublishedscience fiction writer, I had many projects in my head. One of themwas to make the large moons of the Solar System habitable by movingthem to sunnier environments - roughly in Earth's orbit. (Or a littlefurther in. Here on Earth, we're lucky to have an atmosphere thatgives us 33 extra degrees of heat in the form of the greenhouseeffect. We might not be so lucky with another celestial body.)

Iconsidered the four large moons of Jupiter and Saturn's Titan (thehome world of Heinlein's obnoxious Puppet masters), but finallysettled on Triton, the large moon of Neptune. - ‘It can't be usedfor anything useful out there in the cold and dark, four and a halfbillion kilometres from the Sun,’ I thought. - If I transport itinto the warmth, the ice will thaw, and then conditions will belivable!

How would I manage to move it in away that would seem almost believable? I sat struggling with mypencil in one hand and my slide rule in the other. Occasionally Iwould put them down, crumple up another sheet of useless arithmeticand throw the crumpled paper emphatically against the wall. Remember,this was back in the day, before HP invented the calculator and Lotusinvented the spreadsheet: If you needed a calculation like that, youwere welcome to write your own FORTRAN programme. You also needed aten-tonne computer. I melted off more and more nuclear bombs to givethe poor moon speed and direction. I collected asteroids and hurledthem at the stubborn moon. I created a pressurised chamber withnuclear bombs deep in the ice, so that I could start a hydrogen bomb.All to no avail: Triton barely budged. It was too heavy; it wasn'tpossible to get anywhere near the energy I needed.

I resignedmyself to it. I realised that it would never be cost-effective tomove the big moons around. Much easier to improve the moons wherethey are by building heat shields around them (read ‘Farmer in theSky’ by Heinlein), or build artificial worlds that you can placewhere it suits you (read ‘The Saboteurs’ by me). Later, I took upthe hydrogen bomb again in another novel. But then it was just a tinyasteroid that had to be moved, not a huge globe. And I'm not at allsure that... Anyway.

But I was thinking far too small! Myinventions pale in comparison to Liu Cixin's idea: He moves our ownplanet to a star 4.3 light years away, and spends 2,500 years on thejourney.

Liu Cixin (or Cixin Liu: Liu is his surname) writesstories in a cosmic format. He conveys a sense of wonder and awe atthe marvellous universe that I find in very few other writers. Hegives the reader a sense of wonder that is completely lacking in theentertainment industry's stories about cowboys in space suits. Thesettings in his stories are grand yet (somewhat) realistic, anddescribed in such detail that the fantastic takes on an almosteveryday realistic feel. The ideas are almost always original. Hecomes up with so many strange ideas that I'm itching to check themout!

I have previously pointed out a number of gaping holes inclassic stories by (among others) Jules Verne and H G Wells. Afterhis global breakthrough, primarily thanks to ‘The Three-BodyProblem’, Liu has now also become as classic as it is possible tobecome in life (other members of this exclusive club: Heinlein,Vance, Anderson, Asimov, Clarke, Le Guin, Atwood). Then he has to putup with having his tricks scrutinised by an old physicist with adegree in classical mechanics. I don't have a slide rule anymore;instead I have a calculator and a spreadsheet! And to replace theone-volume work on ‘The Planets’, I have access to the entireomniscient web - it's just a matter of sorting out both the raw andthe rotten. I rub my hands together and get to work.

The storygoes like this: Using an enormous number of enormous rocket engines,fuelled by nuclear power, the Earth is lifted out of solar orbit andaccelerated towards Proxima Centauri. After 500 years, the planetreaches its maximum speed, which is 0.5 per cent of the speed oflight. It then continues at this speed for 1300 years, untildeceleration begins. That takes another 500 years. Then it is guidedinto its new orbit.

You need 6.08*1036 Nm of energyto pull off a stunt like this (assuming you achieve 100% efficiencyof the energy you release - otherwise you need more. The dieselcooker you're driving around in manages 35%).

Half, i.e.3.04*1036 Nm, is used during the first 500 years, whilethe Earth is accelerating. You need the other half to slow down.That's 6.08*1033 Nm per year - a figure that correspondsto more than half the energy that a medium-sized sun (e.g. our own)produces per year. And we won't be able to get hold of solar energyas we move further and further away, so unconventional solutions areneeded.

Fusion energy? It takes 65 times the volume of waterin the world's oceans to get all the hydrogen needed to power thereactors using hydrogen fusion. The solution is explained on one ofthe first pages: The reactor is fuelled by rock and gravel, which areused for ‘heavy element fusion’. This field is ‘too complex forme to explain to you at your age’, the young first-person narratoris told by the expert on page 4. And so you and I don't get theexplanation either! But we can think:

Gravel and stone areextracted from the earth's crust. It contains 49% oxygen and 28%silicon, so these are the heavy elements that are fused. Such afusion process is entirely possible - it happens in massive starsevery day; this is how stars produce even heavier elements. Thetemperature must first rise to at least 1.5 billion degrees, and thepressure must correspond to the pressure at the centre of Sirius. Andto get enough oxygen and silicon for acceleration and deceleration onthe journey to Centauri, you have to use up the entire Earth's crustand get a good deal more down in the mantle.

So it willprobably be quite difficult.

I have a suggestion that couldhave made the job much easier: The solar system consists of the Sun,Jupiter and some debris. Jupiter is made up of 90 per cent hydrogen.Hang a huge container in stationary orbit above Jupiter, drop down abig, long straw and pump up enough hydrogen for the whole trip. Youwon't need nearly as much mass as when you use water - you only need1/8 as much. Then you can leave the Himalayas, the Andes and the restof the Earth's crust alone!

