Introduction to Rocket Science

[Byzesion]

Before we begin, let me just make sure everyone's here. Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin.

Welcome to the class, everybody. Now, since most of you have chosen to audit the class, I've decided to alter the curriculum a bit. All assignments and tests are now optional, but if you decide you want to try them, you'll be given credit for it. I know it's kind of an intimidating subject, but I'll do my best to make it accessible without dumbing it down.

Before we get into rocketry, we have to cover the basics of aerodynamics. There are four basic forces that act on a craft in flight: lift, thrust, weight and drag. In order, lift is pressure on the surface of the craft pushing it upwards; thrust is the force, usually derived from engines, that propels the craft forward; weight is just that: the mass of the craft multiplied by gravity, which acts to counter the lift force; and drag is the air pressure at the front of the craft acting against the thrust.

Now, lift is one of the trickier forces to explain. It's usually represented something like this:



However, this explanation is oversimplified to the point of being incorrect. The actual explanation does involve pressure, but not the speed of the air. In fact, it's more about the angle of attack of the wing, which is the angle up or down the nose of the airfoil is meeting the air. Put plainly, rather than slow moving air creating the pressure, an airfoil that's pitched upwards compresses the air under it, which then pushes it upward. Naturally, it's more complicated than just that, but this explanation will do for our purposes.

Thrust is much simpler, and can be most easily understood as Newton's Third Law of Motion ("A body, acted on by a force will react with an equal and opposite force"), applied. A propeller pulls air over the wings, and pusher propellers, jet engines, and rocket engines push the craft forward. In a propeller-driven craft, an internal combustion engine or (usually in model aircraft) electric motor turns a shaft, at the end of which a propeller pushes or pulls the air, similar to how an airfoil generates lift. In jet and rocket engines, a mixture of fuel and an oxidizer (compressed air in a jet engine, liquid oxygen in most large rockets and occasionally concentrated peroxide in some of the larger amateur rockets) is burned and the exhaust through a nozzle creates the thrust.

[Note: The rest will be completed in the near future, as I am literally so furious about the Lightning-Blackhawks game that I can't think straight.]

[Byzesion]

Sorry about that. Now, where were we? Weight, I believe.

Weight, and its counterpart, mass, come into play mostly in the area of center of mass and center of lift. The long and the short of it is, the farther forward the center of mass is compared to the center of lift, the harder it will be for the craft to take off. Accordingly, the farther behind the center of lift the center of mass is, the easier it will be for the craft to take off and gain altitude. Based on this, it would seem to make sense to have the center of mass as far back as possible, but this isn't the case because, at a certain point, the craft will gain altitude so fast that the pilot will be unable to control it. Too far back, and the airfoil will exceed its critical angle of attack. The critical angle of attack is the point where the airfoil is blocking the air from flowing over the top, resulting in a pocket of air. All of a sudden, the lift is turned into drag, and even a very skilled pilot might not be able to recover.

Drag is simple. Drag is the force of the air pushing back against the craft. Air is, physically speaking, a fluid. It flows when pressure is applied to it (see "Lift" and "Critical angle of attack", under "Weight", above), and if too much pressure is applied, it will be unable to flow around the craft, and a flat or blunt face will allow more air to be compressed against its surface, which, in accordance with Newton's Third Law, will push back equally hard, requiring the craft to use more fuel to increase its speed. Think of it like trying to cut bread with a dull knife and then a sharp one. The sharp knife will easily slice through because there's less surface area in contact with the bread, while the dull knife will tear the bread because its larger surface area will just crush through it.

These will all be relevant in rocketry, but that's next week. For now, though, here are this week's classroom discussion topics:

How do you think planes can fly upside down?

Why do you think having the center of mass behind the center of lift makes it pitch up?

Assignment: Rocket engines typically have a combustion chamber on top of a bell-shaped nozzle. Using Newton's Third Law of Motion, explain why this is more efficient than an open-bottomed combustion chamber.

If you do the assignment, send me a PM with your answer.

[Ater Nox]

Why do you think having the center of mass behind the center of lift makes it pitch up?

One way I think about centre of mass is that it is the point that an object will balance on. In my poorly drawn picture, the 'plane' or white line would balance on an imaginary pole at the red dot, representing the centre of mass.

If the centre of lift is in front of this, it is pulling up towards the front. The plane will then act like a see-saw and the front will go up while the back sinks down. I find the see-saw image helps me out when thinking about these two centres.

