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kepler.py
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'''Meeus: Astronomical Algorithms (2nd ed.), chapter 30'''
import numpy as np
def method1(e,M,eps=1e-8):
'''1st method for solving Kepler's equation'''
#type of output (same as input - number, list, numpy.array)
out_type='lst'
if isinstance(M,int) or isinstance(M,float):
#all input args are numbers
out_type='num'
if isinstance(M,np.ndarray):
#numpy.array
out_type='np'
if isinstance(M,list): M=np.array(M)
if out_type=='num': M=np.array([M])
M=np.deg2rad(M)
E=M
E0=E+1e3
#i=0
while max(abs(E-E0))>eps:
E0=np.array(E)
E=M+e*np.sin(E)
#i+=1
#print i
E=np.rad2deg(E)
if out_type=='num': E=E[0]
elif out_type=='lst': E=E.tolist()
return E
def method2(e,M,eps=1e-8):
'''2nd method for solving Kepler's equation'''
#type of output (same as input - number, list, numpy.array)
out_type='lst'
if isinstance(M,int) or isinstance(M,float):
#all input args are numbers
out_type='num'
if isinstance(M,np.ndarray):
#numpy.array
out_type='np'
if isinstance(M,list): M=np.array(M)
if out_type=='num': M=np.array([M])
M=np.deg2rad(M)
E=M
E0=E+1e3
#i=0
while max(abs(E-E0))>eps:
E0=np.array(E)
E=E+(M+e*np.sin(E)-E)/(1-e*np.cos(E))
#i+=1
#print i
E=np.rad2deg(E)
if out_type=='num': E=E[0]
elif out_type=='lst': E=E.tolist()
return E
def method3(e,M,eps=1e-8):
'''3rd method for solving Kepler's equation'''
#type of output (same as input - number, list, numpy.array)
out_type='lst'
if isinstance(M,int) or isinstance(M,float):
#all input args are numbers
out_type='num'
if isinstance(M,np.ndarray):
#numpy.array
out_type='np'
if isinstance(M,list): M=np.array(M)
if out_type=='num': M=np.array([M])
M=np.deg2rad(M)
F=np.sign(M)
M=np.abs(M)/(2*np.pi)
M=(M-M//1)*2*np.pi*F
M[np.where(M<0)]+=2*np.pi
F=np.ones(M.shape)
F[np.where(M>np.pi)]=-1
M[np.where(M>np.pi)]=2*np.pi-M[np.where(M>np.pi)]
E=np.pi/2.*np.ones(M.shape)
D=np.pi/4.
E0=np.ones(M.shape)
#i=0
while max(abs(E-E0))>eps:
E0=np.array(E)
E+=D*np.sign(M-(E-e*np.sin(E)))
D/=2.
#i+=1
#print i
E*=F
E[np.where(E<0)]+=2*np.pi
E=np.rad2deg(E)
if out_type=='num': E=E[0]
elif out_type=='lst': E=E.tolist()
return E
def method4(e,M,eps=1e-8):
'''4th method (approximation) for solving Kepler's equation'''
#type of output (same as input - number, list, numpy.array)
out_type='lst'
if isinstance(M,int) or isinstance(M,float):
#all input args are numbers
out_type='num'
if isinstance(M,np.ndarray):
#numpy.array
out_type='np'
if isinstance(M,list): M=np.array(M)
if out_type=='num': M=np.array([M])
M=np.deg2rad(M)
E=np.arctan2(np.sin(M),np.cos(M)-e)
E[np.where(E<0)]+=2*np.pi
E=np.rad2deg(E)
if out_type=='num': E=E[0]
elif out_type=='lst': E=E.tolist()
return E