from vpython import *
import numpy as np

#Earth-Moon gravity EMmulation

#IMPORTANT CONSTANTS

G = 6.67e-11    #Newton's Constant

EM = 6e24       #Earth's Mass
MM = 7e22       #Moon's Mass

ER = 6.3e6      #Earth's Radius
MR = 1.7e6      #Moon's Radius

Distance = 3.8e8


Earth = sphere(pos = vector(0,0,0), radius = ER, color = color.blue)
Earth.m = EM
Earth.v = vector(0,0,0) #Velocity
Earth.p = Earth.m*Earth.v #Momentum

Moon = sphere(pos = vector(Distance,0,0), radius = MR, color = vector(0.5,0.5,0.5), make_trail=True)

Moon.m = MM
Moon.v = vector(0,np.sqrt(G*Earth.m/Distance),0)
Moon.p = Moon.m*Moon.v

dt = 0.01

while True:
    Vec = Earth.pos + Moon.pos
    Fg = -G*Earth.m*Moon.m/mag(Vec)**3*Vec #Vector form of the Gravity Equation

    # 1. We will update the momentum according to Pf = FΔt + Pi

    Earth.p = -Fg*dt + Earth.p
    Moon.p = Fg*dt+Moon.p #-Fg becDistancese forces are equal and opposite

    #2. Update the velocites of each object, p = mv, so v = m/p

    Earth.v = Earth.p/Earth.m
    Moon.v = Moon.p/Moon.m

    #3. Update the positions
    Earth.pos = Earth.pos+Earth.v
    Moon.pos = Moon.pos+Moon.v
    print("Vector Velocity: ",Moon.v,"Magnitutde: ",mag(Moon.v))
    rate(10000)