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.

The post In Praise Of: Kerbal Space Program. appeared first on The Scientific Gamer.

Rockets suck. This is a thing that we have established here; they’re terrifically awful ways of getting into space that are only used because nobody has really come up with anything better. There’s all sorts of ideas for wacky drive systems once your spacecraft is actually in space – ion drives, solar sails, Bussard ramjets – but these all sidestep the real problem facing future space travel, which is that you have to get out of the Earth’s gravity well first. This is not easy; even though the Earth is pretty small for a planet it’s still the heaviest of the four terrestrials and has what is to us a very hefty gravitational pull.

In order to exit Earth’s gravity well, an object being launched on a ballistic trajectory from the Earth’s surface must attain escape velocity. Escape velocity is calculated by

where G is the gravitational constant, M is the mass of the Earth and R is the radius of the Earth. For “ballistic” you can read “in freefall” – i.e. an object moving without any other forces acting on it. Rockets do have external forces acting on them thanks to their propulsion systems, so a rocket doesn’t necessarily have to reach escape velocity of 11.2 kilometres per second in order to escape the Earth’s gravity so long as it’s under constant power. However, the amount of energy it will have to expend will be the same as this hypothetical ballistic object, and that can be worked out by using the equation for kinetic energy.

where m is the mass of the spacecraft. With Earth’s escape velocity being 11.2 km s^-1, we can rearrange this equation to find out how much energy per kilo of mass a launch vehicle will need to have to escape Earth’s gravitational pull, and this turns out to be about 63 megajoules per kilogram. I always get a little lost when trying to visualise what a joule is in everyday terms, but Wikipedia tells me that 63 megajoules is roughly the amount of energy you’d release if you detonated fifteen kilograms of TNT. So for a crude method of visualising this, go and look at a picture of a rocket. Imagine a pile of TNT fifteen times as big. Blowing up this pile of TNT would release the same amount of energy as would be needed to get that rocket out of the Earth’s gravity well.

(One significant caveat here: rockets going into orbit don’t need to expend this much energy. They just need to go fast enough that they never hit the ground.)

This amount of energy is fixed. There is no way of getting around it; if you want to go into space, you have to expend at least 63 MJ per kilo of spacecraft mass and this energy has to come from somewhere. For rockets, it comes from rocket fuel; unfortunately rocket fuel increases the mass of the rocket, which requires more rocket fuel, which increases the mass of the- actually I think I’ve done this already, haven’t I. Anyway, rockets suck, but we still use them because the alternative solutions are, to put it mildly, just a little bit far-fetched.

Solution 1: Build better rockets.

Ahaha. Ahahaha. Ahaha. No. Rocket science isn’t necessarily all that complicated – I can understand it, after all – and one of the things that struck me when I was studying space science in the second year of my undergraduate degree was that rockets are a dead end. Well, that’s a bit harsh. Better to say that they’ve been refined as much as they can be.

Two things affect the amount of thrust you can get out of a rocket: the expansion velocity of the exhaust gas you’re creating by burning the fuel, and the size of the rocket nozzle. Rapidly expanding rocket fuels tend to be rather unstable – again, see the Nedelin catastrophe – and so there’s an upper limit on just how volatile you want to make that. What about the rocket nozzle? How wide/narrow this is determines the pressure at which the exhaust gases exit the rocket. For reasons I won’t go into, rockets produce the maximum amount of thrust when the pressure of the exhaust gas equals the pressure of the ambient atmosphere through which the rocket is flying. Atmospheric pressure decreases as you ascend into space, so ideally you want a rocket nozzle that automatically adjusts in size with altitude to keep the rocket working as efficiently as possible. This has been done. After that, there’s no real way to further improve a chemical rocket. We’ve taken them just about as far as we’re going to.

Solution 2: Don’t launch them from Earth.

One of the attractive things about a Moon colony – aside from the whaling opportunities – is that the Moon has a gravitational pull less than one-sixth that of Earth’s. It has an escape velocity of 2.38 km s^-1, and consequently it would only take 2.83 MJ to get one kilogram of mass out of the Moon’s gravity – under a twentieth the energy you’d need to get the same kilo off of Earth! Probably the best way to illustrate this is the ascent module on the Apollo lunar landers; that little capsule was able to create enough thrust to return to orbit to rendezvous with the command module.

