Getting Into Orbit
A Primer, Part I
The Kármán line is a commonly used standard that purports to mark the boundary of space. It's easy to remember, because it's 100 kilometers (62 miles) high. It's by no means the edge of the Earth's atmosphere, which extends quite a bit further above it. In fact, there is no hard edge to the Earth's atmosphere; its top layer, the exosphere, tapers off very gradually into the vacuum of space. But above the Kármán line the air is diffuse enough that, for all practical purposes, you're in space. You're an astronaut.
To get to that altitude, you don't need massive launch vehicles like the Saturn V, or the Delta IV, or the Space Shuttle. Research teams regularly reach the Kármán line and above with relatively small rockets called sounding rockets that carry scientific instruments. In 2004, an amateur team of enthusiasts crossed the line with their own 10 inch diameter rocket, and repeated the feat for the 10th anniversary last year.
The thing about all of these rockets is that, inevitably, they'll fall back down. They will exhaust their propellant, Earth's gravity tugging on them all the while, reach their highest point, and plummet back into the atmosphere and back to impact with the surface. Not even the largest rocket is immune to gravity. Every rocket -- every thing -- will fall. The trick of it is to always miss the Earth. You accomplish this by achieving such monumental horizontal velocity that the Earth is constantly curving away beneath you as you fall. This is orbit.
To put it another way, consider this:
In fact, scientists know that on average, the Earth curves approximately 5 meters downward for every 8000 meters along its horizon. If you were to look out horizontally along the horizon of the Earth for 8000 meters, you would observe that the Earth curves downwards below this straight-line path a distance of 5 meters.
Say you were standing on a ladder at a height of 5 meters, and threw a baseball straight ahead of you. Discounting air resistance, the Earth's gravity pulls that baseball (and everything else) downward from its 5 meter height in about 1 second. But remember the above: 8000 meters ahead of you, the ground is 5 meters lower, due to the curvature of the Earth. If you threw the baseball with such velocity that it traveled those 8000 meters in the one second that it took the ball to fall 5 meters, it would still be 5 meters above the ground at the end of that trip. It falls at the same rate the Earth curves away from it. That velocity in our rough example -- 8000 meters in one second, or 8 km/s -- is very close to the 7.7 km/s velocity at which the International Space Station orbits the Earth, and that's not a coincidence.
Of course, once you factor Earth's thick atmosphere into the problem, things get bothersome. You have to achieve that target velocity and be above the meaningful atmosphere -- above the Kármán line -- so that atmospheric drag doesn't sap your velocity and bring the Earth rising up to meet you. And anything worth putting in orbit is going to be a lot bigger than a baseball. But that's the essence of it: having enough velocity so that you can fall without worrying about hitting the ground. Objects in stable orbit are said to be in freefall -- gravity is the only force acting on them.
Getting There
Isaac Newton figured all of this out in the seventeenth century. By the end of the nineteenth, all kinds of smart folks were thinking seriously about the best ways to accomplish it. Scads of different methods have been imagined: immense tracks lined with electromagnets, elevators crawling up massive tethers anchored by geostationary satellites, and giant cannons, to name a few. Barring massive advances in materials science and other technologies, the most practical way, and by most accounts the best way, is with a rocket. Take a fuel, take an oxidizer, combine them and ignite to burn at tremendous rates, and force the exhaust through a nozzle that accelerates it to extreme velocities. The equal and opposite reaction accelerates your launch vehicle.
Right now, sitting (more or less) on the surface of the Earth, you are traveling at a constant velocity of about 465 meters per second towards the east, because of the planet's rotation (the precise velocity actually depends on your latitude, but let's keep it simple). As established above, the basic problem we face, tasked with getting into a low Earth orbit, is accelerating our launch vehicle to about 7.7 kilometers per second. This is why almost all rockets launch on an easterly path; in the quest for 7.7 km/s of velocity, why not take advantage of the 465 m/s the Earth is spotting you? Launch sites are consequently generally located in places where rockets can launch to the east without flying over populated areas -- hence Cape Canaveral, for example.
So we're going to launch to the east, 465 m/s of velocity already in our pocket. Here is where the popular iconography of rocket launches falls well short of what actually happens. The classic clips of rocket launches played on television and in film usually only depict the first few seconds of launch. The rocket goes up. That's pretty much all one might see. But we know we need 7.7 km/s of horizontal velocity. If we merely rocket upwards, when the engines burn out and we fall, we definitely won't miss the surface.
For this reason rockets spend nearly all of their ascent tilting towards an increasingly horizontal (with respect to the Earth's surface) trajectory, to gain both altitude and velocity. In many cases the rocket achieves a fully horizontal orientation right at the time the engines shut down. Rockets accomplish this with what is called a gravity turn. Early in the ascent, perhaps after having accrued only 150 meters per second of velocity, the rocket purposefully pitches (tips) slightly in the direction of the heading (or azimuth -- hey, the blog name!) it will follow to orbit. Since it is no longer pointing directly vertical, gravity begins to gradually pull it into a horizontal orientation.
