Hitting the Books: How to huck a human into low Earth orbit

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The phrase orbital mechanics—like nuclear particle physics or the theory of relativity—is something that makes many people’s eyes glaze over. The average person thinks that subjects like these are far too complex to understand. But if you strip away all the math and simply try to understand what is going on, they are actually not that hard to grasp. As for orbital mechanics, it is the physics of spaceflight—it describes how objects move relative to one another in space. Once you understand the mechanics of how planets and spacecraft interact with gravity, it’s easy to make a spacecraft do what you want it to do.

If you take a baseball and throw it straight away from yourself, it will eventually hit the dirt—it runs out of speed, and then gravity pulls it to the earth. If you’re a major league pitcher, your throw will probably go farther than mine because it launches off your hand faster. But gravity eventually does its thing, and the ball will come down to the earth. Now, let’s build a machine to throw the ball faster—it will go farther, of course…but the ball will always curve down and hit the dirt. That curve the ball follows, by the way, is known as a ballistic path. Because of gravity, any object thrown or fired into the air will eventually be pulled back to the earth. With every increase in speed, the ball goes farther. If we change the ball to a projectile, and start firing it from a gun, then it will go farther still.

Naval guns can fire projectiles so far that they go over the horizon before falling back to the earth (hopefully on their targets). That phrase, over the horizon, is key to understanding orbital mechanics. The spherical shape of Earth means that as you travel horizontally, the surface is always curving down. If you can throw the object fast enough that its drop, its ballistic path, is equivalent to Earth’s curvature, then it will never hit the planet—and voilà— it has gone into orbit!

It takes a tremendous amount of speed to reach that point where your object is not going to hit the earth—in the neighborhood of 25,000 feet per second (that’s over 17,000 miles per hour) if you’re talking about flying in the region known as low-Earth orbit (LEO). Let’s call that anywhere from about 100 miles above the surface to about 400 miles—give or take. That’s where the Space Shuttle did all its work. If we take our imaginary baseball or projectile and keep upping the speed, eventually it will go so fast that it never falls back to Earth. The speed at which that occurs is known as escape velocity. We never worried about escape velocity with the Shuttle—it didn’t have the capability to go that fast. Unlike the Apollo spacecraft that took men to the moon, the entire Shuttle spacecraft was always coming back to Earth. It would have taken approximately its own weight in fuel to propel the Orbiter to the moon. (I asked my navigators to figure that out one night…)

So the first element of orbital mechanics isn’t that hard—make an object move fast enough relative to the planet, and it will never hit the planet. It will just keep going around and around and around—until, of course, something slows it down to where it begins dropping toward the surface. What might slow it down? Well, one thing might be running into the thinnest wisp of the atmosphere, the widely spaced molecules of gas that reach for hundreds of miles into space. The atmosphere doesn’t just end abruptly, it gradually gets thinner and thinner as you move away from the planet’s surface. It never really goes away completely, it just eventually fades in density until it no longer has any effect. Just about 100 miles above Earth’s surface, there are enough air molecules that if a spacecraft runs into them, an infinitesimal amount of energy is lost with every collision. You can’t measure the energy from any one collision, but if you add up enough of them you can eventually discover that you have lost some speed. And that speed loss adds up.

The slower you go, the more you fall back to Earth. So the effect of running into the atmosphere is that it drags you back down. If you don’t add some velocity with a rocket motor burn every once in a while, you won’t stay in orbit. It doesn’t take a lot—just a couple of feet per second every day—but if you don’t account for it, your mission isn’t going to last very long. We use this effect to our advantage, of course—it’s how we bring a spacecraft home. If you point your spacecraft so that when you ignite an engine it slows the craft down significantly, then you will drop lower into the atmosphere where the gas is thicker, which then slows you down even more—eventually to the point where you have been captured by the atmosphere, and you fall to the earth. This is what happens when a meteor becomes a meteorite: it generates enough heat from the friction of the atmosphere to quickly burn up, which creates the streak we see in the night sky. Of course, burning up on reentry is the last thing we want a spacecraft to do, so we have to enter in a controlled fashion. We’ll talk about that later.

For now, let’s remember that if we go fast enough horizontally, we end up orbiting Earth rather than falling back to the surface. The faster you go, the higher you go. The slower you go, the lower you go (until you fall out of orbit and are captured by the planet’s atmosphere). These are the basics of orbital motion (or mechanics). With that mental picture, you can understand almost anything else we’ll talk about when it comes to the Space Shuttle’s trajectory.