It would be far easier, therefore, if we could somehow launch rockets from the Moon instead. Unfortunately this idea merely replaces the problem of getting out of the Earth’s gravity well with the even larger problem of building the necessary industrial base on the Moon to build and launch rockets. I’m not saying it couldn’t be done, and if somebody did manage to do it there’s every chance we’d see the commonplace spaceflight depicted in movies like 2001 (if you were lucky enough not to live on Earth, anyway), but the level of commitment and resources it would require would be staggering.

Solution 3: Mass drivers.

This one is simple, and operates on the principle that while achieving 63 MJ per kilo is a tall order for a chemical rocket, if we could somehow use electricity instead it’d be far easier to generate the energy required. The idea is you have a long, long, long, long launch track, kind of like a very high-tech version of Japan’s bullet train network (see maglevs for further information), and you accelerate the thing you want to launch down this track using superconducting electromagnetism. The track slopes upwards towards the end, and so once it reaches the end of the line your launch vehicle is shot into the stratosphere. At this point some small rocket boosters would take over and move the launch vehicle to the desired orbital trajectory. Building this thing would be a bit more feasible than the Moon colony, but there’s just one tiny snag: room temperature superconductors capable of carrying the currents required haven’t been invented yet.

Solution 4: Project Orion.

In which the Orion spacecraft is supposed to fart out shaped nuclear explosions, the brunt of which is directed against an impact plate on the ass of the spacecraft which makes the nukes “push” the spacecraft along. Utterly, utterly mad.

Solution 5: A space elevator. Also unicorns.

A very old concept that’s rather in vogue in 4X games, for some reason. As mentioned here geostationary satellites orbit the earth with a period of one day – that is, they remain above the same point relative to the Earth’s surface throughout their orbit. In theory, if you had access to a material strong enough as well as the combined and focused resources of the largest superpowers on Earth over a half-century or more, you could lower a cable from geostationary orbit all the way down to the surface of the Earth and simply have vehicles ride up and down the cable just like an elevator car. This is attractive because the energy costs are similar to those of a mass driver launch with the added bonus that you get most of it back as elevator cars come back down from orbit. If we then wanted to launch stuff further out into the solar system we could take advantage of the fact that the space elevator would kind of act like a giant sling to any payload launched from the far end.

Sounds fun, right? Perhaps so, but space elevators have several minor niggles past the huge advances in space technology, robotic manufacturing, materials science and megastructure construction (I just made that last one up, but someone’s going to have to invent it before they can build the elevator) that would be required, not to mention the totalitarian world government that’d have to be in place to keep everyone pointed in the right direction long enough to finish the bloody thing.

• In order to make it work you need a big counterweight of some kind to produce the necessary centrifugal force to keep the elevator cable taut. These days space elevator designs merely pay out the cable a little further past geostationary orbit to provide a counterweight mass rather than the previous idea of moving an asteroid to GEO to act as counterweight, but even if you do this you still need the asteroid because a) you need to build the elevator from both ends at once and so you’re going to need a base of operations in space from which to do it, and b) an asteroid would provide necessary raw materials for cable construction. So first you need to move several million tonnes of rock into geostationary orbit. This is just a little bit tricky to do, and I imagine it might make people down on the surface a little bit nervous as well what with the potential consequences if something goes wrong.

• There is no material which can currently be mass-produced in the quantities required which has the necessary tensile strength to support thousands of kilometres worth of its own weight. People always point to carbon nanotubes as the catch-all solution, but while they have the theoretical capacity to support the quantity of mass required, it would require the cable to be structurally flawless over its entire 40,000 km-odd length. Even one flaw would introduce a weakness which could be potentially fatal to the whole shebang.

• Transmitting power to the elevator cars is also going to be a bit of a bugger, since you still need that 63 MJ/kg to get into orbit. A nuclear power source would do it, but that’d probably make passengers a bit uncomfortable. Solar panels would increase the weight of the car, while using the cable itself to transmit power is going to run into the very inefficiency problems the space elevator is supposed to avoid. The current favoured proposal is wireless energy transfer via lasers or something, which has the tiny drawback that it is literally space magic.

• Elevator cars would travel fairly slowly, with an ascent to GEO taking anywhere from 6-12 hours to a full day. This brings the Van Allen radiation belts into play; the cars would travel through them slowly enough that anyone inside would end up taking lethal doses of radiation. It would be necessary to shield the cars in some way, which again would add to the weight.

