Strudel asks

So after the recent White House response about Death Stars (well only one) we were talking in the office about how powerful it would need to be to destroy Jupiter (obviously just the power of one Death Star to destroy Earth, right?) and also, if a puny laser won’t work against Jupiter, what effect would deflecting our moon into Jupiter have?

Ah, an easy one.

On the one hand we have the Death Star. The Death Star blows up Alderaan without breaking a sweat, vaporising most of the planet’s mass and giving the rest a decent whack of kinetic energy. One of the weird things about impact physics is that it tends not to draw much distinction between something you just manage to disrupt and something you destroy so completely there’s little of the target body left, but Alderaan is an outcome very much towards the latter end of the scale. If we assume that Alderaan is analogous to one Earth (it certainly seems to be in the film) then we can say that the Death Star is more than capable of disrupting planets even larger than the Earth, and that one Earth is merely the lower bound of its destructive power.

On the other hand we have Jupiter. Jupiter is the big boy of the solar system; it might be slaved to the Sun but otherwise it runs the show, gravitationally speaking. The orbits of nearly every other body in the solar system are highly sensitive to their resonances with Jupiter, which has 318 times the mass of the Earth. Since gravity is the primary factor in determining how hard a particular body is to disrupt, this makes Jupiter the very definition of a hard target if you’re trying to blow the thing up.

You may recognise this graph because I’ve used it roughly half a dozen times before; it’s a computer model of how an object’s critical energy density (read: the amount of energy you have to hit it with to blow it up) varies with object size. Note that despite being composed of two vastly different materials – ice and basalt – the models are practically identical past object diameters greater than 1 kilometre, meaning that it doesn’t matter what your target body is made of. It can be a rocky terrestrial planet like the Earth/Alderaan, or it can be a big gas giant like Jupiter; all that matters is how much mass is contained within the target, and hence how strong it is gravitationally.

Now, let’s extrapolate that model out to Earth- and Jupiter-scale bodies.

Sorry for the rather rough Excel graph; if I had any other graphing software that wasn’t Origin I’d use that instead. This model has several caveats: in the absence of any other data I’ve used information for the 5 km/s impacts onto basalt, and while I do not think the overall density of the body will have an effect on how hard it is to disrupt the same can’t be said for impact velocity.  Jupiter in particular is at the bottom of an extremely deep gravity well, and so any body colliding with it is going to have quite a hefty impact speed – the Shoemaker-Levy comet fragments hit at velocities of around 60 km/s, for example. Faster, more energetic impacts are actually slightly less effective at disrupting a target than slower ones thanks to the way cracks propagate through a solid medium, so I doubt using data for 5 km/s basalt is going to be particularly accurate, but it should at least allow us to ballpark the critical energy densities of the Earth and Jupiter.

Some numbers. The critical energy density required to disrupt the Earth is 1.18 × 10⁸ J kg^-1. The critical energy density required to disrupt Jupiter is some 26 times larger at  3.06 × 10⁹ J kg^-1. Our two scenarios are a) firing the Moon at either body and trying to disrupt them that way, and b) hitting them with an unspecified number of Death Stars.

Scenario a) is easy¹ to figure out; you just calculate the impact energy of the Moon given its likely impact velocity and then divide it by the mass of the target.

This is what we’d have to do to destroy each body, then: fire the Moon at the Earth at a rather nippy 138 km/s,  and fire it at Jupiter at around four percent of the speed of light. These impact speeds are rather unlikely, to say the least; comets can hit the Earth at velocities of up to 70 km/s but those come all the way in from the Oort cloud and have a lot of time to pick up speed. Something as large as the Moon would get nowhere near those velocities; it would do serious damage to the Earth (and somewhat less to Jupiter) but each planet would eventually recover after a few million years or so.

Then you have the Death Star scenario. This is even easier; if we assume that one Death Star can destroy 2 Earths (as established in the opening paragraph) then it would take the power of 4,000 Death Stars to destroy Jupiter. As far has hard numbers go, one Death Star has a destructive power roughly equivalent to 300,000,000,000,000,000 one megaton nuclear weapons focused into a coherent beam.

Isn’t it great what we can achieve with science?

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The Curiosity rover landed on Mars a few weeks back. To do this it went through a complicated atmospheric entry procedure to slow down from orbital velocity before deploying a very large parachute capable of providing an effective drag force in the thin Martian atmosphere. Curiosity made it to the surface safely, and did so largely because it’s the beneficiary of about forty years of experience in successfully – and not so successfully – landing stuff on Mars. But probe landings were not always so refined.