[Jin]

I couldnt describe it better than Ater Nox did, i fully agree with what he said.

How do you think planes can fly upside down?

If there is a small angle of attack then the wings create negative lift allowing the plane to fly upside down, i am not quite sure i understand what we discussed today so correct me if i am wrong.

[Byzesion]

Ater Nox: You're close in thinking of it as a see-saw, but you're not quite there. The fulcrum wouldn't be the center of mass, but at a point equidistant between the the CoM and the center of lift. With a CoM far behind the CoL, it would look something like this:



While a CoM closer to the CoL looks like this:



And a CoM in front of the CoL is a really bad idea, looking like this:



So to put it as simply as possible, the lift force pushes up from the underside of the craft, and the weight force (represented by the center of mass) pulls down from the top of the craft. Of course, this all applies while in flight. On the ground, you just have to get the center of mass between the front and rear landing gear so that the nose or tail doesn't immediately smash into the runway.

Jin: Well, not exactly. In fluid dynamics all forces are positive, so you can't really create negative lift. What upside down flying is doing, in essence, is changing which side of the airfoil the lift force is acting on. In most aircraft, being upside down is an indicator that something has gone very, very wrong, so the airfoils are designed for relatively level flight. In stunt planes, however, the wings are designed so that the top and bottom are the same so they can sustain inverted flight for longer periods.

[Baden-Wuerttemberg]

A fascinating start. Thank you very much everyone.

Calculation of drag to overcome: Does it matter at what height above sea level you start, or are the differences in air pressure so minimal that they are negligible?

[Byzesion]

Baden-Wuerttemberg: During takeoff it's mostly negligible. It might be a little bit easier for a craft to take off at sea level that it would be from, say, Denver, but it's twenty kiloPascals difference which is only about two pounds per square inch. Remember, the important factors for drag are the air pressure and speed. The air pressure makes much more of a difference at high speed, so a craft would require less thrust and therefore less fuel to maintain say, 300 knots at thirty thousand feet than it would at two thousand feet.

[Byzesion]

Okay, first going to take the roll. Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin.

I touched on rocketry briefly last week as aeronautics applies to it, but now we're really tackling it. The earliest examples of what we now think of as rockets were 13th century Chinese fire-arrows, essentially a small tube full of gunpowder, open at one end, and tied to an arrow. We don't know how effective fire arrows were, but the psychological effects must have been terrifying. Imagine you're a Mongol warrior, used to facing arrows and swords and spears, and now all of a sudden there are shafts of fire screaming towards you.

Gunpowder and rocketry eventually made their way to Europe, most likely along the Silk Road, and soon Europeans began to experiment with the technology. An English monk named Robert Bacon worked on refining the gunpowder formula to make it burn longer. In France, Jean Froissart made the discovery that launching a rocket from a tube made it more accurate, inventing the forerunner to the bazooka. And Italian Joanes de Fontana developed a rocket powered, water skimming torpedo designed to set enemy ships on fire. By the 1500s, however, rockets had mostly fallen out as a weapon of war, and so the next innovation came from German firework maker Johann Schmidlap, who created multi-stage rockets. When the larger rocket burned out, the second ignited, sending the charge higher and generally making the display a bigger spectacle.

By the 1700s, rocketry had taken off as a science, influenced in part by Isaac Newton and his laws of motion. German and Russian scientists started using rockets larger than forty-five kilograms, and by the end of the 18th century, rockets were regaining status as a weapon. After the success of Indian rocket barrages on the British in 1792 and 1799, a British artillery colonel, William Congreve, developed a rocket for military use. The Congreve rocket was essentially a scaled-up version of the Chinese fire arrows. Even with his designs, rockets were still inaccurate and capable of destruction fired en masse. Again, rockets began to fall out of military favor.

At this point, rocketry became a mostly civilian field. By 1898, Russian schoolteacher Konstantin Tsiolkobvsky (remember that name, it'll be relevant later) began investigating using rockets for space exploration and, in 1903, suggested using liquid fuel in rockets and that a rocket's speed and range would only be limited by the speed of it's exhaust gasses. Soon after, American Robert Goddard started experimenting with his own designs, achieving the first successful flight of a liquid fueled rocket on March 16, 1926.

At the same time in Germany, Hermann Oberth was developing his own ideas about spaceflight. Inspired by the works of Jules Verne, his 1923 book Die Rakete zu den Planetenräumen ("By Rocket into Planetary Space") and the 1929 follow-up, Wege zur Raumschiffahrt ("Ways to Spaceflight") inspired the formation of rocketry societies worldwide. One such society, formed in Germany, would lead to the development of the V-2 rocket during the Second World War.