Personally I think the space elevator is the ultimate manifestation of Archimedes and his lever; something that is theoretically possible but practically stupid. We can’t even agree on the best way to fly three people up to LEO; we abandoned the moon after sending barely two dozen guys up there. We are nowhere near being ready to take on the incredible engineering challenges of building something like this, and so anyone who thinks the space elevator is going to be built in the next half-millenia needs their head examined.

Where do I think the likely future of spaceflight lies? Well, assuming the world doesn’t enter a period of terminal dystopian senescence in the next couple of decades I think the mass driver concept is probably the most feasible solution as long as somebody comes along to solve the superconductor problem. It’s the smallest engineering project, it has the very great advantage of the thing being built on Earth rather than in space or on another planet, and it has the fewest question marks over necessary technology advances. Plus, if aliens ever try to invade we can use it to shoot rocks at them. Welcome to Earth.

The post The Future Of Spaceflight. appeared first on The Scientific Gamer.

Warning: post contains moderately difficult algebra along with hints of calculus. But don’t worry, it’s not that bad.

Rockets are kind of sucky for getting into space. Right now, though, they’re all we’ve got.

Rockets work by the classic principle of Newton’s Third Law: every action has an equal and opposite reaction. Push against a wall, and the wall also pushes against you with the same force. Friction between your feet and the ground stops you from moving backwards in response to this force, but if there wasn’t any friction – if you were standing on a big sheet of ice or something – then if you thumped the wall hard enough you would start to slide away from it. In a true Newtonian environment like space, even a simple action such as throwing a wrench away from you can nevertheless produce an appreciable impulse on you in the opposite direction to which you threw it, and that’s where you’d end up drifting.

This is basically how rockets work, except instead of a wrench they’re using thousands of kilograms of rocket fuel shot out of the back of the rocket at several kilometres per second. This creates an equal and opposite force which pushes the rocket upwards – thrust, in other words. When they’re considering how much fuel to put in a rocket, rocket scientists don’t think “Well, we want the rocket to reach such and such an altitude so we need this much fuel,” because that would be needlessly complex. Instead they think in terms of something called delta-V, or ΔV, which is the change in the velocity of the spacecraft that will be caused by burning X amount of rocket fuel. If your rocket’s delta-V is roughly equal to the Earth’s escape velocity, then congratulations! You’re on your way out of Earth orbit.

The amount of fuel you need to accelerate a given payload to a certain delta-V is dependent on how heavy that payload is. A bigger payload means more fuel. And as mentioned in the post on satellite orbits, it’s not enough just to add more fuel to the rocket, because now you’ve just added a whole bunch of extra kilograms that also needed to be lifted into orbit. So you need more fuel to lift the fuel, and then more fuel to lift the fuel to lift the fuel, and the whole thing would get dreadfully complicated if it weren’t for something called the Tsiolkovsky rocket equation. Because I’m trying to re-teach myself some basic physics I’m going to derive it from first principles. Don’t worry if you can’t or don’t want to follow what I’m doing, just skip to the end.

WARNING. WARNING. AWFUL CALCULUS STARTS HERE. SKIP FORWARD IF YOU’RE ALLERGIC TO MATHS.

Start with the principle of conservation of momentum.  Momentum is mass times velocity. Consider the state of the rocket at two different times: t, which for our purposes is the rocket sitting on the launch pad just before blast off, and t + dt, which is a time dt after that when the rocket has burned off all of its fuel.

(Note: dt is part of the Leibniz notation of calculus. The d doesn’t stand for a specific quantity, but instead basically means “change in”. So dt is the change in time, dm is the change in mass, and so on. They can be combined, too, so dm/dt would be the rate of change in mass over time. For a real world example, dV/dt is the rate of change in velocity over time, which is equivalent to acceleration a. Here, t + dt is similar to saying something like “D-Day +17”, where the +17 is equivalent to + dt.)

The rocket will start with a mass M(t), and will eject a quantity of exhaust gas as it burns its fuel which will have a total mass dm (because the mass of the rocket will change by this much). Due to conversation of momentum, the momentum of the payload after the fuel burn  — which for our purposes we will treat as everything on the rocket that isn’t the fuel (i.e. M(t) – dm) – will be equal and opposite to the momentum of the exhaust gas dm. We can model these separately to find out their respective momentums at the times t and t + dt, but to do this we need to make some assumptions about the velocity of the payload and the fuel.

