The third and last of this short series on orbits was inspired by a Chinese science fiction film I have been watching on Netflix, together with an analysis I read of the science proposed. The film is The Wandering Earth, and is based on a novella by Liu Cixin, who is perhaps better known as the author of the splendid book The Three-Body Problem. Chinese science fiction is interesting to read – of course it is based on the same sorts of postulated scientific breakthroughs as European or American books, but the perception of recent history is very different, as is the kind of future society that we might expect to live in. There is an assumption that international cooperation will happen naturally in a crisis, led by Chinese technology and expertise. It’s a refreshing change (for a European) than the typical assumption many American authors make, that a world government would be bound to be based on American soil and largely staffed by US citizens!

Now, The Wandering Earth is set some forty years in the future, in which the sun is rapidly expanding, and humans are forced to try to migrate the entire planet Earth to a new home in the neighbouring star system, Alpha Centauri. The entire journey is expected to take something like 2500 years. It’s a bold twist on the idea of the generation ship, in which a group of a few hundred or thousand individuals live on board a large but conventional spaceship, expecting to pass through many generations before arriving at their destination. Here, the ship is the whole planet, and the hopeful survivors are numbered in billions. To achieve this, the Earth is equipped with a huge number of fusion-powered thrusters which slowly propel the planet away from our sun. The crisis of the film occurs as they attempt to use the gravity of the planet Jupiter as a slingshot to get more speed.

Now, the basic scenario of the sun expanding is not actually expected to occur for another five billion years or so, so a forty year time horizon is a bit crazy… but it does allow us to witness near-contemporary technology and human attitudes at work in a crisis, and I am enthusiastic about books set in this near time horizon! But could the thruster idea actually work? Could the Earth’s orbit be altered by such a means?

The perennial threat of a meteor or asteroid on collision course with Earth has triggered a few suggestions as to how we would shift the orbit of that incoming body. A large bomb, for example, or a long series of smaller ones, detonated on the surface of the meteor so as to deflect irts course. These methods only really work on something that is small to start with, and any explosion large enough to shift the Earth’s orbit is probably going to do something catastrophic to the land, sea, atmosphere, or all of them together! So we can forget that one, or similar (but less explosive) variations such as docking a spaceship and pushing the body to one side using the main engines.

You could imagine launching a long series of rockets all from (roughly) the same place, which would tend to push the Earth in the opposite direction. And they would also carry up material from the Earth in the form of body and fuel weight. If you wanted to get our Earth to the orbit of Mars doing this, you’d use up around 85% of the Earth’s mass to do so – in other words you would get there, but with only 15% of the planet left. Doesn’t sound appealing.

A more effective solution is an ion drive thruster (which I am keen on for other reasons as well, and which features in my own science fiction series). This, indeed, is the solution adopted in The Wandering Earth – large thruster drives are located on the Earth’s surface at major cities, while the population move underground to keep warm and avoid pollution. You keep more of the Earth’s native material this way – getting to Mars only uses up 13% of the Earth. Indeed, lots of the outdoor shots in the film show colossal excavation and earth-moving machinery tirelessly at work to feed the engines.

To avoid swallowing up the Earth as fuel, you have to use some external source. Two come to mind. The first is the light of the sun,. captured with some sort of mirror or solar sail. It’s slow, but you could achieve the desired effect in about a billion years. Not good enough for the film’s plot, but actually it would easily suffice for the real situation our remote descendants will need to tackle. The second is to exploit the huge amount of matter drifting around our solar system in the form of asteroids, and deflect these into new orbits which graze past our Earth. As they do this, the same slingshot effect that we normally use to accelerate small spacecraft can be exploited to move the Earth. Each interaction achieves a minuscule change, but a huge number of them eventually gets the job done. Of course, you’d have to have extreme trust in the orbital calculations, since the method relies totally on getting this long stream of asteroids as close as possible to the Earth without actually colliding with us! This, bizarre as it sounds, seems to be the most effective way to solve the problem. Each asteroid or comet can be used multiple times (until their own orbit degrades so much that they fall into the sun), so you just keep the asteroid train going round and round, pulling the Earth a little at a time. Again, it wouldn’t do for the immediate crisis presumed by the film, but it could work in the real-life long-term scenario.

So here is the conclusion of the series – we have migrated from the problems of getting into Earth orbit, to moving around between orbits, to the vastly bigger goal of moving the entire Earth in its own orbit around the sun. The common feature – you’d better do the calculations right in order to get where you want, and your intuition about how to go from A to B is not always right!

Last time I talked a bit about orbital paths for getting from the Earth to the Moon, and how there are several alternatives, each using different amounts of time and fuel. Today I want to talk a bit about orbits around Earth – the kind of trajectories used by a multitude of satellites today. This post was partly motivated by a conversation in the film Gravity – a film which I quite enjoyed for the human interactions, but was seriously disappointed by the cavalier attitude to orbital mechanics! There’s a point fairly late on where George Clooney’s character points out to Sandra Bullock’s character an orbital space station where she can find additional supplies, and directs her to fire her own capsule engines while keeping the other station central in her forward window.

