Conclusion

Over the course of this blog series, we discussed the nature of human spaceflight as it exists today, which can be broken up into four major categories.  Ascent from a planets surface, maneuvers in orbit near a planet, transfer trajectories to the moon(s) of this planet, and interplanetary transfers which can vary significantly in complexity.  We will take this page to briefly recap everything that we covered here.  The ascent phase is one the most critical because, as mentioned, we cannot as yet produce spacecraft in space.

The ascent phase amounts to boosting into a fast enough trajectory that you never reach the ground.  In practical terms, this means leaving the atmosphere so that drag doesn't eventually slow you down and pull you down to the surface.  Therefore, one of the first steps is accelerating almost directly upwards to leave the thicker parts of the atmosphere.  The rocket then begins a turn which eventually leads to it burning sideways, in order to establish its trajectory.  It was noted that getting to orbit quickly is efficient, because you can spend less time fighting gravity.  Building up your sideways velocity is reserved for after you are most of the way out of the atmosphere so that you can build up lots of speed without burning up or being torn apart by atmospheric forces.  Once you have gotten away from the atmosphere, its a free run to orbit.

Orbit itself in this context refers to the space relatively close to Earth, or whichever arbitrary planet you have picked.  In general, whatever you want to do that doesn't involve orbiting some other object.  We discussed the principles behind how to perform a number of maneuvers.  This included raising and lowering your apoapsis and periapsis, rendezvous with another spacecraft or object, and inserting yourself into a formation.  We also explained the general concept of Earth-Sun Lagrange Points.  This wasn't a complete picture, but it covered a lot of the basics.

We then built on these concepts with the idea of transferring to a planet's moon.  We discussed how this in many ways amounts to a rendesvous with another spacecraft.  Very similar, except for the fact that as you approach the moon, its gravity begins to influence your trajectory.  We talked about the fuel savings associated with a 'suicide burn', which is somewhat similar to the reasoning behind flying very fast during the ascent phase.  It was also noted that inserting yourself into orbit around a moon is very similar to lowering your apoapsis during an orbital maneuver.

Next we discussed the basics of interplanetary transfers, and how they bear some resemblance to planet-moon transfers.  There was the idea of an escape trajectory, and how that in its barest form amounts to a co-orbit with the Earth.  Once in a co-orbit, you can essentially transfer to any planet in the system as if you were transferring to one of the Earth's moons.  In this case, one of the Sun's moons.  We noted how the point where you start your transfer burn could be seen as your launch window, and the ideal time to start your mission if you want to avoid months waiting around in space.  Finally, it was noted that settling into the orbit of another planet is very similar to settling into the orbit of a moon.

Finally, we discussed some of the more advanced techniques that could be used to achieve interplanetary transfers.  You can achieve orbit, or even a direct landing via aerobraking, where you intentionally descend into a planets atmosphere in order to slow yourself with the air drag.  Gravity assists were explained, although not as rigorously as previous concepts.  Lastly, we roughly characterized a continuous thrust trajectory, as well as why they exist.

All of these concepts combined give you a rough picture of what human spaceflight looks like today.  We launch our craft into orbit from the surface, and then perform various missions.  Perhaps we want to fly to the international space station, or build a constellation of sattelites.  Alternatively, we may want to fly to the Moon and insert ourselves into orbit, perhaps deploying landers.  Lastly, we may want to travel to another planet in our solar system.  There are many techniques we can use to make this cheaper.  This has been a long time hobby of mine, and I learned a lot while studying in order to write these blog posts.  I enjoyed making them, and hope you enjoyed reading them, at least to some degree.

Advanced Interplanetary Transfer

There are several techniques I would like to discuss that allow you to put together more sophisticated interplanetary transfers.  Not all of them can be reasonably described in terms of the previous post (basic interplanetary transfers).  Nevertheless I would like to characterize them as well to some degree.  First I will discuss aerobraking, then gravity assists, and finally continuous thrust trajectories that came with the advent of ion drives.

Aerobraking is the general process of reducing your velocity relative to a planet for free.  Free here meaning you don't have to spend fuel in the process.  The big downside is you need protection from the atmosphere of some kind unless you are performing a relatively gentle maneuver.  The concept of aerobraking is diving into a planets atmosphere, and using the drag in order to slow yourself down.  The atmosphere of a planet is effectively stationary relative to a planet, so it will keep trying to slow you down until you have effectively stopped relative to the planet.  In actuality, it is stationary relative to the surface of the planet, so it will effectively have some velocity.  This can be used to lower the apoapsis of your orbit, via principles discussed previously, or it can be for the purpose of leaving orbit entirely and landing on the surface.  In general the amount of velocity you bleed off is related to how close you come to the surface of a planet in the process.  Aerodynamics is extremely complex, so the amount of speed it is possible to bleed off can vary significantly.  Different spacecraft will get different results.

