This is laying out the system of equations for aircraft flight. It is using a reference frame of stationary with respect to the aircraft to make the calculations easier. This is a very common reference frame for setting up equations of motion because it can, in many cases make the math a whole lot easier. This is especially true for a rotating frame or a spherical frame. The Earth happens to be both.
Once the equations of motion are laid out in one reference frame they can be described in any reference frame using a transformation matrix that describes the transformation (changing the point of view of the equations) to the reference frame of choice.
In this starting case, the reference frame is one where the earth is flat and non-rotating. To translate it to another reference frame, such as a spherical rotating reference frame one would run the equations in this document through a transformation matrix that described such a change of reference frame. The resulting equations btw would be a nightmare, but laying them out in this easier reference frame first, makes life a whole lot easier for people to communicate with each other.
If someone STARTED their paper with the equations in a spherical rotating reference frame and it was my job to read their paper I would leave my office, go down to the author's office and shoot them, just so that they would hire someone else.
That's not what I said at all. But yes, I do. Being able to read math (or really in this case physics) is just like reading any other language. It takes time and practice to learn it.
This is why these things get so much traction. That document/picture asks all the wrong questions, making so many false assumptions, that have nothing to do with physics. Going through the whole thing is far too much work, there are so many errors, but I will do a couple to help you understand what I mean.
Does lunar lander look like it could launch off the moon and intercept and dock with the lunar orbiter?
Your answer was "Not really."
The real answer is, it's an absolutely nonsense question. What does it mean to "look like" it can do something? It either has enough fuel, and efficient enough rockets to do what it needs to do or it doesn't. That would be determined by calculation, not by visual inspection. Even the answer given was not definitive, but one of biased guessing because there is no way to actually answer it. There are several nonsense "leading" questions in there designed to manipulate bias.
Have you ever tried to park a vehicle in a garage while driving at 3500 MPH?
3500 MPH relative to what? The orbiter and the landing vehicle were going at the same speed (or close enough) when they docked. When a rocket takes off it doesn't go straight up, it follows a curved path, which means as it accelerates its direction changes. This launch to a particular orbit (the orbit the orbiter vehicle was in) was done by launching at a slight angle, so gravity pulling down changed the total path into a curve with respect to the starting condition on the moon.
These questions make this mistake a ton, not taking into account what travel in a gravity well is actually like. Like this one:
If satellites are travelling so fast that they "fall around" the Earth in an orbit...
This is not the best way to look at orbit paths as it creates a lot of false ideas. It is better to think of an orbit as an equipotential. Think of a round hill. If you travel around the hill you can go all the way around without going up or down. If there is no friction, and you have path, you can go around the hill forever without any energy expenditure.
If a rocket is travelling at 25,000 MPH and cuts its engines, would you expect the rocket to "coast" uphill to the Lagrange point for another hour?
Similar to the equipotential around the hill, a rocket will travel in a curved path which could be an equipotential. Regardless of the path this rocket took, it travelled in a curved path that was not "uphill" even if it was not an equipotential. Just like a car going up hill that you take your foot off the gas, the car can in fact coast up the rest of the way if it had enough kinetic energy to overcome the remaining potential energy it would gain by attaining the top of the hill. In every case the car, or the rocket, will follow the path of least energy required to get there (similar to an equipotential curve, though including an exchange of its initial kinetic energy to the potential energy it gains as it goes up the potential well). These paths are calculated, they aren't difficult, and every physics student calculates them. They are done all the time.
There is no voodoo here. This is not complicated stuff. That questionnaire asks a lot of the wrong questions in a way that confirms bias without addressing actual physics. It takes the familiar physics (what we experience on Earth) and applies it to orbital mechanics or more specifically, rocket science. While those things are related, they are not the same. They require different equations, and a better understanding of a curved space. Its a very similar problem to the difficulties some people are having in this particular paper interestingly. Thinking that things that work in flatland, apply to curved land.
To elaborate a little bit:
This is laying out the system of equations for aircraft flight. It is using a reference frame of stationary with respect to the aircraft to make the calculations easier. This is a very common reference frame for setting up equations of motion because it can, in many cases make the math a whole lot easier. This is especially true for a rotating frame or a spherical frame. The Earth happens to be both.
Once the equations of motion are laid out in one reference frame they can be described in any reference frame using a transformation matrix that describes the transformation (changing the point of view of the equations) to the reference frame of choice.
In this starting case, the reference frame is one where the earth is flat and non-rotating. To translate it to another reference frame, such as a spherical rotating reference frame one would run the equations in this document through a transformation matrix that described such a change of reference frame. The resulting equations btw would be a nightmare, but laying them out in this easier reference frame first, makes life a whole lot easier for people to communicate with each other.
If someone STARTED their paper with the equations in a spherical rotating reference frame and it was my job to read their paper I would leave my office, go down to the author's office and shoot them, just so that they would hire someone else.
hmm, so what you are saying is that pilots are too stupid to understand the math, but you do?
That's not what I said at all. But yes, I do. Being able to read math (or really in this case physics) is just like reading any other language. It takes time and practice to learn it.
yeah, it took me a couple of years to do the math...
most people can't get past question 4 without resorting to a thought-terminating cliche
https://i.redd.it/g287hbmcb94z.png
This is why these things get so much traction. That document/picture asks all the wrong questions, making so many false assumptions, that have nothing to do with physics. Going through the whole thing is far too much work, there are so many errors, but I will do a couple to help you understand what I mean.
Your answer was "Not really."
The real answer is, it's an absolutely nonsense question. What does it mean to "look like" it can do something? It either has enough fuel, and efficient enough rockets to do what it needs to do or it doesn't. That would be determined by calculation, not by visual inspection. Even the answer given was not definitive, but one of biased guessing because there is no way to actually answer it. There are several nonsense "leading" questions in there designed to manipulate bias.
3500 MPH relative to what? The orbiter and the landing vehicle were going at the same speed (or close enough) when they docked. When a rocket takes off it doesn't go straight up, it follows a curved path, which means as it accelerates its direction changes. This launch to a particular orbit (the orbit the orbiter vehicle was in) was done by launching at a slight angle, so gravity pulling down changed the total path into a curve with respect to the starting condition on the moon.
These questions make this mistake a ton, not taking into account what travel in a gravity well is actually like. Like this one:
This is not the best way to look at orbit paths as it creates a lot of false ideas. It is better to think of an orbit as an equipotential. Think of a round hill. If you travel around the hill you can go all the way around without going up or down. If there is no friction, and you have path, you can go around the hill forever without any energy expenditure.
Similar to the equipotential around the hill, a rocket will travel in a curved path which could be an equipotential. Regardless of the path this rocket took, it travelled in a curved path that was not "uphill" even if it was not an equipotential. Just like a car going up hill that you take your foot off the gas, the car can in fact coast up the rest of the way if it had enough kinetic energy to overcome the remaining potential energy it would gain by attaining the top of the hill. In every case the car, or the rocket, will follow the path of least energy required to get there (similar to an equipotential curve, though including an exchange of its initial kinetic energy to the potential energy it gains as it goes up the potential well). These paths are calculated, they aren't difficult, and every physics student calculates them. They are done all the time.
There is no voodoo here. This is not complicated stuff. That questionnaire asks a lot of the wrong questions in a way that confirms bias without addressing actual physics. It takes the familiar physics (what we experience on Earth) and applies it to orbital mechanics or more specifically, rocket science. While those things are related, they are not the same. They require different equations, and a better understanding of a curved space. Its a very similar problem to the difficulties some people are having in this particular paper interestingly. Thinking that things that work in flatland, apply to curved land.
Kek.