To get the Shuttle into orbit, you have to do two things: get it out of the atmosphere and accelerate it to orbital velocity. In the simplest terms, the first part of that is done with the Solid Rocket Boosters (SRBs). These two monsters had enough energy to loft the entire Shuttle stack up to an altitude where the air was so thin as to be negligible. They did this in just a little over two minutes. Each SRB put out about 3 million pounds of thrust, for a combined total of 6 million pounds. By comparison, the three Shuttle main engines contributed another half-million pounds of thrust each, for a total of 1.5 million pounds—a much smaller portion of the overall thrust available at liftoff. Not insignificant, of course, but still—the SRBs dominated during what we referred to as the first stage.

When the SRBs dropped off, the vehicle was up where the air was not a real factor, but it was only going a couple thousand feet per second horizontally. It was now the job of the main engines to accelerate the ever-lightening stack (the Orbiter and External Tank) to that magic number of 25,000 feet per second to get it to stay in orbit. That “ever lightening” part is important—as you burn fuel, you get lighter, but with a constant thrust (about 1.5 million pounds, remember?) you are going to accelerate more quickly. That’s a consequence of Newton’s basic law of motion—if the force remains the same and the mass decreases, the acceleration goes up! Now the Orbiter was designed for a maximum acceleration of three times the force of gravity (3 Gs). A “G” is about 32 feet per second per second, so 3 Gs is just about 100 feet per second per second—you’re really gaining velocity quick! When the acceleration reached that point, the only thing you could do to keep from over stressing the vehicle was to throttle the engines back, and that is what we did. In the last two minutes or so, the throttles would come back to make sure we didn’t break anything.

In the simplest terms, when you reached the desired velocity to make orbit, you shut down the engines and coasted into orbit. It sounds simple—but it isn’t. Let’s stretch our knowledge of orbital mechanics a bit. Let’s assume that you are in a circular orbit—the same altitude above Earth at all points in the orbit. If you decide that you want to go higher, then you have to increase your speed. This is done with a thrust event, known as “doing a burn,” because we thrust by firing—burning—an engine. If you squint and allow yourself to approximate, doing a burn to increase your speed by 1 foot per second will increase your altitude by about a half mile. That’s not an instantaneous gain—what you are actually doing is driving yourself uphill until you reach that new altitude, which you will reach when you are halfway around Earth. But you won’t remain there. Think of the ballistic path that a ball takes when you throw it—it first increases in height, then gravity pulls it back down, and so it comes back down again. The same thing happens when you increase the Orbiter’s velocity—it will go uphill to the new altitude, but it eventually comes back to where it started…right to the altitude where you increased the speed. It so happens that you’ll reach your new altitude halfway around the world, and then you’ll be back where you started when you complete the orbit. It will continue in this elliptical path for as long as you let it. 

However, if we want to raise the orbit all the way around, we can simply thrust again by the same amount when we reach our new height (referred to as the apogee). We will have raised our altitude at the starting point by a half mile as well, meaning that we will be in a new circular orbit a half-mile higher than when we started the pair of burns. We will have also increased our velocity by 2 feet per second total.

The math is really convenient if you’re trying to do it in your head—if you want to raise the orbit by 10 miles, you simply burn 20 feet per second (fps) initially, then another 20 fps at the new apogee, and voilà—you’re in a new circular orbit 10 miles higher, and it cost you a total velocity change (referred to as delta V) of 40 fps. Raising and lowering the orbit is how you execute a rendezvous. But for now, it’s important that we get into, and then know how to get out of, orbit.

Let’s take a look at the very end of the initial launch. There we are, thrusting all three main engines, accelerating at 100 feet per second every second. Knowing what we now know about orbital mechanics, we know that for every second we burn the main engines at this point, we are raising the orbital altitude by 50 miles when we get around the planet. We need about 100 miles of altitude to reliably stay out of the atmosphere—consider it the minimum safe altitude we want to end up in. The International Space Station is at an altitude of about 200 miles, the Hubble Space Telescope is about 350. The Orbiter lived in the altitude band between 100 miles and 350 miles—a difference of just 250 miles. In terms of orbital insertion speed, that is just five seconds of burn time.

A full ascent, from the launch pad to Main Engine Cutoff (MECO) was about eight and a half minutes, or about 510 seconds. The orbital altitude range of the vehicle meant that cutoff would be plus or minus five seconds, which is a very small percentage of that total burn time. Miss it by 1 percent and we were either not in orbit or we were going way too high, without enough thrusting capability to circularize the orbit—or to get home. So MECO was critical—you had to time it exactly right in order to get precisely into the orbit you wanted, and we considered precise to be within a couple of miles.