At time t, the fuel is unburnt and flying along with the payload, so it and the payload have the same velocity V(t). At time t + dt, the fuel will have been converted into exhaust gas travelling at a constant velocity U (since for the purposes of simplicity we’ll say a single fuel type will burn at a constant rate). The payload will be travelling at the same velocity V(t) plus some positive change in velocity dV provided by burning the fuel, making its total velocity V(t) + dV. The fuel will be travelling in the opposite direction with velocity U, but it had a velocity of V(t) to start with, so its true velocity with respect to the payload will be V(t) – U. (The U is negative because the fuel is travelling in the opposite direction to V(t)).

Right, now we can get on with the interesting stuff. The momentum of the payload and the fuel can be expressed as:

To find out the change in momentum over time dt, we have to subtract the intial momentum at time t from the final momentum at time t + dt.

Because we’re treating the rocket as a closed system with no external forces, conservation of momentum means the sum of the change in momentum of the rocket and the payload will be zero. In other words, adding together the terms we’ve derived for ΔP_payload and ΔP_fuel should equal zero.

We’re trying to find the rocket’s change in velocity – its delta-V, or dV – so we rearrange this in terms of dV.

And now comes the part where I’ll probably lose even the more dedicated amongst you. The mass of the burned fuel dm will be equivalent to the change in mass of the rocket M(t), or -dM(t), so we can substitute that in for dm.

Then we do a wonderful, magical thing called integration. Say you have a line on a graph which is described by the equation y = x. Integrating that equation will give you the area underneath the line y = x. This is bloody complicated and there’s a whole bunch of different rules for doing it. For our simple example, the integral of y = x will be x²/2. Don’t understand? Don’t worry, I don’t either. The one thing you should grasp about integrals is that since most lines described by set equations will be technically infinite, we need to identify the bit we actually want to find the area under and integrate between upper and lower limits that define that part of the line.

We integrate the left hand side of the equation with respect to V between the limits V_o and V_final, the initial velocity of the rocket and the final velocity of the rocket respectively. This gives

Simple, right? Unfortunately we then have to integrate the right hand side with respect to M between the limits of M_payload and M_o, the mass of the payload and the original mass of the payload plus the fuel.

That’s substantially gnarlier. Fortunately there’s a neat way to simplify logarithms by smooshing them together, so

Since the final velocity minus the original velocity is the change in velocity, or delta-V, then

IF YOU ARE SKIPPING ALL THE HORRIBLE CALCULUS START READING AGAIN HERE.

It’s a lot of effort to go through for such a little thing, but the final product of all that work is Tsiolkovsky’s rocket equation. From it you can easily see that the delta-V you’ll get out of a given rocket will depend on the velocity of the exhaust U and the logarithm of the ratio of the total mass of the rocket divided by the payload mass. However, since I said rocket scientists usually think in terms of “How much fuel do I need to reach a given delta-V?” rather than “What delta-V do I want to reach today?”, a more useful form of the equation is

Everything on the right side of the equation is stuff the rocket scientist should know in advance – the exhaust velocity U, the desired delta-V and the mass of the payload. And if you subtract the mass of the payload from the total mass of the rocket M_o, what you have is the mass of the fuel. This can therefore be used to quickly and easily calculate what amount of fuel you’ll need to boost a given payload to a given delta-V. Just for the lols we can make a graph of how the fuel-to-payload ratio changes for that given delta-V depending on what sort of fuel you use. For a desired delta-V of 9.4 km s^-1 (the lower limit required for low Earth orbit)

Obviously there’s a law of diminishing returns in effect here, but we can see from the graph that in order for your rocket to even be feasible you need a fuel with an exhaust velocity of at least 4-5 km s^-1. Happily there are fuel mixtures which exist which are capable of this, and some go even higher, but there’s a limit to how big you can make U. Remember the Nedelin catastrophe I referenced last week? That neatly demonstrates that high-power rocket fuels are very, very volatile and prone to exploding, and so you don’t really want a U that’s too big. It’s essentially fixed at 4-6 km s-1. Assuming that you’re not willing to reduce the mass of your payload at all, is there any way we can further increase the efficiency of a rocket?

Well, I wouldn’t have asked the question if there wasn’t an answer. There is. It’s called rocket staging. The idea is that once you have burned X amount of fuel, whatever you were using to keep that X amount of fuel in is useless dead weight. Lifting it along with the rest of the spacecraft is inefficient; it’s better to just cut it loose entirely if you can. Rocket staging is basically a matter of perching a small rocket on top of a larger, more beefy rocket. The beefy rocket fires first and uses all of its fuel, and then a series of explosive bolts cut it loose from the small rocket which then starts burning its engines. We can work out how efficient this is by using the rocket equation for each successive stage.