The first probe to successfully reach the surface of another solar system body was Luna 2. Note that I say “successfully reach the surface of” and not “land on” because Luna 2 didn’t land on the Moon. Instead it was pretty much fired into it; when Luna 1 missed the Moon by 6000 km because of a mis-timed engine burn just hitting the target was seen as a success. There wasn’t a huge amount left of Luna 2 after the impact (or at least I assume so; it’s not like we can just send someone up there to check), but believe it or not the Soviets did actually intend for some of it to make it through intact. The rear-facing side of the probe contained several Soviet pennants as well as a small explosive charge designed to fire just before impact and slow the pennants down to the point where they wouldn’t be vaporized on contact with the lunar surface, so who knows? Maybe there’s a couple of burnt and twisted Soviet flags up there who have had to live for the last half century without the PR benefit of a full colour photo of Buzz Aldrin standing next to them.

That’s a hard landing. The space race demanded that one or the other of the competing nations eventually perfect a method of soft landing whereby the landing craft (and the occupants) made it through intact. The Americans plumped for the method documented on here last week, testing it extensively with their Surveyor series of lunar probes: a retrorocket fired to slow the Surveyor craft down from orbital velocity and the descent was handled automatically by attitude thrusters and doppler radar. It might sound sophisticated compared to the Soviet efforts, but it was far from perfect to begin with as two of the seven Surveyor spacecraft (unintentionally) crashed into the moon. Still, as a method of prototyping the lunar lander mechanism the Surveyor program was a great success and contributed immensely to all twelve Apollo astronauts that actually landed on the moon getting back alive.

NASA was taking things comparatively slow and steady compared to the Soviets (although they too fired a bunch of Ranger probes into the moon in 1964 and 1965 so it’s not like celestial target practice was a purely Russian conceit). After a frenetic series of failed attempts – likely because they were trying to beat the Surveyor program which successfully touched down later the same year and so weren’t fully testing everything – the Soviets got Luna 9 to make a soft landing on the Moon in 1966. This pioneered the landing bag method whereby a huge bag inflated just before impact to cushion the spacecraft and slow it down to the point where it could survive the landing, just like the airbag in a car. Sounds a bit crude, but more refined versions of the concept are used in pretty much every single probe that lands on Mars these days; the picture above is the Pathfinder landing bags being tested, although they’re much smaller than Luna’s as Pathfinder also had the benefit of a parachute to slow it down.

(The Soviets did eventually switch to the Surveyor method of attitude-adjusting engines controlling descent when they wanted to do some serious lunar exploration; Luna 17 disgorged the terrifying Lunokhod 1 rover upon landing, which made history as the first mobile robot explorer of another planet)

That’s how you land on the Moon. It’s both easier and harder than landing elsewhere because the lack of atmosphere preclude the use of parachutes/other atmospheric maneuvers while simultaneously allowing very efficient RCS systems to control descent. Landing on Mars is a pretty well-worn path thanks to the Viking and Pathfinder landers, the Spirit/Opportunity/Curiosity rovers and so on; thanks to the relatively forgiving environment they all use the same method of protecting the payload in an aeroshell, slowing descent using parachutes and then cushioning the landing with airbags. But what if we want to go somewhere a little more… exotic?

As far as I’m aware the only other solar system bodies we’ve managed to land probes on are Venus and Titan. I’m actually kind of surprised we went for Venus at all when there’s other much lower-hanging fruit to be found out there; Venus is one of the most hostile environments in the solar system with a surface pressure of close to 100 bar (that is, 100 Earth atmospheres) and a temperature of about 450 degrees Celsius. That the Soviets managed to get half a dozen probes down there at all was a massive achievement. That they actually got pictures back was nothing short of astonishing. Still, it’s not like the Soviets ever took half-measures when it came to space exploration; the Venera landers weighed several tons, which in probe terms means they were armoured like tanks. To get such a heavy load through the thick Venusian atmosphere at all they had to do this:

During descent, heat dissipation and deceleration were accomplished sequentially by protective hemispheric shells, three parachutes, a disk-shaped drag brake, and a compressible, metal, doughnut-shaped, landing cushion.