I don't have quite as satisfactory an explanation for gravity assists.  I will try to lean on your spatial intuition to give you some kind of idea.  Imagine you are riding a bike into a valley, as pictured below: 

You could expect yourself to come out the other side of the valley at more or less the same speed.  Now imagine that the valley is moving forward at a substantial speed as you come into it.  Gravity is strong enough to keep pulling you to the bottom of the valley, but you can feel the valley pulling you forward.  By the time you reach the other side you have gained a bunch of speed from the movement of the valley.  This is basically how a gravity assist works.  You may have seen a diagram like this before (credit AllenMcC from wikipedia):

These are actually a pretty good metaphor for the effects of gravity.  A cross section of that would resemble a valley.  Travelling through that gravitational valley while Jupiter is moving around the sun allows you to pick up quite a bit of speed.  Jupiter has been a common target of gravity assists, and by the law of conservation of energy is actually slightly slowed by every spacecraft that has utilized it.  The amount of energy that Jupiter loses (and the amount that you gain) is equal to the gravitational effects of your spacecraft on the entire mass of Jupiter.  A reverse gravity assist if you will.  Jupiter is immense, so this amounts to quite a bit of energy that you are gaining.

The general utility of this sort of maneuver is that you can get some free forward velocity to throw you onto a higher orbit on your way to your destination.  As to how exactly you would go about making use of that, that is a much more complicated question.  It doesn't really map to the more simplistic stuff we discussed earlier.  I'll close this section out with a diagram of the probe Rosettas trajectory, which made use of multiple consecutive gravity assists over the course of its ten year flight.  (courtesy of the ESA)

The last thing that I wanted to discuss was a continuous thrust trajectory.  Out of all of them it is probably the most alien to what we have discussed previously, in some ways.  The trajectories overall resemble a basic interplanetary transfer, due to the excess of fuel that tends to be available (relatively few gravity assists and such).  Ion drives have until recently been something of a fictional technology.  Very high specific impulse, but very low thrust.  Due to the low thrust, you have to fire your engines continuously for a long time in order to reach escape velocity and eventually ascend (or descend) to your destination.  The reason this low thrust is considered tolerable is because of the specific impulse factor that I have mentioned.  Imagine you are sitting on a skateboard and have three basketballs at your disposal.  You want to get moving, and in this example can only propel yourself by throwing the basketballs.  Will you choose to throw them really hard, or will you gently toss them in order to get yourself moving?  The answer will probably be throw very hard.  This is the general idea behind high specific impulse.  Ion drives throw the fuel very very hard (at very high speed, at least compared to rockets), so you need less fuel in order to change your speed by a certain amount.  The only downside is they can't throw lots of fuel at once, so there is relatively minimal thrust.  You might be throwing basketballs really fast, but the multi-ton probe is hardly budging.  The physical reason this works is because of the idea of impulse and momentum.  When you throw something, you impart a certain momentum.  The mass of the object multiplied by its speed.  That momentum gets transferred back to you in the opposite direction per Newtons Third Law.  The higher the speed, the more momentum you gain.  This allows spacecraft to get a lot more momentum out of their fuel and do a lot more maneuvering over the course of their missions.  The downside of the low thrust is that it greatly complicates entering and leaving gravity wells.  Dwarf planets and asteroids are generally easier to deal with as far as that goes.

I implied that Ion drives entered use at some point.  The recent Dawn mission utilized Ion drives, and was able to pack enough fuel to visit two dwarf planets over the course of its mission, entering into orbit of both (rather than a measly flyby).  Ceres and Vesta, if you were wondering.  You can look up lovely high resolution maps of both planets because of that mission.  Here is a diagram of its continuous thrust trajectory, courtesy of NASA:

As you can see, the thrust wasn't entirely continuous, but it most definitely was not freefall.

To recap, we discussed the concept of aerobraking.  Diving into an atmosphere to reduce your velocity relative to a planet, specifically relative to its surface.  The idea of a gravity assist, as well as a metaphor to describe how it allows you to gain speed.  Finally, continuous thrust trajectories were described, as well as the reason that they exist.