Assume that your rocket requires 1% of storage mass for every 8% of fuel mass. For a one stage-rocket with a payload that is 1% of the total mass, this allows for a fuel mass of 88%. Your achievable delta-V will therefore be

Compare this with two rockets stacked on top of each other, using the same fuel/storage ratios. The first rocket has a fuel mass of 80% and a storage mass of 10%, with the second rocket making up the last 10% of the mass. The first stage will boost the second stage to a delta-V of

So this first stage has less delta-V than our big one-stage rocket. However, once it’s finished burning it’s cut loose and the second rocket fires as a standalone entity with

i.e. exactly the same as the first rocket since the fuel/storage mass ratio is identical. This is added to the delta-V from the first stage to give a total delta-V of 3.22 U – half as much again as a one-stage rocket carrying the same payload with the same total mass. Depending on how far you want to go and how complex you want to make your rocket you can add even more stages; the Saturn V which sent the Apollo astronauts to the Moon was a five-stage monster.

So! Hopefully this has at least been useful for crystallising in your minds the reason why we use multi-stage rockets. It’s certainly been helpful for me; I learned this stuff back in 2004 so it was good to spend an afternoon deriving the Tsiolkovsky rocket equation from first principles. Good. Yes.

*eye twitches*

The post You Have Discovered Rocketry. appeared first on The Scientific Gamer.

Edit: I forgot the best orbit of all, the Hohmann transfer orbit. This has now been amended.

Yes yes I’m twenty minutes late. Sue me. It occured to me while thinking of ideas for future science articles that it might be useful to talk about satellite orbits for a little bit so that I have some explanations on hand for why LEO sucks and why geostationary orbit is hard. There’s no ultimate conclusion here, just background information on the most common types of satellite orbit and their advantages/disadvantages. Enjoy.

Low Earth Orbit – The most boring kind of orbit. Anything orbiting below an altitude of 2000 km is in a low Earth orbit because 2000 km isn’t very high up – it’s not even high enough for the Earth’s gravity to be substantially diminished in any way, so the only reason you see astronauts larking about in what appears to be zero-G on the ISS is that they’re technically freefalling around the Earth. Nevertheless LEO is a very, very attractive orbit to put satellites in because it is comparatively a very easy and cheap orbit to reach. The main problem rocket engineers face in boosting stuff to higher orbits is that they need more fuel to do so. Then they need to carry that extra fuel up to where the rocket was originally going to do, so they need more fuel to do that. And to get the extra extra fuel up to where… anyway, it’s much less of a headache for them if you just park your satellite a few hundred kilometres above the surface of the Earth, which is a perfectly cromulent orbit for 90% of satellite applications.

 It’s not without its drawbacks, however; the major one being that if you don’t put your satellite very high up it’s still going to be partially within the Earth’s atmosphere, and thus subject to atmospheric drag as gas molecules bounce off the surface of the satellite and reduce its orbital velocity. If we just left satellites in Low Earth Orbit they’d eventually drop out of the sky and plummet back down to Earth because losing orbital velocity means losing orbital altitude. So satellites in Low Earth Orbit have to do a lot of what’s called station keeping – that is, orbital adjustments to counteract atmospheric drag and other effects which alter the satellite’s orbit in order to keep the satellite on station where it should be. For example, this is a graph of the orbital altitude of the ISS since it was launched; the altitude decreases over time because of drag, and every so often it gets boosted back up to a higher orbit by one of the supply vehicles they regularly send up to it.

Polar Orbit – A special variant of the Low Earth Orbit that’s been specifically shifted to have an orbit that’s inclined ninety degrees to the equator – in other words, it orbits from pole to pole. This is useful because it means that as the Earth rotates underneath the satellite, the satellite flies over a different part of the Earth every time it makes an orbit. If you orbit your satellite at a low enough altitude – say, 600–1000 km – then it will have both a very short orbital period (often 90 minutes or less) and be close enough to the Earth’s surface to get some very, very nice pictures of all the pretty scenery down there. The Polar Orbit is therefore of especial interest to people who like to look at stuff on Earth – i.e., Earth imaging scientists and spy agencies.