And even then the longest a Venera probe ever lasted on the surface of Venus was just short of two hours before it succumbed to the hellish environment and stopped transmitting. Now Venus is spoken with in the same hushed tones as Ravenholm: we don’t go there any more.

Then there’s Huygens, the only man-made probe that ever made a landing in the outer solar system. Compared to Venus, Titan is a paradise with a reasonably thick methane atmosphere you can deploy a parachute in, but which won’t crush the probe once it’s down on the surface. Huygens only transmitted for about two hours; however, it was a probe on a budget and that’s all it was designed to do. The only complication facing Huygens was the fact that it landed on a “shoreline” adjacent to a large dark area that may or may not have been a huge ocean of hydrocarbons. If it had been an ocean, and if Huygens had landed in it, it would have been an even shorter mission than intended; while the possibility that the probe might land in a liquid environment had been considered, it was only designed to transmit for a few minutes before sinking below the sub-zero waves.

We’re pretty good at landing stuff in oceans thanks to the space race, though, to the point where it’s actually the least of our worries as long as we can plan for it. In fact, as the Venera Venus landers show we can land probes pretty much anywhere with a solid surface as long as we know about the environment they’re going to be landing in. Again, this demonstrates the iterative nature of spaceflight; you need to make a lot of failed attempts in order to gather the data you need to make the successful one. Even smashing a probe into a planet a la Luna 2 yields some useful data in that it proves you can hit the target. Luna 9 just landing on the moon was of great interest because it proved the moon had a solid surface you could walk around on (it was thought that the dust on the lunar surface might be so deep it would effectively constitute quicksand). So really there are no true failures in probe spaceflight.

(Except for Beagle 2, where they don’t even know what happened to it.)

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And now, the thing that indirectly led to last week’s post on Race Into Space: the Kerbal Space Program.

KSP has been in development for a while now. I first played it this time last year, when it was a free alpha and had a grand total of two rocket engines, two couplers and one capsule. Even then its potential was clear, because even though that version was the most basic bare-bones version of the concept, the concept just happens to be making a pseudo-accurate simulation of building and launching your own space rockets. It’s fantastic. No, really.

These days you have to pay $15 for the latest alpha version (although the old one is still free). You totally should, though; a year of development has added two moons you can land on, an improved UI that indicates atmospheric pressure and your projected orbital — or escape – trajectory, and a whole host of new rocket parts including RCS thrusters, jet and ramjet engines, wings, control surfaces, landing struts, fuel lines… it’s a very long list and the game isn’t even close to being finished yet, with a slowly-expanding BARIS-style space centre that remains mostly non-functional at the moment while the developers nail down the sandbox element of the game.

In Kerbal Space Program you are the omnipotent designer, builder, launcher and pilot of the Kerbal race’s Heath Robinson-esque attempts to escape the gravity well of their home planet, Kerbin.  You start your spaceship design with a command capsule containing three suicidal Kerbal astronauts. As your first rocket you might decide to keep things simple by adding just a fuel tank and an engine of some kind underneath the capsule; the builder is fairly intuitive with the modular rocket parts automatically snapping to pre-determined connection points, so this wouldn’t take more than thirty seconds or so. Then you rush it out to the launch pad to see what happens.

Now, I can’t speak for what will happen to this simple rocket design, but I can tell you what would probably happen. You’d ignite the engines, increase the throttle, lift off – and then nosedive into the ground because you forgot to include any control surfaces or the automatic SAS stabilisation system to keep the rocket stable as it ascends through the atmosphere. Or if that doesn’t happen, you burn your engines too hard and they overheat and explode. Or if that doesn’t happen, you run out of fuel well before you get anywhere near orbit, the rocket starts dropping back towards Kerbin, and you suddenly realise that not only is there no way to separate the command capsule from the main body of the rocket, but that even if there was the three Kerbal astronauts would be doomed anyway because you didn’t include that most basic piece of spacecraft equipment: a parachute,

There’s a lot of ways you can fail in KSP, and seeing just what kind of unanticipated disaster will befall your spacecraft next is half of KSP’s fun, especially when the failures are so spectacular. It can honestly take a bit of work just get a spacecraft design off the launchpad when they have a penchant for falling to bits if not structured correctly. Rocket engines that run on liquid fuel need some way for the fuel to get to them, either directly or through a fuel crossfeed. Somebody new to the game might be tempted to attach some solid fuel rocket boosters onto their spaceship, but while these have the great virtue of being simple they also  have the slight drawback of essentially being an unstable lump of explosive material stuck to the side of your rocket. Even if you manage to get it off the ground you have a hell of a task ahead of you just controlling your heading, orientation and fuel burns to get into orbit. KSP is a game where succeeding in your chosen goal for the first time – suborbital, orbital, moon landing, whatever — does not come easily. However, behind the succession of comedy failures lurks a surprisingly deep iterative learning process which mimics the way real space programs are developed.

