*Ada's stats

import Foundation

private let G: Double = 6.6743e-11  // gravity, number found from an apple, update me when we find a graviton
private let T: Double = 21600  // 1 step = this time (in seconds (six hours))

// not using 3rd axis, but we could!
// simd because i cba writing a 2d/3d vector type
typealias Vec3 = SIMD3<Double>

struct Body {
  var name: String
  var mass: Double
  var pos: Vec3
  var vel: Vec3

  public mutating func imp(_ i: Vec3) {
    vel += i * T
    pos += vel * T
  }

  public func mag(_ other: Self) -> Vec3 {
    let r = other.pos - pos  // distance
    let d = sqrt(r.x * r.x + r.y * r.y + r.z * r.z)  // length
    let f = G * ((mass * other.mass) / (d * d))  // newton's headache
    let n = r / d  // normalize
    return f * n  // distance to vector
  }
}

// note: without the sol and jupiter, terra will slowly approach luna
// but i am too lazy to look up the values for other bodies
// also; this doesn't have axis inclination
// so it's going to be inaccurate to real life regardless
// but pretend it's real and earth is slowly going sideways
var bodies = [
  Body(
    name: "terra",
    mass: 5.972e+24,
    pos: Vec3(repeating: 0),
    vel: Vec3(repeating: 0)),
  Body(
    name: "luna",
    mass: 7.348e+22,
    pos: Vec3(3.844e+8, 0, 0),
    vel: Vec3(0, 1022, 0)),
]

// tsv we can plot~
print("index\tbody\tx\ty\tz")
for t in 0..<500 {
  var f = [Vec3](repeating: Vec3(repeating: 0), count: bodies.count)

  for i in 0..<bodies.count {
    let body = bodies[i]
    for j in 0..<bodies.count where i != j {
      f[i] += body.mag(bodies[j]) / body.mass
    }
  }

  for i in 0..<bodies.count {
    bodies[i].imp(f[i])
    print("\(t)\t\(bodies[i].name)\t\(bodies[i].pos.x)\t\(bodies[i].pos.y)\t\(bodies[i].pos.z)")
  }
}