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The problem with such tools is that they may be considered a national security risk as the principles are similar to those of missiles. However, there are excellent Master theses and PhD dissertations on the topic of optimal control for landing rockets, such as this MSc thesis and this SpaceX paper. These will explain the equations of motion and part of the ...


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Your intuition is quite correct. The Hohmann transfer orbit is a bi-tangential orbit, so at the point where the spacecraft leaves Earth, it is travelling in parallel to us. In the case of Mars, we want to travel slightly faster than the Earth in order to lift our aphelion up to the orbit of Mars, meaning we want a little extra velocity on top of the prograde ...


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