Rocket Science & Engineering with Vithu — Part 02: Introduction to launch trajectories
Hello, there!
I am glad to start with another topic in this series. Previously I discussed the basics of Rockets & Orbits in part 01. Here, I will be going through the trajectories of a Rocket launch.
So, let’s get started with the basics. First of all, we need to understand that there are two main trajectories to be considered when it comes to a Rocket launch. As we already stated that the launch will be on a particular radius to create a parabolic motion that leads the vehicle into orbit. And that’s what we call orbital trajectory and if the parabolic motion created by the launch doesn’t reach orbit rather it falls again towards the Earth surface like a projectile motion and hits back Earth surface its suborbital trajectory. But, suborbital trajectories could be higher or lower than orbital trajectories.
Here we will be mainly focusing on the orbital trajectories. Before I get into the core theory of orbital trajectories, I would like to clarify a misconception among people. That is people think that on the LEO and above the objects & human doesn’t realize the weight because of zero gravity. which is not true. Just think about it in this way, if the people in the LEO don’t have the gravity of Earth how come to the moon which is way far away is still in the gravity of Earth. so gravity is there but the point is the gravity of the Earth at LEO is not working towards the center of the Earth, it’s just a free fall in the orbital. Because it’s a free fall you are not feeling the weight. To experiment with things like these, there are some ways of replicating the scenario by a normal aircraft such as a passenger flight. It’s like flying away from the Earth's surface and suddenly stopping the flight engine, so it becomes a free fall. therefore, people inside the flight will feel a similar experience as space. If you are interested in knowing more about this effect you can have a look at the research paper in the further learning section.
Now let’s get back to the main discussion point. Another important thing you need to know is about the escape velocity. According to the gravitational laws every plant has its own escape velocity which is the minimum velocity to escape from the gravitational force towards the center of that planet and reach the orbit. For Earth, it’s 11.2Km/s. but for the moon, it’s only around 2km/s. why it’s easy and do you need less propellant to launch from the Moon’s surface where for the Sun it’s more than 600Km/s which is almost impossible to leave the solar system as of now.
The next important part you need to know is the stages of the Rocket and the burns until it reaches Orbit. Basically, Rockets are separated into multiple stages just because considering the efficiency, I will describe more about that when we go into the discussion of propellant and efficiency. for now, what you need to understand is the initial stage which helps for the take-off and the initial thrust will be a solid engine most of the time. again it’s considering the efficiency. and at one point after all the propellant got burned the main engine will be turned off. this is known as Main Engine Cut Off (MECO). at this point, the velocity of the Payload reached so-called burnout velocity. So there it’s like a free fall.
Then from MECO, there will be some additional burns if required for the Orbit insertion. So, when once the burnout velocity reaches 11.2 km/sec, the Rocket trajectory downrange distance becomes equal to the diameter of the Earth. Therefore, it gets into Orbit. One important note here is a real launch the burn-out velocity would not be equal to the escape velocity. There are so many factors that impact this. I will be discussing those in-depth in an upcoming part of this series and I guess I have gone through the basics of the trajectories which would help you to get into the depth of it. In the next part of this series, I will be focusing on practical explanations for launch trajectories with the help of applied mathematics & projectile motion equations.
Further learnings
Projectile motion effect on flights: https://www.researchgate.net/figure/Aircraft-ballistic-free-fall-trajectory-approximated-as-an-arc-of-a-parabola-in-a_fig2_256935400
Main Engine Cut Off:
https://www.researchgate.net/figure/9-Schematic-engine-thrust-profile-upon-main-engine-cut-off-signal-MECO-the-thrust_fig9_292103815Trajectory optimizations:
https://core.ac.uk/download/pdf/25829426.pdf
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