""" Acknowledgement: Converted from the C++ code Author of the
python code: Alankar Dutta & Ranajay Dutta Pesidency University
Physics Department Kolkata, West Bengal, India presiuniv.ac.in
General Description: ==================== This module contains the
most up-to-date physical and astronomical constants in SI units.
"An Introduction to Modern Astrophysics", Appendix I Bradley W.
Carroll and Dale A. Ostlie Addison Wesley, 2007 Weber State
University Ogden, UT [email protected]
-------------------------------------------------------------------
""" #The smallest non-zero number and the number of significant
figurestiny_sp = 3.4e-38tiny_dp = 1.7e-308tiny_qp =
tiny_dpsig_fig_sp = 7sig_fig_dp = 15sig_fig_qp = sig_fig_dpeps_sp =
1E-6eps_dp = 1E-15eps_qp = eps_dp #The largest number for given
precisionbiggest_sp = 3.4e38biggest_dp = 1.7e308biggest_qp =
biggest_dpbiggest_i2 = 32767biggest_i4 = 2147483647biggest_i8 =
9223372036854775807 #Values related to pi and epi =
3.14159265358979323846264338327950two_pi = 2*pifour_pi =
4*pifour_pi_o3 = four_pi/3pi_over_2 = pi/2natural_e =
2.71828182845904523536028747135266 #Conversions for radians to
degrees and degrees to radiansdegrees_to_radians =
pi/180radians_to_degrees = 180/pi #Physical constantsG = 6.673e-11c
= 2.99792458e08mu_0 = four_pi*1e-07epsilon_0 = 1/(mu_0*c*c)e_C =
1.602176462e-19eV = e_CkeV = eV*1.0e3MeV = eV*1.0e6GeV = eV*1.0e9;
h = 6.62606876e-34hbar = h/two_pik_B = 1.3806503e-23sigma =
2*pow(pi,5)*pow(k_B,4)/(15*c*c*pow(h,3))a_rad = 4*sigma/ca_rad_o3 =
a_rad/3four_ac_o3 = 4*a_rad_o3*cm_e = 9.10938188e-31m_p =
1.67262158e-27m_n = 1.67492716e-27m_H = 1.673532499e-27u =
1.66053873e-27 N_A = 6.02214199e23R_gas = 8.314472 a_0 =
four_pi*epsilon_0*hbar*hbar/(m_e*e_C*e_C) R_infty =
m_e*pow(e_C,4)/(64*pow(pi,3)*epsilon_0*epsilon_0*pow(hbar,3)*c)R_H
= m_p/(m_e + m_p)*R_infty #Time constantshr = 3600day = 24*hrJ_yr =
365.25*dayyr = 3.15581450e7T_yr = 3.155692519e7G_yr = 3.1556952e7
#Astronomical length constantsAU = 1.4959787066e11pc =
206264.806*AUly = c*J_yr #Solar constantsM_Sun = 1.9891e30S_Sun =
1.365e3L_Sun = four_pi*AU*AU*S_SunR_Sun = 6.95508e8Te_Sun =
pow((L_Sun/(four_pi*R_Sun*R_Sun*sigma)),0.25) #Solar
magnitudesMbol_Sun = 4.74MU_Sun = 5.67MB_Sun = 5.47MV_Sun =
4.82Mbol_Sun_ap = -26.83MU_Sun_ap = -25.91MB_Sun_ap =
-26.10MV_Sun_ap = -26.75BC_Sun = -0.08 #Earth constantsM_Earth =
5.9736e24R_Earth = 6.378136e6 #Unit Conversionscm = 1e-2gram =
1e-3erg = 1e-7dyne = 1e-5esu = 3.335640952e-10statvolt =
2.997924580e2gauss = 1e-4angstrom = 1e-10jansky = 1e-26"""
Acknowledgement: Converted from the C++ code Author of the python
code: Alankar Dutta & Ranajay Dutta Pesidency University
Physics Department Kolkata, West Bengal, India presiuniv.ac.in
General Description: ==================== Orbit computes the orbit
of a small mass about a much larger mass, or it can be considered
as computing the motion of the reduced mass about the center of
mass. "An Introduction to Modern Astrophysics", Appendix J Bradley
W. Carroll and Dale A. Ostlie Second Edition, Addison Wesley, 2007
Weber State University Ogden, UT [email protected]
-------------------------------------------------------------------
"""import Constantsimport mathimport matplotlib.pyplot as pltfrom
prettytable import PrettyTableclass orbit: #This is the __str__()
method to display information on orbit instances def __str__(self):
message='This program computes the orbit of a small mass about a
much larger mass,\n or it can be considered as computing the motion
of the reduced mass\n about the center of mass.' return message
#This is the initializing method def __init__(self): """ From
Constants module the following constants will be used: Constants.G
Constants.AU Constants.M_Sun Constants.pi Constants.two_pi
Constants.yr Constants.radians_to_degrees Constants.eps_dp """
#Write introductory information for user print(' Orbit computes the
orbit of a small mass about a much larger mass.\n') print(' Details
of the code are described in: \n') print(' An Introduction to
Modern Astrophysics \n') print(' Bradley W. Carroll and Dale A.