No problem, right? I mean, throw the switch at the right time to cut off the engines, and you’ve got it made. Well it’s not that simple, because you don’t just shut off an engine that’s putting out a half million pounds of thrust. It doesn’t go from full thrust to zero in an instant—it tapers off. Every engine tapers off a little differently, so you need to know the exact shutdown characteristics of each engine. You can measure these characteristics on a test stand on the earth, and then use that information to figure out when to command the engines off, in fractions of a second, so that you end up with exactly the amount of thrust you need to end up at the target altitude. When you look at the hundreds of variables involved, you quickly realize that it’s going to take a lot of smart people to figure this out. Fortunately, there are lots of engineers and physics guys who are smart enough to model it and come up with the right answer. In the earliest of rocket flights, way back to Mercury, they were happy just to know that they’d made it into orbit. In the Apollo and Shuttle eras, we needed to have precise control of where we were going to end up—and the accumulation of rocket flight experience made that possible.

Now those who are following closely have already figured out that spaceflight is much more complicated than this. Recall the basics of orbital mechanics, remembering that what goes up must come down. If we have thrusted ourselves from the ground up to an orbital altitude, say 200 miles, we are only at our apogee. Like throwing a ball straight up into the air, we’re going to be coming back down to our starting altitude. This will happen when we get all the way around Earth. The nitty gritty, of course, is that we need to do some shaping of the trajectory to make sure we aren’t going to come all the way back down to the ground. Remember we need to travel horizontally at a high enough speed so that we don’t fall back to the surface. If we really want to end up in a circular orbit (and not an ellipse), we need to do a burn about halfway around the planet. Since we go around the planet in ninety minutes, it means that forty-five minutes after launch we need to do that burn—and we can’t use the main engines to do it. For that, we switch to our Orbital Maneuvering System (OMS) engines.

The OMS engines are mounted in pods on the upper rear corners of the Orbiter. There are two of them, and each produces about 8,000 pounds of thrust. You can burn them together, or separately, depending on how much thrust you need and how finely you want to manage the final velocity. These engines burn propellant stored in their pods, the same kind of fuel and oxidizer used for the attitude control jets—in fact, the tanks for the OMS and Reaction Control System (RCS) jets can be shared (or interconnected) between the two systems, if need be. Once you have shut down the main engines, and jettisoned the big External Tank (about eight and a half minutes into the flight), the OMS and RCS are all that you have. Because these engines are so much smaller than the main engines in terms of thrust, you have to burn them longer to get the same amount of velocity change—in fact, the acceleration available from the OMS engines is barely noticeable inside the vehicle.

But getting back to circularizing the orbit. In the simplest terms, when you get halfway around Earth from your launch site (over the Indian Ocean when launching from Kennedy Space Center), you point yourself in a direction to thrust ahead, and then burn the OMS engines to add the velocity that you need. It can be in the neighborhood of 100 feet per second or more. In the earliest Shuttle flights, we were happy to see that it worked to keep us in orbit—later on, we had learned enough about trajectory shaping and burn times that we were pretty unhappy if we missed our orbital parameters by more than a couple miles. We used ground and space tracking to confirm the orbit we needed to be up in, and we added what we learned into planning for every flight until we became very good at putting the Orbiter exactly where we wanted it to be.

Once you made it to orbit, changing that orbit was simply a matter of adding or subtracting velocity by adding speed with a burn or taking it away (you did that by thrusting backward). When you wanted to come home, you needed to thrust backward. That’s called retrograde. This is where we got the term retrofire, which was done in the early years of space travel with retrorockets. The backward thrust lasts until you slow down the vehicle enough to lower its perigee to about 80 miles, which is where you are assured of being captured by the atmosphere. If you decrease velocity by too much, you lower the perigee by too much, and that means you enter the atmosphere too steeply. Too steep of an entry means that you decelerate too quickly and have to dissipate your orbital energy in a shorter amount of time, which means that you get much higher temperatures on the skin and you burn up. Too little velocity change means that you enter the atmosphere at too shallow of an angle, and you could effectively skip off its surface, much as a rock skips off a pond. The problem with a skip is that you scrub off speed, which makes you slower, so you drop back into the atmosphere more steeply the second time, and eventually you end up with that steep entry again and burn up—sort of how those stones always drop into the water and sink. By now, however, you can see that to bring the Orbiter home from a 200-mile orbit, you need to drop the perigee (the low point of the orbit) by about 120 miles (200 minus 80), and to do that, you need to slow it down by about 240 feet per second. If you filled the Orbiter’s tanks before launch, then you had approximately 600 feet per second total orbital maneuvering capability (the total delta V) that could be used throughout the mission—to raise and to lower the orbit. The key to mission planning and execution was to use that delta V wisely.

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