Ex_3.1_ToF_to_Given_True_Anomaly.ipynb

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    "#Calculate Time of Flight From Perigee to a Given True Anomaly, given perigee and apogee\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def ToF(perigee,apogee,theta_f,mu): #distances in km, angles in rad, mu = mu_earth\n",
    "    e = (apogee-perigee)/(apogee+perigee) #find e\n",
    "    h=np.sqrt(perigee*mu*(1+e*np.cos(0))) #find h from the orbit equation at perigee\n",
    "    T = (2*np.pi/mu**2)*(h/np.sqrt(1-e**2))**3 #find orbit Period\n",
    "    E=2*np.arctan(np.sqrt((1-e)/(1+e))*np.tan(theta_f/2)) #find E\n",
    "    Me = E-e*np.sin(E) #find Me\n",
    "    t = (Me*T)/(2*np.pi) #find ToF\n",
    "    \n",
    "    print('e =',e,'h =',h,'T =',T,'E =',E,'Me =',Me, 'ToF =',t)\n",
    "    return(e,h,T,E,Me,t)"
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