Ostlie \n') print(' Addison Wesley \n ') print(' copyright 2007\n\n
') #Trying to open a new Orbit.txt file or appending to a previous
one #Its just a check to see whether a file can be written on
orbital infos if not the program terminates try: orbit_file =
open('Orbit.txt', 'a') orbit_file.write("\n") except: try:
orbit_file = open('Orbit.txt', 'w') orbit_file.write("\n") except:
print('Unable to open Orbit.txt --- Terminating computation')
self.dummy=input('Enter any character to quit...') exit()
orbit_file.close() #Get input from user def user_input(self):
self.Mstrsun = float(input(' Enter the mass of the parent star (in
solar masses): ')) self.aAU = float(input(' Enter the semimajor
axis of the orbit (in AU): ')) self.ecc = float(input(' Enter the
orbital eccentricity: ')) self.user_input_tuple = (self.Mstrsun,
self.aAU, self.ecc) #Convert user entered values to conventional SI
units Mstar = self.user_input_tuple[0]*Constants.M_Sun a =
self.user_input_tuple[1]*Constants.AU self.user_input_tuple_conv =
( Mstar, a, self.ecc) del self.user_input_tuple return
self.user_input_tuple_conv #Calculate the orbital period in seconds
using Kepler's Third Law def orbital_period(self,inp_tuple): P =
((4*(Constants.pi**2)*(inp_tuple[1]**3))/(Constants.G*inp_tuple[0]))**(0.5)
#Convert the orbital period to years and print the result print('\n
The period of this orbit is ' , (P/Constants.yr), ' yr') return P
#Enter the number of time steps and the time interval to be printed
def step_time_input(self): n=int(input('\n\n'+ 'Please enter the
number of time steps to be calculated and the \n'+ 'frequency with
which you want time steps printed. \n\n'+ 'Note that taking too
large a time step during the computation \n'+ 'will produce
inaccurate results. \n\n'+ 'Enter the number of time steps desired
for the computation: ')) n+=1 #increment to include t=0 (initial)
point kmax=int(input('\n\n' 'How often do you want time steps to be
printed? \n' ' 1 = every time step \n' ' 2 = every second time step
\n' ' 3 = every third time step \n' ' etc. \n\n' 'Frequency: '))
step_tuple = (n, kmax) return step_tuple #Print header information
for output file def ouput_file(self,inp_tuple,time): orbit_file =
open('Orbit.txt', 'a') orbit_file.write(' Elliptical Orbit
Data\n\n') orbit_file.write(' Mstar = ')
orbit_file.write(str(inp_tuple[0])) orbit_file.write(' Msun\n')
orbit_file.write(' a = ')
orbit_file.write(str((inp_tuple[1]/Constants.AU)))
orbit_file.write(' AU\n') orbit_file.write(' revolution time period
= ') orbit_file.write(str((time/Constants.yr))) orbit_file.write('
yr\n') orbit_file.write(' eccentricity = ')
orbit_file.write(str(inp_tuple[2])) orbit_file.write('\n\n') #Start
main time step loop def time_step_loop(self, data_tuple,
step_tuple,time_period): orbit_file = open('Orbit.txt', 'a') #open
the file Orbit.txt for printing #Initialize print counter, angle,
elapsed time, and time step counter = 1 #print counter theta = 0
#angle from direction to perihelion (radians) t = 0 #elapsed time
(s) dt = time_period/(step_tuple[0]-1) #time step (s) delta =
2*Constants.eps_dp #allowable error at end of period #Start of loop
plotx = [] #collects x co ordinates for plotting ploty = []
#collects y co ordinates for plotting r = 0.0 #Variables inside the
loop LoM = 0.0 #Variables inside the loop dtheta = 0.0 #Variables
inside the loop x = PrettyTable(['t (yr)', 'r (AU)', 'theta (deg)',
'x (AU)', 'y (AU)']) #prepare data Table Headers x.align['t (yr)']
= 'l' x.padding_width = 1 while (((theta - Constants.two_pi) <
(dtheta/2)) and ((t - time_period) < dt/2)): #Calculate the
distance from the principal focus using Kepler's First Law r =
data_tuple[1]*((1 - data_tuple[2]**2)/(1 +
(data_tuple[2]*(math.cos(theta))))) #If time to print, convert to
cartesian coordinates. Be sure to print last point also if
(counter==1): x.add_row([(t/Constants.yr),(r/Constants.AU),
(theta*Constants.radians_to_degrees),
((r*math.cos(theta))/Constants.AU),((r*math.sin(theta))/Constants.AU)])
plotx.append((r*math.cos(theta))/Constants.AU) #x co ordinates
ploty.append((r*math.sin(theta))/Constants.AU) #y co ordinates
orbit_file.write('\n') #Prepare for the next time step: Update the
elapsed time. t += dt #Calculate the angular momentum per unit
mass, L/m LoM = (Constants.G*data_tuple[0]*data_tuple[1]*(1 -
data_tuple[2]**2))**(0.5) #Compute the next value for theta dtheta
= (LoM/(r**2))*dt theta += dtheta #Reset the print counter if
necessary counter += 1 if (counter > step_tuple[1] or (theta -
Constants.two_pi)/Constants.two_pi > delta or (t -
time_period)/time_period > delta): counter = 1
plt.plot(plotx,ploty) orbit_file.write(str(x)) #plots the Orbit
curve print( '\nOrbit Graph successfully Generated!\n\n' ) print(
'\n\nThe computation is finished and the data are in Orbit.txt\n\n'
) dummy = 'dumb' dummy = input ( 'Enter any character and hit to
exit: ')
