ITT: Derivations of concepts in Physics that you never

>>7914574
Physics

>>7914575
\thread

Kepler's laws

Physic books typically jump to Kepler's laws right after teaching Newton's axioms and then totally ignore that the sun gets pulled towards the earth too.
To this day I have never seen a derivation of Kepler's laws that is consistent with Newton's third law.

>>7914574
De Broglie wave.

>>7914631
The mass of the Sun makes the pulling by the earth negligible, you can sleep happily now

>>7914574
Anything that uses the asymptotic behavior of sin.
IE sin(x) ~ x as x->0
Like when you first derive the pendulum equation and use this approximation or when dealing with the double slit experiment (in this case the angles generally are quite small so it's not as dissatisfying).

>>7914693
I don't think that's what asymptotic means.

>>7914645
Read his thesis. Supposedly it is very good and very short.

>>7914693
It's just an approximation, physics is a model and not reality itself; don't confuse the map with the territory. You neglect friction all the time.

x and sin x are the same for their first 3 terms of their taylor series, so it's not a bad approximation. You can see this visually on the interval -pi/4 to pi/4 which is a 90 degree spread overall that x and sinx are practically the same on a graph:

https://www.desmos.com/calculator/omzlopmseh

>>7914693
I'm completely fine with approximations but in the case of the pendulum I tend to agree simply because it's a bit lame having a pendulum and barely making it swing. That's sorta unsatisfying.
It's a completely sound derivation though and in general if your 'x' is infinitesimal the solution will actually be exact, not just an approximation.

>>7914700
Want me to read the definition for you?
f(x) ~ g(x) as x->a (read: f is asymptotic to g as x approaches a) iff lim f/g as x-> a = lim g/f as x-> a =1
You can verify sin(x) ~ x as x-> 0 for yourself.

>>7914706
The annoyance is with the fact that there exists a better model in using sin(x) instead of its asymptotic behavior. Harder to calculate answers of course which is where the model fails with its usability, but still closer to the ACTUAL physical picture.

>>7914575
kek

everything solid state physics i've been exposed to so far desu. does it get better?

>>7914822
good luck calculating anything serious with that method pal

>>7914841
Solid is my fave. Stat mech and solid state are both excellent fields

>>7914851
That's what I said dumb fuck. Its just annoying when I study some physical system and use 7 approximations to get to something calculatable. It feels like I'm not even studying the same system anymore. This is coming from a math guy so that's why I'm all autistic about these kinds of situations.

>>7914877
You should never try statistical mechanics mate, your little weak maths brain would explode at the approximations

>>7914877
Calculable*

>>7914884
>your little weak maths brain
?
You have to use approximations to even be able to come close to understanding what's going on and you're trying to call my brain weak?
C'mon anon try again bud.
If you like using approximations that's cool but it just doesn't sit well with me in certain cases.
I actually like a lot of asymptotic analysis inside of physics like the wkb approximation in quantum mechanics.
It's just ugly when an asymptotic behavior of a function is used and then the result isn't expressed as an asymptotic result.