It sounds good – and it would sort of work on Earth if you translate Sandra Bullock’s plight into moving cars around a car park – but there is absolutely no way that such a strategy would get her to her target up in orbit. Quite apart from the matter of getting the two space vehicles to meet up in space, there’s also the problem of matching speeds so that she could easily move across to the second capsule. Earth orbits simply don’t work like that – it is certainly possible (with sufficient fuel) to transition from one orbit to another, but getting the engine burn right is a difficult task, and one which needs to be carried out by computer program rather than optimistic guesswork.

The most energy-efficient way to transition from one circular orbit to another is by means of what is called a Hohmann transfer orbit – an elliptical path that touches both circles at a tangent. Other transfers can be used, and may well take less time to complete, but they will use more fuel. The simple picture here assumes that both orbits are in the same plane – in a more general case it will be necessary to shift orbital plane from the old angle to the new one. But that aside, just looking at the two objects shows that the engine burn required is not at all directed straight at the target – indeed in this case it is almost diametrically opposite. (Hohmann transfers are also used on a larger scale for trajectories between planets, and exactly the same principles apply).

Now, the great majority of satellites are in Low Earth Orbit (LEO) – not a single trajectory, but a zone of space from about 200 to 2000km altitude, or equivalently with an orbital period of under two hours. LEO is easy to get to, and hence economical of fuel, but especially at the lower end of the range, orbits will slowly decay because of the very tenuous atmosphere still present there – hence either the lifetime is limited, or occasional actions must be taken to lift the orbital height. A consequence of such a low orbit is that the spacecraft transits the sky quickly – or equivalently, any one part of Earth stays in view for only a short time. Satellites providing the various GPS systems orbit much higher, around 20-30000km (12-15 hours). And higher still, a little over 40000km, are the geostationary orbits, in which a satellite takes 24 hours to orbit the planet, and so appears to be stationary over a particular place.

What does this have to do with writing? Well, maneuvering around a planet in low orbit is a tricky thing to get right, and not something you want to leave to intuition. In Far from the Spaceports, Mitnash gets a shuttle up to his spaceship, The Harbour Porpoise, which the AI persona Slate has been keeping in LEO waiting a decision on where they were heading off for. They end up going off to the asteroid belt, but their first move would be to get out of LEO and leave Earth’s gravity well behind. That’s not something where Mitnash would glance out of the window, push a couple of buttons, and hope for the best – Slate, or possibly the ship’s own onboard controller, would do some real calculations before firing up the main engines. And then off they go…

Next time, a zany idea I just read about concerning moving the orbit of the Earth itself…

A few weeks ago now, an Israeli space probe called Beresheet (“Beginning”) reached the moon’s surface – sadly a system glitch in the last few seconds of approach meant that it crashed rather than soft-landed, but nevertheless it was a remarkable achievement. A particularly interesting feature of the trajectory that the ground crew chose is that it is quite unlike the method adopted by pretty much every probe before now, including the Apollo spacecraft.

The typical way to reach the moon has been in three phases – up to Earth orbit first, then a substantial burn of the main engines to escape Earth orbit and head towards the moon, then another burn to enter lunar orbit. The long leg of this is traversed with no engine activity at all, barring some trivial course corrections. Beresheet, however, adopted quite a different approach, as shown in the accompanying picture. A series of much smaller engine burns shifted the orbital path round Earth into ever-longer ellipses, until the path was close enough to the moon to be captured by the gravity there. The probe never attained escape velocity from Earth, and the trip took rather longer to arrive – a couple of months rather than a few days. However, it used less fuel and had the advantage that the successive changes in orbit allowed for lots of checking and fine-tuning.

Almost all probes to date, including Beresheet, have been driven by chemical rockets. They can exert huge acceleration at need, but have the disadvantage that the fuel tanks empty comparatively quickly. The times when the engines are used have to be rationed and carefully calculated, in order to have enough left over for critical events late on in the spacecraft’s journey. About the only exception to this is the Dawn probe, which visited the asteroid belt and returned remarkable new details about Vesta and Ceres. Dawn used an ion drive, which yields comparatively little acceleration but can be run continuously for weeks or months at a time. It’s a neat way to pile up substantial velocity without using much fuel at a time. It’s also the spaceship drive that I presuppose for Far from the Spaceports and successive books in that series – from a human-traveller point of view it has the huge advantage that you don’t have to put up with long periods of weightless travel, as well as considerably reducing travel times. The fact that the drive runs continually for all that time hugely offsets the fact that the actual propulsive power is much smaller.

That’s it for this week – next week there’ll be a few more thoughts on orbits. Meanwhile, here’s the last picture Beresheet took before crashing into the lunar surface…