And while we're on the subject ofJupiter: At the beginning of the trip, the clever engineers utilisethe slingshot effect by giving Earth an extra boost in gravity fromthe largest planet. This saves them several tonnes of grey rock. Theauthor paints a stunning picture of the view of Jupiter from theEarth's surface: "I realised that the red edge ... was an arc somassive that it stretched from one end of the horizon to the other.As it rose, the sky beneath it turned red, as if a velvet theatrecurtain was being draped over the rest of the universe." Alittle later: ‘As Jupiter continued this terrible ascent, itgradually filled half the sky.’ This is followed by an intensedescription of the storms on Jupiter, of the red spot, of the colourpattern. Like the protagonist, you can't help but be gripped.

Butthe protagonist should have been gripped in a very literal sense too!I haven't done my calculations on a Jupiter that fills ‘half thesky’. I've just let it fill an arc of ninety degrees across thesky, out of the 180 from horizon to horizon. In practice, it onlyfills a quarter of the sky, but that's certainly dramaticenough.

Jupiter has a mass of 1.9*1027 kg and aradius of 71,492 km. When it's right above your head and fills 90 ofthe 180 degrees, you can use geometry to work out that the distancefrom the surface of the Earth you're standing on to the centre ofJupiter is just over 100,000 km. Newton said that if you're an 80 kgperson, the monster up there is pulling on you with a forceequivalent to 101.4 kg. (https://en.wikipedia.org/wiki/Newton%...) This means that Jupiter produces a gravitational field that isalmost 30% stronger than the gravitational pull of Earth. In otherwords, you're hurtling upwards - perhaps straight towards the redstorm on the giant planet. In actual fact, Earth will have been tornto pieces long before you ended up in this predicament. It happenedwhen the planet came within the Roche radius(https://nn.wikipedia.org/wiki/Roche-grensa).

A little later, Liu lets Jupiter fillthe entire sky. In a literal sense, this would mean that the Earth isresting on the surface of Jupiter. Liu has let himself get carriedaway with his own story, but perhaps he should have realised thislast point without any calculations.

You'll recall that theEarth was to be accelerated for 500 years, up to a speed of 0.5 percent of the speed of light. Still with good support from Newton, Icalculate that the acceleration amounts to 9.52*10-6 m/s2(i.e. completely imperceptible compared to the Earth's gravity). In500 years, the Earth thus travels 0.125 light years.

The Earthis now travelling at its maximum speed, 0,5 percent of the speed oflight. This speed is maintained for 1300 years, which means ittravels 6.49 light years. Then it decelerates for another 500 years, travelling as far as it did during the acceleration - 0.125 lightyears. In total, the Earth has travelled 6.74 light years.Therefore, it will end up 2.44 light years beyond Proxima Centauri.It should have stopped in time.

A couple of other items shouldalso be mentioned: The Earth passes through the asteroid belt. Theclever engineers struggle bravely to avoid being hit by asteroidslarge and small, devising ways to get rid of the worst threats. In anemergency, they will use anti-matter bombs.

My childhood heroJack O'Hara, who operated for a couple of seasons in the cartoonsection of the evening paper, was a space pilot. He had a devicelooking much like a radio tube implanted in his brain, enabling himto think and react at lightning speed - which he had to do if he wasgoing to be able to navigate his spaceship between rocks across theasteroid belt.

But both Liu's engineers and Jack O'Hara couldhave relaxed: The asteroid belt - like the rest of space - consistslargely of empty space, and the risk of hitting a really big one isvanishingly small. And in that case, these engineers, with theirsuperior technology, will recognise the impending collision years inadvance and take action. In all likelihood, the worst that willhappen is that earthlings experience a sharp increase in shootingstars.

One more thing to pick on while I'm in the criticalcorner:

The reason why earthlings have to transport the entireEarth instead of sending humans and all their creatures off in anarmada of spaceships is that the nearest star with a habitable planetis 850 light years away. And as yet, spaceships cannot fly fasterthan 0.5 per cent of the speed of light, it says. It would take170,000 years to travel there, and it's not possible to maintain aclosed ecosystem for that long.

But there is nothing inphysics that prevents the spacecraft from continuing to acceleratewhen its speed reaches 0.5 per cent of the speed of light, providedit still has energy and reaction mass! And, of course, this will notbe a challenge to a civilisation that is capable of making antimatterbombs and conducting controlled fusion at a temperature of 1.5billion degrees. So using a tiny fraction of the energy required tomove Earth, humans could have sent an armada of starships towardsthis habitable planet. The ships could be accelerated at acomfortable 1 G, equal to Earth's gravity, until they were halfwaythere. Then they could slow down again. With this kind ofacceleration, the journey takes 854 years, measured in stationarytime. But thanks to the time dilation, only thirteen years pass onboard. Transporting Earth to Proxima Centauri in the way Liudescribes, on the other hand, takes 2,500 years. That's assuming theplanet and humans survive the Jupiter flyby.

Seen through thephysicist's stern eyes, this short novel has some flaws andshortcomings, to say the least. Viewed as a cosmic drama, however, itoffers breathless excitement from beginning to end. Cixin Liu is aprogenitor of such stories. And in several essays, articles andinterviews, he shows a breathless wonder, an insatiable curiosity,about the great mystery we call the universe. It is this wonder andcuriosity, coupled with imagination and a wealth of ideas, that makeshis stories vivid and worth reading.

I once said that JackVance could be forgiven some sloppy mistakes in physics because hewas Jack Vance. Liu Cixin can also be forgiven a lot - because he isLiu Cixin. Dream of having him as a guest of honour at a convention.