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!
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