Damn

where my Leibniz homies at
- In the best of all possible worlds.
  
  I too wish I was in Harambe-1A. ;-;
- In the grocery store, buying cookies
  
  what kind of cookies

You know I learned all that calculus and never learned how it applies to orbits. Can someone connect the dots for me? (In a little more detail than calculus is rates of change.)
- Orbits, it turns out, are mostly just rates of change.
  
  As long as it took me to really comprehend the rate of change thing and understand how calculus is that, until I read that sentence I didn't think of all the gravity parts impacting a stellar body and velocity in a direction being impacted by multiple forces. Mean I always knew the story of Newton inventing calculus for that but never clicked exactly how it related. The sad thing is it's a sort of thing I pondered a bit on but never quite made the connection.
- So, the heart of the issue is that each object's path changes continuously, and the forces involved change in kind. Even worse, the objects interact with each other, again continuously - it's not one-sided.
  If you imagine trying to do it pre-Calculus, some kind of "just map it all out into a grid, etc.", you can see the problems this continuous change imposes (exercise left for the reader).
  By involving the Stravinsky Interpretation, it quickly becomes clear that the dimorphic superposition destabilizes. The clever reader might object "but what if you fold in all the noodly surfaces to recohere the manifold?"
  And that clever reader would be right! But we didn't know that until old Dr. Isaac "Zeke" Newton came along and made it that way.
  Some say the devil himself taught him how it's done, because no one else can read his notes! So keep your eye on old Zeke when you run into him.
- Orbit is esspetially free falling past the side of the planet, fast enough that the force of gravity doesn't completely pull you in. So you kind of fall past the planet, but get curved towards it enough you don't go flying out away either. The minimum velocity to orbit around a planet with radius r and gravity g is Vorbit = √(rg) I believe
- An orbit is analogous to position. Trying to predict the position of planets proved difficult to do accurately. People had figured out velocity a long time ago, but no one had ever explored the concept of describing an orbit just from the accelerations of the planets. It turns out acceleration has a fairly simple equation, and in order to get back to the observable thing of orbits, you need to integrate it twice. Newton was the first person to describe acceleration and to use it to predict the motion of planets. Especially for predicting Mars, it was essential because Jupiter is massive enough and close enough to alter its orbit, so simple Kepler's Laws aren't sufficient to describe the orbit.
  
  Hell yeah! And another dope thing about the whole shebang, turns out the derivative < - > integral operation is wildly useful for describing...everything.
  The simplest example, that I love the most, is just the very pedestrian (pun intended) relationship between a car's position, velocity, and acceleration. It's just enough "levels" (of diff < - > int) to have some instructional "meat", and it's a totally ubiquitous experience.
  And then, when peered at more closely, that kind of relationship starts to crop up everywhere, suggests so much more!
  Calculus is best maf
- in simplification, you could derive that curvature of the orbit is basically the force between objects, with radius, from the centre of mass. Once you know curvature at a point, you ca define a series of curves fitting, and substitute with other postions to find all constants. And what is curvature? you can find online, that curvature is just a function of second order derivative, and you just have to solve a second degree differential equation.

Can someone ELI5 why pre-Newton mathematics wasn't up to the task?
- Newton's laws, including gravity and motion, can be expressed in terms of differential equations.
  Differential equations pretty much requires calculus, which just hadn't been formalized yet.
  Newton's laws also provide convincing reasons for the necessity and legitimacy of calculus, by being able to derive orbits from his simple laws.

the entire world comes to a screeching halt for a plague...
"guess I'll develop opticks I dunno shit...."

What kind of man was Newton? Would he have been into this meme? I'm both too lazy to look it up and not sure how to find the answer to this question.
- I mean, just in general he was a genious, but also like many geniouses, he fell prey to a shit ton of nonsense. From how I understand it, he spent equal time and believed in equal importance on his study of physics, alchemy and finding hidden codes in numerology of the bible.
  Sense of humor and personality, no clue, don't think that generally is super strongly carried in surviving literature.
  
  Introverted, paranoid, insecure and thus easily angered asexual or incel.
  So like that weird programmer you know but if they were actually good at their job.
- My math prof told me he just paved over the small, itsy bitsy problem that all of his equations fell apart if any value was zero... so he just ignored it. Then Leibniz seen it and fixed everything to solve for that pesky little issue of dividing by zero.
  
  Leibniz discovered calculus on his own without intervention from newton, also probably before newton, also his notation is basically what we use today.
  newton looked at calculus from a physical pov, velocity -- acceleration.
  Leibniz came from more of a 'number theory' perspective, (although i dont believe that term would have existed) this is why his formulations covered a wider field of numbers.
  please correct me if im wrong someone :3

“Math and Physic”, surely?
- Yeah, just the one. They weren't as confused back then.