(Continued in next post because I feel like I should break up the history and design portions.)

[Byzesion]

In modern rocketry, the two main types of rocket are classified by the fuel system: Solid rockets and liquid rockets. The main difference between the two, besides the fuel composition, is how they control their thrust. To put it bluntly, solid rockets can't. Once a solid rocket is ignited, it burns until all the fuel is used up because the reaction chamber and the fuel storage chamber are one in the same. In a liquid rocket, the fuel is stored in two tanks above the engine where the fuel and oxidizer are combined and combusted, the exhaust flowing out the nozzle.


Solid Rocket


Liquid Rocket

The fuel used in the rocket is mostly dependent on the size of the rocket. Solid rockets can use anything from gunpowder in fireworks and hobby rocket motors to specially designed composites incorporating high explosives in industrial or military rockets, while smaller liquid rockets commonly use fuels like kerosene, gasoline, or alcohol and an oxidizer (commonly peroxide) and government or advanced commercial/industrial rockets use cryogenic fuels, usually liquid hydrogen and liquid oxygen.

Now, the big advantage to a liquid-fueled rocket is that it's able to control it's thrust. Instead of burning up all your fuel going flat out from the launch, you can control your burn, using as little fuel as necessary and ultimately achieving a higher altitude. This sort of controlled burn is ultimately what makes manned orbital flight possible. Without the ability to control thrust, the amount of fuel you'd need would be just too expensive to be practical. On the other hand, the advantage to a solid-fueled rocket is the fact that its thrust is immediate, and when the propellant is lit the thrust is consistent, which makes it ideal for tasks that require a lot of thrust over a short period, such as a booster for heavier liquid rockets.

And with that, onto the discussion questions:

The V-2 rocket was one of the most devastating weapons of the Second World War. After the war, however, captured V-2s were used as sounding rockets to send scientific instruments into the upper atmosphere. Why do you think they were used instead of solid-fueled rockets?

Pictured below is the Launch Escape System of the Apollo program's Command Module. Which type of rocket do you think would be more suited to this task?



Assignment: The Saturn V rocket uses liquid hydrogen as its fuel and liquid oxygen as its oxidizer. Given the difficulty of keeping these elements in a liquid state, why are they preferred for modern liquid-fueled rockets?

[Jin]

I don't see a picture below of the Apollo system

[Byzesion]

Sorry about that. I've edited the post to include it.

[Byzesion]

As always, let me call the roll before we begin. Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin.

Now, last week we covered some of the history of rocketry and designs of modern rockets. This week, we're going to start getting into the meat of the science, specific impulse and thrust. Thrust we're already familiar with, but the specific impulse, that's a new topic for us. Specific impulse is measured one of two ways: the thrust of the engine or the time that the engine will run, and the difference is how the propellant is measured. When the propellant is measured in terms of mass, that is to say matter not being acted on by a gravitational force, the specific impulse (or I_sp) is given as thrust, basically meaning "How fast can mass x accelerate itself?". When the propellant is given as a weight, in this case mass being accelerated by the gravitational constant 9.81 m/s, the I_sp is given as time, essentially saying "How long can mass x hold itself up, against the Earth's gravity?".

Note that a higher specific impulse doesn't necessarily translate to speed, just that it takes less propellant to give the craft a certain momentum. Ion engines, for instance, usually have an extremely high I_sp, but the thrust is less than an average box fan, which makes it ideal for correcting the course of an object outside of a planet's influence, but worthless for getting anything off the ground.

So now that we've established what specific impulse is, let's talk about how to find it. To find the specific impulse, you need to start with the total impulse. This is determined through engine testing and should be calculated by whoever's doing the test, but in case it isn't, it's calculated by adding the thrust generated at a series of intervals and multiplying that result by the interval. For a model rocket with propellant weighing .731 kilograms, generating 985 total kilograms of force, and measured in 0.1 second intervals, the equation for total force in Newtons would look like this:

F_Total = (985 * 0.1) * 9.81

and would give a total force of 966.285 Newtons.

In order to get the I_sp, you would then divide the force in Newtons by the weight of the propellant, and then by the gravitational constant 9.81, resulting in an equation that looks like this:

I_sp = (966.285 / .731) / 9.81

which results in an I_sp of roughly 135 seconds.