Basic Interplanetary Transfer

The basis of traveling between two planets can be broken into three main concepts.  Escape from the gravity well of your starting point, adjusting your trajectory to intercept your destination, and capturing yourself in your destinations gravity well.  This will be building on concepts from previous blog posts.

We will first discuss the idea of inserting yourself into an escape trajectory.  We will assume that you are starting in orbit of the earth.  An escape trajectory essentially amounts to raising the apoapsis (peak altitude) of your orbit to some altitude where the Earth's gravity is negligible.  In other words, putting yourself onto a trajectory where you have escaped the Earth's gravitational influence.  Once you start to approach your apoapsis on this escape trajectory, the Earth will definitionally stop influencing your velocity (and therefore trajectory).  Imagine that you have given yourself just enough velocity to reach this point.  You have come to a standstill just as Earth's gravity has lost its grip on you.  This leaves you in a co-orbit around the Sun on almost exactly the same trajectory as the Earth.  Indeed, for all intents and purposes you are orbiting the Sun and are preparing to travel to one of its moons.

This leads to the second part of the post, creating an intercept trajectory.  Lets assume you want to travel to Mars, since it is in a higher orbit around the Sun than the Earth is, allowing for a direct analogy to the previous post.  Just like when you were flying to the Moon in the previous post, there is a certain point in your orbit where you want to accelerate in the prograde direction so that you can intercept your destination.  This point is what is generally referred to as a launch window.  For a direct flight to Mars (we will discuss less direct methods of travel in the next post) the ideal time to launch your spacecraft is when the Earth is in that position.  This is because, as described earlier, you are on a trajectory that leaves you stationary relative to the Earth.  If you are effectively at the Earth, then you may as well leave your spacecraft on the Earth until you are ready to immediately start flying to Mars, rather than sitting for months or years in your co-orbit waiting to start your flight.  There is less time for things to break, and in the case of manned missions, you don't need to bring as much food and various assorted life support.

In this situation you would launch once the Earth is in position to allow an intercept with Mars, escape the Earth, and then perform the intercept burn in order to travel to Mars.  This is not, however, exactly how it is done.  Frequently there is what is called an 'ejection burn', where you accelerate onto an escape trajectory, and then keep accelerating until you have achieved an intercept trajectory with your destination.  This is essentially combining the two steps into one long acceleration burn.  This is for various reasons more efficient.  I wont explain every reason, but I will try to explain one of them.

A strange artifact of physics is that it is more efficient to fire your engines deep within a gravity well.  That is to say, it generates more mechanical energy than otherwise.  This is called the Oberth Effect.  The basis of the theory is the equation dictating how much energy you gain when accelerating.  The energy you can is equal to force times distance (W = F*d).  Your engines generate the same force no matter what, and over a certain period of time use the same amount of fuel no matter what.   So more distance over the same period of time means you get more energy for the same fuel.  How do you do that?  Well, you need more velocity.  You could imagine your spacecraft in its co-orbit, stationary relative to the Earth, vs it having all of the Earth's velocity plus whatever velocity it needs to stay in orbit around the planet.  This can lead to much higher speeds.  Therefore, it is more efficient to perform your intercept burn while close to the Earth, since gravity is leeching away your precious velocity as you climb out of the gravity well.  Using this concept, it is sometimes possible to gain more energy than the chemical energy stored in the rocket fuel.  This somewhat surreal fact allows for more efficient travel between planets.

Once you have achieved your basic interplanetary transfer trajectory, the final phase is to capture yourself in the orbit of the destination planet.  This essentially amounts to an escape velocity burn in reverse.  You will arrive at Mars at well over the escape velocity for the planet, and will carry on past it unless you do something.  This generally amounts to a retrograde burn in order to bring your apoapsis down to within the gravity well of Mars, much like a transfer to the Moon from low orbit.  Typically you can achieve this with your engines, although this is not the only option.  At this point you have successfully reached Mars, and can perform whatever mission you went there to carry out (building a space-cabin on Mars, perhaps).

To recap, we discussed the concept of an escape trajectory, and how this allows us to re-use the idea of planet to moon transfers for planet to planet transfers.  We then discussed the Oberth effect, and how this encourages us to complete our intercept burn while still close to the Earth, rather than taking things slowly by first escaping from the Earth and then setting up our intercept trajectory.  Finally, we talked about achieving orbit around Mars.