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.
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.
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