import UIKit import SceneKit import PlaygroundSupport
// Constants let c: Double = 299792.458 // speed of light in km/s let H0: Double = 70 // Hubble constant in km/s/Mpc let G: Double = 6.6743e-11 // gravitational constant in m^3/kg/s^2 let rho_crit: Double = 1.878e-26 // critical density of the universe in kg/m^3
// Parameters let N: Int = 1000 // number of particles let t0: Double = 0 // initial time in Gyr let tf: Double = 13.8 // final time in Gyr let dt: Double = 0.01 // time step in Gyr let a0: Double = 1 / (1 + t0 * H0 / 2997.92) // initial scale factor
// Generate initial conditions let x = (0..<N).map { _ in return SCNVector3( CGFloat(Double.random(in: -10...10)), CGFloat(Double.random(in: -10...10)), CGFloat(Double.random(in: -10...10)) ) } let v = (0..<N).map { _ in return SCNVector3( CGFloat(Double.random(in: -100...100)), CGFloat(Double.random(in: -100...100)), CGFloat(Double.random(in: -100...100)) ) } let m = (0..<N).map { _ in return CGFloat(Double.random(in: 1e11...2e11)) }
// Define Friedmann equations func HubbleParameter(_ a: Double) -> Double { return H0 * sqrt((rho_crit / 3) * (1 / pow(a, 3))) }
func Acceleration(_ x: SCNVector3, _ v: SCNVector3) -> SCNVector3 { let r = x.length() let a = SCNVector3( -G * x.x / pow(r, 3), -G * x.y / pow(r, 3), -G * x.z / pow(r, 3) ) * m.reduce(0, +) a -= SCNVector3( Float(HubbleParameter(1) * Double(x.x)), Float(HubbleParameter(1) * Double(x.y)), Float(HubbleParameter(1) * Double(x.z)) ) return a }
// Plasma Electric Motor class PlasmaElectricMotor { let plasmaDensity: Double let magneticFieldStrength: Double
init(plasmaDensity: Double, magneticFieldStrength: Double) {
self.plasmaDensity = plasmaDensity
self.magneticFieldStrength = magneticFieldStrength
}
func calculateThrust() -> Double {
// Constants
let ionCharge: Double = 1.6e-19 // Coulombs
let plasmaSpeed: Double = 1e5 // m/s
// Calculate the thrust
let thrust = 0.5 * plasmaDensity * pow(plasmaSpeed, 2) * ionCharge * magneticFieldStrength
return thrust
}
func calculatePower() -> Double {
// Constants
let plasmaCrossSection: Double = Double.pi * pow(0.1, 2) // m^2
let plasmaSpeed: Double = 1e5 // m/s
let ionCharge: Double =