(Except those tend to have less dead astronauts, obviously.)

KSP is a game that – for now, at least – fosters experimentation. At the moment it consists of a basic sandbox mode where all rocket parts are free and you can have as many as you want on your spaceship, while pile-driving your three astronauts into the bottom of a burning crater carries no penalties besides having to take that particular rocket design back to the drawing board. You are free to try as many launches as you want in order to make it work. And slowly, gradually, you’ll start to figure out what you should and shouldn’t be doing. It becomes apparent that more engines do not necessarily equate to more thrust when your burn all six of them at once and your rocket only gets about a foot off the launch pad, and that experimenting with explosive decouplers that separate a rocket into discrete stages is far more efficient. How many stages do you want, though? How many boosters per stage? Do you really need that tri-coupler there? Fine-tuning this, as well as the fuel/payload ratio, is what occupies you during the first couple of dozen launches. Eventually, though, you’re going to refine your design to the point where it’s capable of escaping Kerbin’s gravity well, and it’s at this point that you encounter a whole new challenge: getting into orbit.

This is not as simple as you might think. Orbit is often described as “falling without hitting the ground” and hey, falling’s pretty easy, right? It’s just a matter of giving yourself enough sideways velocity so that you fall towards the planet you’re trying to orbit at the same rate as the ground falls away from you due to its curved surface. Surely, then, orbit must be a matter of going up high enough and then turning your spacecraft ninety degrees to the side and making a full burn of all remaining engines.

Uh, no. Spacecraft kinematics are actually really difficult to get your head around when you’re trying to manage throttle and keep the thing pointed in the right direction without exploding like a giant firework. I did manage to make a successful orbit using this very stupid method – even got the astronauts back to Kerbin safely afterwards – but it looked like this:

A highly, highly elliptical orbit with the periapsis about 100km above the surface of Kerbin and the apoapsis out beyond the orbit of the sodding moon. It took over a day to complete one orbit. My problem was I went up to a height I thought would be sufficient to fall from without hitting the ground and then made my sideways burn, but I forgot that a spaceship isn’t a car and that it still had a vertical velocity of over 2km s^-1. The sideways burn didn’t help either because it was still pointed slightly up, hence the ridiculous orbital altitude.

Clearly I have some way to go before I can even think about attempting a moon landing. Here, again, I have some inkling that it’ll be far trickier than I think because if you point a spaceship directly at the moon and blast away for 48 hours then by the time you get there the moon will have moved on in its own orbit and you’ll have missed. A successful moon landing requires you to get yourself into an orbit that crosses the moon’s orbital path, and then for the two orbiting bodies – spacecraft and moon – to occupy the same area of space at roughly the same time. The patched conics system that makes up KSP’s map makes this a little kinder on the prospective lunar explorer (although it has been done without by a crazy person, which incidentally demonstrates how much easier it is to get out of a moon’s gravity well compared to a planet’s gravity well) but it’s still a challenge that is going to result in lots of failures, and hence lots of hapless Kerbal astronauts floating helplessly around the solar system inside their steel coffins.

KSP is something that everyone should try, I think. That alpha I played last year is still free, after all, and you’ll get some idea of what it’s like to try to launch a rocket into orbit. The full (well, fullest) version adds spaceplanes to the mix, giving you a whole new type of craft to ram into the ground at 5000 km h^-1, and the next release seems to be adding in EVAs for the little Kerbals giving them a physical presence in the game beyond the three perpetually-terrified portraits in the lower right-hand corner of the screen. It says something about Kerbal Space Program that I’m currently trying to figure out some way to tie it into genuine science education; it’d be excellent for demonstrating why staged rockets are superior, along with a lot of other basic concepts of rocketry. It’s nowhere near a 100% accurate simulation, but then I don’t think I’d want it to be. KSP successfully walks the fine line between player enjoyment and technical verisimilitude without ever falling off of it, and that, I think, is its greatest accomplishment. Kerbal Space Program  makes rockets fun.

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