torsdag 22. mai 2025

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

 

As a young and as yet unpublished science fiction writer, I had many projects in my head. One of them was to make the large moons of the Solar System habitable by moving them to sunnier environments - roughly in Earth's orbit. (Or a little further in. Here on Earth, we're lucky to have an atmosphere that gives us 33 extra degrees of heat in the form of the greenhouse effect. We might not be so lucky with another celestial body.)

I considered the four large moons of Jupiter and Saturn's Titan (the home world of Heinlein's obnoxious Puppet masters), but finally settled on Triton, the large moon of Neptune. - ‘It can't be used for anything useful out there in the cold and dark, four and a half billion kilometres from the Sun,’ I thought. - If I transport it into the warmth, the ice will thaw, and then conditions will be livable!

How would I manage to move it in a way that would seem almost believable? I sat struggling with my pencil in one hand and my slide rule in the other. Occasionally I would put them down, crumple up another sheet of useless arithmetic and throw the crumpled paper emphatically against the wall. Remember, this was back in the day, before HP invented the calculator and Lotus invented the spreadsheet: If you needed a calculation like that, you were welcome to write your own FORTRAN programme. You also needed a ten-tonne computer. I melted off more and more nuclear bombs to give the poor moon speed and direction. I collected asteroids and hurled them at the stubborn moon. I created a pressurised chamber with nuclear 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't possible to get anywhere near the energy I needed.

I resigned myself to it. I realised that it would never be cost-effective to move the big moons around. Much easier to improve the moons where they are by building heat shields around them (read ‘Farmer in the Sky’ by Heinlein), or build artificial worlds that you can place where it suits you (read ‘The Saboteurs’ by me). Later, I took up the hydrogen bomb again in another novel. But then it was just a tiny asteroid that had to be moved, not a huge globe. And I'm not at all sure that... Anyway.

But I was thinking far too small! My inventions pale in comparison to Liu Cixin's idea: He moves our own planet to a star 4.3 light years away, and spends 2,500 years on the journey.

Liu Cixin (or Cixin Liu: Liu is his surname) writes stories in a cosmic format. He conveys a sense of wonder and awe at the marvellous universe that I find in very few other writers. He gives the reader a sense of wonder that is completely lacking in the entertainment industry's stories about cowboys in space suits. The settings in his stories are grand yet (somewhat) realistic, and described in such detail that the fantastic takes on an almost everyday realistic feel. The ideas are almost always original. He comes up with so many strange ideas that I'm itching to check them out!

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

The story goes like this: Using an enormous number of enormous rocket engines, fuelled by nuclear power, the Earth is lifted out of solar orbit and accelerated towards Proxima Centauri. After 500 years, the planet reaches its maximum speed, which is 0.5 per cent of the speed of light. It then continues at this speed for 1300 years, until deceleration begins. That takes another 500 years. Then it is guided into its new orbit.

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

Half, i.e. 3.04*1036 Nm, is used during the first 500 years, while the Earth is accelerating. You need the other half to slow down. That's 6.08*1033 Nm per year - a figure that corresponds to 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 energy as we move further and further away, so unconventional solutions are needed.

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

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

So it will probably be quite difficult.

I have a suggestion that could have 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 a big, long straw and pump up enough hydrogen for the whole trip. You won't need nearly as much mass as when you use water - you only need 1/8 as much. Then you can leave the Himalayas, the Andes and the rest of the Earth's crust alone!

And while we're on the subject of Jupiter: At the beginning of the trip, the clever engineers utilise the slingshot effect by giving Earth an extra boost in gravity from the largest planet. This saves them several tonnes of grey rock. The author paints a stunning picture of the view of Jupiter from the Earth's surface: "I realised that the red edge ... was an arc so massive 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 theatre curtain was being draped over the rest of the universe." A little later: ‘As Jupiter continued this terrible ascent, it gradually filled half the sky.’ This is followed by an intense description of the storms on Jupiter, of the red spot, of the colour pattern. Like the protagonist, you can't help but be gripped.

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

Jupiter has a mass of 1.9*1027 kg and a radius of 71,492 km. When it's right above your head and fills 90 of the 180 degrees, you can use geometry to work out that the distance from the surface of the Earth you're standing on to the centre of Jupiter is just over 100,000 km. Newton said that if you're an 80 kg person, the monster up there is pulling on you with a force equivalent to 101.4 kg. ( https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation ) This means that Jupiter produces a gravitational field that is almost 30% stronger than the gravitational pull of Earth. In other words, you're hurtling upwards - perhaps straight towards the red storm on the giant planet. In actual fact, Earth will have been torn to pieces long before you ended up in this predicament. It happened when the planet came within the Roche radius (https://nn.wikipedia.org/wiki/Roche-grensa).

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

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

The Earth is now travelling at its maximum speed, 0,5 percent of the speed of light. This speed is maintained for 1300 years, which means it travels 6.49 light years. Then it decelerates for another 500 years, travelling as far as it did during the acceleration - 0.125 light years. 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 should also be mentioned: The Earth passes through the asteroid belt. The clever engineers struggle bravely to avoid being hit by asteroids large and small, devising ways to get rid of the worst threats. In an emergency, they will use anti-matter bombs.

My childhood hero Jack O'Hara, who operated for a couple of seasons in the cartoon section of the evening paper, was a space pilot. He had a device looking much like a radio tube implanted in his brain, enabling him to think and react at lightning speed - which he had to do if he was going to be able to navigate his spaceship between rocks across the asteroid belt.

But both Liu's engineers and Jack O'Hara could have relaxed: The asteroid belt - like the rest of space - consists largely of empty space, and the risk of hitting a really big one is vanishingly small. And in that case, these engineers, with their superior technology, will recognise the impending collision years in advance and take action. In all likelihood, the worst that will happen is that earthlings experience a sharp increase in shooting stars.

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

The reason why earthlings have to transport the entire Earth instead of sending humans and all their creatures off in an armada of spaceships is that the nearest star with a habitable planet is 850 light years away. And as yet, spaceships cannot fly faster than 0.5 per cent of the speed of light, it says. It would take 170,000 years to travel there, and it's not possible to maintain a closed ecosystem for that long.

But there is nothing in physics that prevents the spacecraft from continuing to accelerate when its speed reaches 0.5 per cent of the speed of light, provided it still has energy and reaction mass! And, of course, this will not be a challenge to a civilisation that is capable of making antimatter bombs and conducting controlled fusion at a temperature of 1.5 billion degrees. So using a tiny fraction of the energy required to move Earth, humans could have sent an armada of starships towards this habitable planet. The ships could be accelerated at a comfortable 1 G, equal to Earth's gravity, until they were halfway there. Then they could slow down again. With this kind of acceleration, the journey takes 854 years, measured in stationary time. But thanks to the time dilation, only thirteen years pass on board. Transporting Earth to Proxima Centauri in the way Liu describes, on the other hand, takes 2,500 years. That's assuming the planet and humans survive the Jupiter flyby.

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

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

Ingen kommentarer:

Legg inn en kommentar