And so, only one discussion question for this week: The majority of rocket engines measure their specific impulse in seconds and therefore measure the propellant by weight. Why do you think that's done?

And this week's assignment:

1.) The engine design department has calculated the total force of a new design at 2,136,845.66 Newtons with an expenditure of 1,000 kilograms of fuel. Calculate the specific impulse of the engine in seconds.

2.) You're filling in in engine design. A re-test of an older model generated 95,382.0202 kilograms of force measured in two-second intervals. Determine the total force generated in Newtons.

[Byzesion]

Okay, Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin, we have a short week this week. No lecture, no discussion questions, and no assignment, just the midterm. Remember, we're off next week so classes will resume the week of the 20th. So until then, have a good break.

Midterm

Aerodynamics

1. Explain how a non-traditional (traditional being an enlongated teardrop on its side, blunt edge forward) airfoil shape can create lift at speed.

2. Explain how the following methods produce thrust:
a. Jet engine
b. Propeller engine
c. Rocket engine

3. Explain how the drag acting on a craft would change flying from a low pressure weather system into a high pressure system.

Rocketry

4. The first liquid fueled rocket was powered by a mixture of gasoline and liquid nitrous oxide. Why do you think these materials were used?

5. Explain the advantages and disadvantages of solid-fueled rockets.

6. Explain the advantages and disadvantages of liquid-fueled rockets.

Specific Impulse

7. Give a simplified explanation for specific impulse when it's given in seconds.

8. An engine generates 2,500,000 kilograms of force measured in 0.5 second intervals using 800 kilograms of fuel. Determine the force in Newtons and then the specific impulse of the engine.

9. Give an equation for finding the specific impulse using total force generated in kilograms, measurement interval, and mass of fuel used, without converting the force into Newtons.

[Byzesion]

Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin, welcome back. I hope you all had a good break. Today's subject is Δv (also written delta-v) or change in velocity. Where the I_sp measured how efficient a rocket engine is, the delta-v measures how far a certain amount of fuel will take you, or to put it another way, the I_sp is equivalent to the miles (or kilometers) per gallon rating of a car, and the delta-v is equivalent to how far a tank of gas will take you.

Now, the way we find the delta-v is by the Tsiolkovsky rocket equation, named after Konstantin Tsiolkovsky who independently derived and applied it to the idea of spaceflight. The equation can be expressed as

Δv = (I_sp * g₀) * ln(m0/m1)

or put another way, the product of the specific impulse and the gravitational constant (about 9.82 m/s²) times the natural log of the total stage mass divided by the dry (unfueled) stage mass. Let's say, as an example, you have a rocket with carrying a payload of two tonnes. The rocket is carrying 1.75 combined tonnes of fuel and oxidizer, and the unloaded fuel section weighs 0.25 tonnes. The engine has a specific impulse of 280 seconds and weighs 0.5 tonnes. The delta-v calculation would then be

Δv = (280 * 9.82) * ln(4.5/2.75)

and calculating the natural log results in

Δv = (280 * 9.82) * 0.4925

Now, multiplying the I_sp and the gravitational constant gives us

Δv = 2749.6 * 0.4925

giving a total delta-v of

Δv = 1354.178

This isn't nearly enough to make it to low Earth orbit, but might be enough for a small sounding rocket carrying equipment to measure climate data. A valid question to ask at this point is "Well, that's all well and good for single-stage rockets, but what if you have a multi-stage rocket?" That's a simple enough matter - you calculate the delta-v for each stage separately and then add them together.

As an example, let's take that last rocket and slap a couple of solid rocket boosters on it.

So, in the first stage, you have a pair of solid rocket boosters with a specific impulse of 175. The solid fuel for each weighs 7.65 t and the booster itself is 1.35 t. Each one is attached to the main rocket by a separator weighing 0.15 t each. And each one has an aerodynamic nose cone weighing 0.03 t each. Therefore, stage one weighs 18.36 t, bringing the total rocket weight up to 22.86 t. And the stage one delta-v calculation looks like this:

Δv = (175 * 9.82) * ln(22.86/7.56)
Δv = (175 * 9.82) * ln(3.024)
Δv = (175 * 9.82) * 1.107
Δv = 1718.5 * 1.107
Δv = 1902.3795

