Rocket Trajectory and Reaching to orbit
Rocket Trajectory: Let’s understand in 3 parts.
Part 1: Why do rockets follow a curved path? (Also covered in Instagram post).
Short answer: Less fuel usage to get into the orbit around the Earth.
Long answer: We know that the air density of the atmosphere decreases upwards. At the start, the rocket needs great energy to overcome air resistance and gravity, so that it attains enough altitude when most of its fuel is used up. Hence, it flies vertically up very fast to cover the least distance in the thickest part of the atmosphere.
Now the rocket’s aim is not just to escape Earth’s gravity but more importantly it wants to enter Earth’s orbit and stay there. That sweet spot ensures the gravitational pull of the Earth is high enough to keep the rocket from drifting off into outer space; and low enough so that the rocket doesn’t have to spend fuel to keep itself from plummeting back to Earth.
The tilt is gradual until an elliptical orbit is achieved. This technique of optimizing the trajectory of a spacecraft so that it attains the desired path is called a gravity turn or a zero-lift turn. This has two advantages:
1. Rocket maintains a very low or even zero angle of attack during the early stages of its ascent, thereby it experiences less aerodynamic stress.
2. The rocket uses Earth’s gravity to change its direction, and hence a certain amount of fuel is saved. This fuel can be used to accelerate it horizontally, in order to attain high speed, and more easily enter the orbit.
Part 2: How orbit is reached?
Reaching an orbit while may appear complex but is fundamentally as simple as throwing a stone. Check the figure below.
When you throw a stone it lands at A. When a wrestler throws it, it reaches B. And when SpaceX throws it via Falcon 9, it reaches the orbit C and when it uses Falcon Heavy it reaches orbit D. What this means is, a rocket is similar to projectile motion just that its range is optimized in such a way to “keep missing” the earth always. In a way a rocket (or a satellite) is “always falling — always missing” from the earth. Also, once an object is in orbit, it doesn’t need any sort of propulsion to remain in the orbit.
So, how fast you need to throw the stone? Well, one of the methods (and the one which confuses many) is related to escape velocity. If you are able to throw an object (irrespective of mass) with velocity 11.3 km/s at an angle of 45 degrees, it will escape the earth, assuming negligible air drag. Now, this doesn’t mean that an object thrown with lesser velocity cannot escape earth. (Think why?)
Part 3: How an orbit is changed?
Each orbit is an “energy level” in 3D space. Shifting from one orbit to another requires this energy changes which is correlated to a term commonly heard in this field of rocket science as Delta — V (Pronounced as Delta — Vee, V for velocity)
Here each velocity represents the orbital velocity needed at a particular orbit of radius r and “mu” is the product of Gravitational constant and Mass of earth. The difference in the velocities at any two orbit is the required “Delta-V” needed to be imparted for achieving the desired orbital placement.
