ELI5- Can someone the physics behind Zero-G flights (Parabolic flight) ?
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I can’t explain parabolas without algebra, so this will be closer to eli 15, but I’ll try and limit it as much as possible. Basically, there are only 2 things about algebra that you need to understand. I will use letters a, b, c, and t to represent numbers that I don’t know. The important one is t. The number that t can represent is allowed to change, so we have to pay more attention to it. a, b, and c all stay the same, so we can *almost* ignore them.
A parabola is just another term for a degree-2 polynomial. Polynomials can come in many different degrees. Poly means multiple. This means there can be multiple terms in the equation. Doing as little math as possible for eli5, there’s a variable multiplied by itself some number of times. We call that the power. Whatever the highest power among the multiple terms is determines the degree. t²+t+1 is degree-2 because the highest power is 2 (on t²)… If there was an t³, it would be degree 3. So when you read “parabolic” it just means it looks like at²+bt+c and once you enter free fall, the only force acting on you is gravity, in that case, a, b, and c are already set and will not change until the end of free-fall.
Why exactly is free-fall parabolic? Because gravity determines your acceleration. Acceleration is the change in velocity and velocity is the change in position. If you had no acceleration and no velocity, the only thing you would have is position. That’s the place you are right now… And since you have no velocity or acceleration, you will continue to be there forever. This is called a “constant” and just like “parabola,” “constant” is another word to represent a polynomial. This time, a polynomial of degree-0. In my earlier framework, I did t²+t+1 notice there’s a t² that’s power 2. There’s a t (if no small number exists, it’s implied to be t¹) that’s power 1. And there’s a term with no t so that’s power 0. And as I mentioned a degree-0 polynomial means 0 is the highest power. So there is no t anywhere in the equation. The general form of a degree-2 polynomial is at²+bt+c but for a degree-0, it’s just c. There is no term including t. This is actually a bit fortuitous because c stands for constant.
Before I go further, I’d like to point out the parallels to physics that this entails. Notice there’s no t² term or t term. Similarly, to get there, I said there is no acceleration or velocity. That’s not a coincidence that there are 2 terms missing, both tied to t (the thing that can change) and also 2 things that change position also missing. Those are perfectly symmetrical. If I add back in velocity, that defines the change in my position. This makes a degree-1 polynomial. That’s going to look like bt+c. Again, it’s actually kinda nice because the letter b sounds a lot like the letter v for velocity. (This is not important to the explanation, but degree-1 polynomials also have a special name called linear. So degrees 0, 1, and 2 are called constant, linear, and parabolic respectively)
Lastly, if I add back in acceleration, that defines the change in velocity and velocity defines the change in position. So acceleration has double the effect which means we’re going up to a degree-2 polynomial. Which looks like at²+bt+c and once more we have a perfect way to help remember that because a stands for acceleration (due to some calculus, it happens to be half the acceleration, but it’s at least related to acceleration). And notice, a does have twice the effect because it’s part of the t² term. Velocity only has a single effect and b is part of the t term (which is just a shorthand for t¹ don’t forget the 1 is implied).
Ok, so to bring it back, as soon as you enter free-fall, a, b, and c are set and do not change. a is determined by you acceleration due to gravity… The only force acting on you in free-fall. b is whatever your initial velocity happened to be the moment you enter free-fall. And c is whatever your position was whenever you entered free-fall. So what is t? I did say it represents a number that can change, so your first guess might be position because I did say with acceleration and velocity, your position will change, but it turns out the way the position changes is perfectly described by at²+bt+c if we let t be some other number that changes… Time. In fact, it doesn’t matter if there’s acceleration or velocity or not. Time still changes with or without us. It marches on without our consent. It seems like a nice, stable thing to base our function on (oh, and it starts with t).
So let’s say if your position in time is perfectly defined by at²+bt+c (which is a parabola), then what happens if you force a plane to follow the exact same position predicted by that equation? If you were inside that plane and got closer to the walls, that would mean your position is changing relative to the plane, so then you aren’t following the same equation. If you were following the exact same equation, you would not move relative to the plane at all. But that means you wouldn’t get closer to any of the walls, ceiling, or floor. That’s what being in zero-G is like. You float around without falling towards the floor (or any direction).
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