Now the rocket has a total delta-v of 3256.5575 m/s². This still isn't enough to get to LEO, but will get you much higher in the atmosphere. But, you may be asking or may not, what if you have engines that don't have the same specific impulse in a stage? Simple enough, you just take the average of the specific impulses. Let's have another example, shall we? Instead of having two SRBs, let's instead just slap what amounts to two more rockets on either side of the main, but these rockets have thrust vectoring engines that lower their specific impulse to 270 seconds. The fuel tanks are identical to the main rocket, carrying 1.75 t of fuel and weighing 0.25 t empty. The thrust vectoring engines weigh 0.6 t each, and each tank has a 0.03 t nose cone. The delta-v equation now looks like this:

Δv = (((280+270+270)/3) * 9.82) * ln(9.76/4.51)
Δv = (273.33 * 9.82) * ln(2.164)
Δv = 2684.101 * 0.772
Δv = 2072.126

The last important thing to consider when creating a delta-v budget is always budget for more than you think you'll need. Rockets are, at their core, incredibly complex machines. Things happen. Engine misfires, faulty wiring, fuel and oxidizer pumps not working correctly...there's a lot that can go wrong. So take a little extra fuel in case you need an emergency burn.

Okay, so that about covers the main points of delta-v. Here's the discussion question for this week: In the examples above, the single-stage, three engine design has a higher delta-v than the original rocket, but not as much as the two-stage, SRB aided rocket. Why do you think that is?

And this week's assignment: Determine the delta-v of a rocket carrying a payload of 6 t, using a fuel tank weighing 4 t empty and a combined 32 t of fuel and oxidizer, aided by two smaller 0.5 t empty fuel tanks and 4 t of fuel. The main rocket uses an engine with a specific impulse of 285 seconds and weighing 6 t. The assist rockets use engines with specific impulses of 270 seconds each and weighing 1.5 t each. Each assist rocket has a nose cone weighing 0.03 t.

[Byzesion]

As always, let me call the roll: Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin. First, I have an announcement. From here on out, all assignments and discussion questions are dropped, and the final exam is cancelled. Getting to orbit is much more complicated than staying in orbit or coming down from orbit. After all, as Robert Heinlein said, "Once you're in orbit, you're halfway to anywhere."

Being in orbit, however, is not the same thing as orbiting. This may sound contradictory, so let me explain. Once you leave Earth's atmosphere, you're technically in orbit. You have reached hard vacuum, and if you open the door without a pressurized suit, things are going to get real shitty real quick. But because you aren't orbiting, you're going to have a limited time in orbit for whatever experiments you need to conduct. Orbiting, by contrast, is when your entire trajectory is outside the atmosphere. Or to simplify: orbit is a specific point, orbiting is a series of points that forms a trajectory.

The question to tackle now is how do you go from orbit to orbiting, and the answer is you conduct a burn, specifically a circularization burn. Before we get to what exactly that is, there's a bit of vocabulary that needs covering. There are two critical points in an orbit, and there are six cardinal directions that a burn can be performed in. Seeing as all can be represented as four opposing sets, that's how we'll take them.

First and most important are Apoapsis and Periapsis. The apoapsis is the highest point in a trajectory and the periapsis is the lowest point. After a launch, the apoapsis will be somewhere in the upper atmosphere or (if all goes right) outside the atmosphere, and the periapsis will be on the ground. In an orbital trajectory, the the apoapsis will be the point farthest away from the body's surface and the periapsis will be the closest point.

Second, and almost as important, are Prograde and Retrograde. Put simply, prograde is pointing the nose of your craft the direction you're moving and retrograde is pointing the rear of your craft the direction you're moving. A prograde burn is used to increase your speed and thereby your orbit and a retrograde burn is used to decrease your speed and orbit.

Next is Normal and Anti-Normal. Normal and anti-normal burns are used to change the inclination of the craft, or put another way, the degrees off of the equator the craft is. A normal burn will increase the inclination (moving the orbit path north of the equator) and an anti-normal burn will decrease the inclination (moving the orbit path south of the equator).

Finally, there's Radial In and Radial Out. Radial burns...well, they're kind of hard to explain. The easiest way I can think of is to imagine that you have a metal hoop welded to a barrel hinge, which is placed on a rod. Welded directly across from the hoop is a small handle. The hoop represents the orbital path, the hinge represents the craft, and pushing one way or the other on the handle represents the radial burn. Maybe this image will help.



To perform an outward radial burn, your craft should be pointing away from the body you're orbiting - this will shift the orbital path in the prograde direction, like pushing the handle in the picture above to the right. An inward radial is similar, only pointing towards the body and will shift the orbital path towards the retrograde direction.