Geostationary Orbit – The higher an orbit you have, the longer it takes for you to go around the Earth. Since they aren’t very high, satellites in LEO orbit the Earth very very quickly. Sometimes this is desirable, as in the Polar Orbit example above. Most of the time, however, it is not. Quite aside from everything else, if you have a satellite zipping around the Earth at an orbital velocity of several kilometres per second it makes communicating with the bloody thing an absolute nightmare. Even if you know where it is and you have an antenna that can track it as it moves across the sky, eventually the satellite is going to disappear below the horizon and you’re going to be out of contact with it until it comes back around the other side of the Earth. This is not ideal, since if you want to be in communication with the satellite 100% of the time you have to build a daisy chain of satellite ground stations dotted around the planet so that it’s never out of your line of sight.

The solution to this problem is the geostationary orbit. If, as you go higher, the orbit of the satellite takes longer, then it follows that eventually you’re going to find an orbital altitude where the orbital period of the satellite is equal to the rotational period of the Earth – in other words, the satellite goes around the Earth once a day. This means that it orbits at the exact same rate as the Earth rotates, and so if it’s got an inclination of zero it constantly remains above the same point on the Earth’s equator. (Hence geostationary, or geosynchronous – it’s stationary with respect to the Earth.) This is a good orbit for communications satellites since once they’re moved into position they’ll never be out of contact with the country that launched them. It’s also good for other nation-specific applications, like weather monitoring. The drawback is that you need to go very, very high up in order to get an orbital period of 24 hours. 36,000 km up, in fact. That sort of thing requires a lot of fuel.

Molniya Orbit – Unfortunately the fact that you need to orbit stuff around the equator to achieve a geostationary orbit can be a bit difficult if you’re a country that happens to have most of its land mass located at high inclinations – say, for example, if you’re Russia. Since your line of sight to a geostationary satellite has a high angle of incidence, you’re going to need a lot more power to communicate with it. Additionally getting something to a geostationary orbit from the highly-inclined Russian launch sites is also very tricky. The Russian solution is the Molniya orbit. Unlike the other orbits described here a Molniya orbit is highly elliptical – that is, its perigee (point of closest approach to the Earth) is a thousand kilometres or so, but its apogee (point at which it is furthest away from the Earth) is 40,000 km up on the opposite side of the planet to the perigee. If you arrange matters so that the perigee is above the bit of the planet you want to look at/talk to, you can get almost all of the benefits of a geostationary satellite out of it since it’ll be spending 80% of its time on one side of the planet and while it’s doing this it’ll be in line of sight of your country of choice. Unfortunately while the Molniya is a very neat idea it’s not without its drawbacks; namely that you need directional antennae to track it as it moves through the sky as well as multiple satellites in a constellation to provide 24-hour coverage while one or more of your satellite constellation is out of contact on the other side of the planet.

Hohmann Transfer Orbit – Okay so these orbits are all very nice, but what if we want to orbit something around a planet/moon that is not the Earth? How do we even get there? Contrary to what Hollywood would have you believe, spacecraft that go to other planets don’t just point themselves at the planet and then blast off because this would take a shedload of fuel and also you have to account for the gravity of everything else in the Solar System at some point. Instead they enter something called a Hohmann transfer orbit. This is a special type of orbit because the spacecraft will only travel along it for as long as it takes to get to where it’s going.

The idea is this. You’ve got your spacecraft going round the Earth in what’s called a parking orbit. The objective is to get to a destination orbit that is different — geostationary orbit, say, for the most simple example, or an orbit around the Moon or Mars. Instead of trying to get there directly by burning fuel, the idea of the Hohmann transfer orbit is to let gravity do the work for you. The spacecraft just makes one brief burn to get itself onto the Hohmann orbit, which is an elliptical orbit going around the Earth or the Sun or whatever which just happens to intersect with both the parking orbit and the destination orbit. You sit back and wait for a couple of months, and then when you get to where you’re going you burn the engines again to shift the satellite to the destination orbit. It’s a very simple and elegant way of getting around the Solar System, and the only drawback is that it’s introduced the charming concept of the launch window — that is, you have to wait until the starting point (Earth) and the destination are in the right positions relative to each other for a Hohmann orbit to exist. Miss that window, and you have to wait for the next one. But then, as you should have learned by now, you don’t get anything for free where space travel is concerned.

Mlur. Sorry you had to sit through that. Hopefully there will be some payoff coming very, very soon.

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