A typical trajectory that results from this is easily visible in long exposure photographs of rocket launches, such as this one, taken by Reddit user EchoLogic, of a Falcon 9 launch from September:
Note how altitude is gained quickly at first, and how the rocket starts tipping early in the ascent and is eventually near horizontal.
It is, of course, not nearly as simple as just tipping the thing over and calling it a day. Rockets have extensive computer guidance systems to constantly monitor and correct for deviations from the proper azimuth and orientation caused by aerodynamic pressure and other pesky factors.
Furthermore, our hypothetical ascent aside, most rockets are aiming for a very specific orbit that is required by the mission it is undertaking, particularly if they're trying to rendezvous with an object already in orbit, or travel to somewhere else (say, the moon) once in orbit. The size, shape, and orientation of its final orbit are determined by a set of attributes the rocket possesses at the precise time the engines shut down and the ascent is over (often referred to as "burnout"). Shape and size are determined by three numbers at engine burnout -- the rocket's velocity, altitude, and flight path angle (don't worry about it).Orientation is determined by a few more attributes. The upshot is, there is an acceptable range for each of these figures which the rocket must achieve at the time of engine burnout -- its "precise window in space," to borrow a term from Space Shuttle ascents -- in order to attain the proper orbit for its mission.
To correct for deviations from the proper course, and to steer the rocket to its precise window in space, rockets will "gimbal," or swivel, their engines in order to change the vector of their thrust, resulting in precise changes to the orientation. This is a bit difficult to observe during ascent, because the rocket tends to be far away and moving quickly, but you can get an idea from this video of a pre-launch check of the Space Shuttle main engines' gimballing ability.
Payload
Obviously, if we're trying to get to orbit, it's because we want to put something there. This thing is referred to as the payload. When the engines burn out, the ascent is over, and you've achieved orbit, the object or objects that are in orbit are the payload. It might be a satellite, or a container full of cargo to resupply something already in orbit like the International Space Station, or a capsule with people on board. It might be a probe that you intend to send to Mars, or, as in the case of Apollo, a spacecraft with a crew bound for the moon. In these latter two cases, the payload is not only the spacecraft, but the amount of propellant that will be required to get you from your orbit to the place you're going.
The mass of the payload that a rocket is capable of putting into low Earth orbit (LEO) is referred to as Payload to LEO. It's a common measure to compare rockets that is usually expressed in metric tons (1,000 kilograms; Wolfram Alpha helpfully provides for reference that 1 metric ton is about the mass of 2 small cars). The reigning champion is the Saturn V, which had a payload to LEO of 118 tons. It had to put all of the following into low Earth orbit: the Apollo command module, with the astronauts inside it; the service module, which provided consumables like oxygen, electricity, and drinking water; the lunar module or LEM, which carried two of the astronauts to the surface of the moon; and all the propellant required to get the whole assembly from low Earth orbit to lunar orbit, from lunar orbit to the lunar surface, from the lunar surface to lunar orbit, and from lunar orbit to a return trajectory back to Earth. That's a lot of payload.
Nowadays materials are lighter, and humans have stuck to low Earth orbit, so there is no active launch vehicle that has a payload to LEO comparable to the Saturn V. One of the most frequently used vehicles for satellite launches, the Atlas V, lifts 9 tons of payload to LEO. The Delta IV, also by ULA, lifts a 9.5 ton payload. SpaceX's Falcon 9, used to launch resupply missions to the International Space Station and geosynchronous satellites, among other things, can lift 13 tons. Currently, the Delta IV Heavy is the heaviest lifter, able to put 28.7 tons into LEO, comparable to what the Space Shuttle was able to carry in its cargo bay (24.4 tons). If SpaceX's Falcon Heavy, set to launch late this year, operates as designed, it will be the new heaviest lifter, with a 53 ton payload to LEO.
Still, nothing close to the Saturn V. Missions that could conceivably require anything close to that 118 tons involve taking crews of humans to places beyond Earth orbit -- back to the moon, to Mars, and elsewhere. That requires more propellant, more life support consumables, more mission cargo, more mass. This is the goal of NASA's next launch vehicle, currently in development and scheduled to launch in 2018: the Space Launch System (SLS). The first iteration is planned to lift a 70 ton payload, but the eventual goal is to surpass the Saturn V with a 130 ton payload. For reasons beyond the scope of this post, that may not ever happen. Available payload to LEO, and payloads to other orbits -- geosynchronous transfer orbit (GTO), geostationary orbit (GEO), trans-lunar insertion (TLI), Mars Transfer Orbit (MTO) -- define the scope of achievable missions and substantially impact the design of the payload itself.