Now that we've defined our terms, we can talk about a circularization burn. The goal of this burn is to circularize the orbital path, or in simpler terms, get the apoapsis and periapsis as close to each other as possible (in terms of distance above the body). This is usually done soon after launch, but can be done on the return leg of a trip to prepare for reentry. In order to circularize an orbit, you perform a prograde burn near the apoapsis until they match, or as close as you can get.

Of course, once you're up there, you have to get back down, and that requires a reentry burn. A reentry burn is performed by burning retorgrade until the periapsis touches the surface. The key here is to hit the right angle: too low and you'll bounce off of the atmosphere, too high and the capsule will burn up on entry. This picture should spell it out pretty well.



If you don't have a heat shield or parachutes on the capsule, the whole reentry question becomes kind of moot. At that point, all you can really do is leave them up there until you can launch a rescue mission to rendezvous with the capsule, a maneuver that we'll cover next week.

[Byzesion]

Roll call! Baden-Wuerttemberg, Louisistan, Ater Nox, Flemingisa, Scottish and English Kingdom, Jin. Well, today's the final class, and the subject is orbital maneuvers. Put short, there are two basic types of orbital maneuvers: Transfers, where you go from orbiting one body to another, and Rendezvous, where you're trying to catch up to a body in the same orbit.

That should about cover it. I hope you've enjoyed the class.

[Byzesion]

No, I'm kidding. All the detail I've gone into in the last six weeks, I'm not going to end it like that. What I will do is go into as much detail as I can without overcomplicating the matter.

Okay, so transfers. Let's say that you're in orbit at 110,000 kilometers and you want to get to the moon. Also let's say, just for fun, that it's Labor Day weekend. Transferring to an orbit around the moon would, in fact, be less frustrating than trying to go somewhere for Labor Day.

The most common type of orbital transfer is called a Hohmann transfer. In a Hohmann transfer, you burn prograde until your apoapsis is around the distance of the target body or the target orbit. And then you wait until you reach that new apoapsis and then circularize with another prograde burn. There is another common transfer, called a bi-elliptic transfer, which is similar to the Hohmann transfer, except that instead of circularizing at the apoapsis, you burn slightly prograde until your periapsis is at the orbit height you want, wait to reach periapsis, and burn retrograde to circularize.

To be fair, while the bi-elliptic is more complicated, in some cases it's more efficient as far as the delta-v budget is concerned. Personally, I don't feel a one or two percent savings really justifies the extra time, but I'm not a professional rocket scientist, just an enthusiastic amateur.

That brings us to rendezvous. If you can put your spacecraft up exactly where you need it to be, then good on you. Most of the time, however, a rendezvous will require that your either catch up to your target craft or let it catch up to you, and the simplest way to do this is to change your orbit.

If your target is ahead of you, you'll need to go faster than it and as such will need to be in a lower orbit. If you're ahead of the target, however, you need to jump into a higher orbit and take more time to let it catch up. Once you're within about a few hundred meters or so, you can conduct an approach burn by pointing your craft at the target and do a quick burn, just enough to push you in the right direction.

Most of the time, this is done with a reaction control system rather than full engines. A reaction control system is a series of nozzles connected to compressed gas. When RCS is activated, a jet of this gas puffs out, which is plenty to move the craft in microgravity. It's a little more controllable than a full thruster and has a lower chance of a fatal, international incident causing crash.

Well, I hope you've enjoyed the class. If you have any questions, feel free to ask.

[Ater Nox]

Thanks Byzesion. My question is, does the decision to either increase or decrease your orbit to catch up to another object purely rely on how far away it is from you (i.e. closer to being in front or behind)? Is either choice quicker or more efficient?

[Byzesion]

Good question, Ater Nox. The distance from the target is really the thing that matters. Here, let me give you an example:

Say you have a space station in orbit at about 90 kilometers. Your resupply and restaff ship is orbiting at about the same height, but the station is about five kilometers ahead of you. The most efficient way to catch up would be to lower your orbit a little bit, because it puts you on a shorter orbital path so you'll take less time to complete an orbit than the station. You could increase your orbit, but it would take longer because you'd essentially be waiting for the station to lap you

Just the opposite goes for if you're out in front of the station. You want to have a longer orbital path to make it easier for the station to catch up with you. And if the station's on the opposite side of the planet from you...flip a coin, I guess. Actually, personally I'd go with a higher orbit so there's less of a chance of de-orbiting accidentally.