Mass and Staging
Here's a simple little equation you might recall that plays a big role in all this:
Force = Mass * Acceleration
In this case, the operative force is thrust, imparted by the rocket engine(s), which serves to accelerate the mass of our rocket. Rearranging the equation slightly, we get:
Acceleration = Thrust / Mass
You can see, then, how important the mass of the rocket is. The more we have of it, the less acceleration we're able to produce for a given amount of thrust. That translates to more time getting up to our target velocity, and therefore more time spent burning propellant and fighting gravity and aerodynamic drag.
So an enormous amount of effort is put into keeping the mass of a rocket and its payload as low as possible. One side effect of this is staging. It turns out that, rather than build a humongous one-piece rocket to make the entire ascent to orbit, it's more efficient to have a few stages, that is, a few assemblies of propellant and engines stacked on top of one another. Generally, your first stage lights up at launch, accelerating all of the stages above it to a given velocity and altitude before its propellant is exhausted. It is then jettisoned, ridding you of the mass of its empty tank, instrumentation, and engines, and the second stage ignites, continuing the acceleration of the vehicle.
The Saturn V, the rocket that launched the United States' lunar missions, had a first stage that separated, according to its flight manual, at an altitude of 58 kilometers, after accelerating the vehicle to a velocity of 2.8 kilometers per second. The second stage ignited at this point and continued accelerating the vehicle. This picture, taken at the moment of first stage separation, gives you an idea of the kind of mass they were dumping off:
In the quest for 7.7 km/s of velocity, it's a bit like starting with a new, lower mass rocket, already high up in thinner air and already a third of the way towards the velocity you need. Upper stages will often use smaller, lower mass engines that produce less thrust; having shed a lot of its mass, the rocket now doesn't need as much thrust to produce the same amount of acceleration. These are the advantages of staging. Of course, there is a sweet spot. With every stage you add, you're adding the mass of rocket engines that won't be contributing any thrust for the early phases of the ascent. Most modern rockets keep it to two or three stages.
As any stage burns propellant, it becomes lighter, and its acceleration increases. In the later phases of the launch, when the vehicle is approaching its final mass, this can result in uncomfortably high acceleration if your rocket has humans in it. The Space Shuttle intentionally throttled down its engines towards the end of ascent to limit its rapidly increasing acceleration.
All this in mind, take 10 minutes and watch an actual orbital launch. This is the Orb-1 resupply mission to the International Space Station, flown on Orbital Sciences' Antares launch vehicle. I think it fits well with this post because it has some great ascent views of the rocket pitching over, includes some clear call outs of various events, and, beginning with the second stage flight, includes an excellent launch animation that has graphs showing altitude, velocity, and acceleration of the vehicle for a clear sense of exactly what's happening.
As second stage flight begins (6:23 into the video), the vehicle jettisons its payload fairing. That's the smooth egg-shaped shell that splits in half and moves away, exposing the payload. While in the atmosphere, it gives the rocket an aerodynamic shape, allowing it to safely speed through the air. At the altitude of staging (180 kilometers, as you can see on the altitude graph), the air is now far too thin for the fairing to be needed, and it would be wasteful to continue accelerating its mass, so it is ditched.
Just before the second stage engine lights, note that the rocket is traveling 4.43 km/s, still well short of the goal. This is reflected in the shape of its orbit at that time. Its apogee (the furthest distance from Earth that an object reaches in its orbit) is 186 km, but its perigee (the closest an object gets to the Earth in its orbit) is a negative number; it's not really an orbit at all. If the second stage engine didn't light, the vehicle would reach a maximum height of 186 km and then fall back down and impact the Earth. At this point it is still suborbital.
The second stage lights, and the vehicle's acceleration goes from 0 to about 10 meters per second squared. Every second, the vehicle is adding 10 meters per second to its velocity. As the graphs show, the velocity ticks upward as the second stage flight progresses, and, as it burns propellant and becomes lighter, so does its acceleration. Both the apogee and perigee increase as the orbit begins to take shape. The engine burns out when the vehicle is traveling 7.5 km/s (yes, not 7.7 as we've been discussing; though the payload is on its way to the ISS, its orbit does not yet match the ISS's and so its velocity is slightly different), the acceleration halts, and the apogee and perigee show a 269 km by 218 km orbit.
It's a perfectly typical rocket launch, incorporating everything we've covered here. Different vehicles employ different engines, different staging configurations, and different ascent profiles, but the overall principle is the same: get out of the atmosphere, and build up such a tremendous velocity that you never hit it again as you fall. Robert Heinlein famously said that, once in low Earth orbit, "you're halfway to everywhere." Out of the soup of Earth's atmosphere and with substantial velocity under your belt, it's much easier to add velocity, to change your orbit, and thus to go places. Now that we're there, we'll cover what we can and where we can go in the next installment.
For the sake of accessibility, I've made some considered simplifications of certain concepts here. Feel free to pick these apart in the comments, I just wanted to keep the post readable.
Image credits: Cover - Stack Exchange; Long exposure of Falcon 9 ascent - Reddit user EchoLogic; Saturn V first stage separation - Wikipedia