##############################################
# calculates all functions for space travels
#
# constant acceleration a during whole trip
# using special relativity and Python.
#
# T: rocket time (moved system), t: earth time
# s or d: distance travelled, v: velocity,
# a: acceleration
#
# 10/2004 Wolfgang.Urban@schule.at
##############################################

from math import log, exp, sqrt, sinh, cosh, tanh

# constants:
# we measure length in lightyears, time in years, velocity in ly/yr
a = 1.03 # =g of earth,  exact 1.03227
c = 1.0  # speed of light

# alternatively use a=9.81 and c = 300*10**6 for meters and seconds

###################################################################

# missing math functions

def arsinh(x): return log(x+sqrt(x*x+1))

def arcosh(x): return log(x+sqrt(x*x-1))

###################################################################

# get earth time from rocket time
def t_T(T):
    return c/a*sinh(a*T/c)

# get rocket time from earth time
def T_t(t):
    return c/a*arsinh(a*t/c)

# get distance from earth time
def s_t(t):
    r = sqrt(1+(a*t/c)**2)
    return c*c/a*(r-1)

# get distance from rocket time
def s_T(T):
    return c*c/a*(cosh(a*T/c)-1)

# get speed
def v_t(t):
    return a*t/sqrt(1.0+(a*t/c)**2)

def v_T(T):
    return c*tanh(a*T/c)

# get acceleration observed by earth
def a_t(t):
    return a/(sqrt(1.0+(a*t/c)**2))**3

# get gamma
def gamma_t(t):
    return sqrt(1.0+(a*t/c)**2)

def gamma_T(T):
    return cosh(a*T/c)

# gamma from travelled distance
def gamma_d(d):
    return 1.0+a*d/c**2

# earth time from distance
def t_d(d):
    return sqrt((d/c)**2+2.0*d/a)

# rocket time from distance
def T_d(d):
    return c/a*arcosh(1.0+a*d/c**2)

###########################################################

# newtonian movement

def v_t_newton(t): return a*t
def s_t_newton(t): return a*t*t/2.0
def v_d_newton(d): return sqrt(2.0*a*d)
def t_d_newton(d): return sqrt(2.0*d/a)

###########################################################
# fuel mass calculations

# fuel mass M/m from rocket time
def fuel_T(T):
    return exp(a*T/c)-1

# get M/m needed for flyby in distance d
def fuel_flyby(d):
    T = T_d(d)
    #t = t_d(d)
    #print "d,T,t,M",d,T,t,fuel_T(T)
    return fuel_T(T)

# get M/m for landing in distance d
def fuel_landing(d):
    T = T_d(d/2.0)
    #t = 2.0*t_d(d/2.0)
    M1 = fuel_T(T)          # fuel mass for slowing down m
    M2 = (M1+1.0)*fuel_T(T) # fuel mass for speeding up M1+m
    M = M2+M1               # total mass of fuel
    #print "d,T,t,M",d,2*T,t,M
    return M

###################################################################
###################################################################

# test all functions
def test(T=1.0):
    T = float(T)
    t = t_T(T)
    d = s_T(T)

    print "T,t",T,t_T(T)
    print "s_T,v_T     ",s_T(T),v_T(T)
    print "s_t,v_t,a_t ",s_t(t),v_t(t),a_t(t)
    print "gamma T,t,d ",gamma_T(T),gamma_t(t),gamma_d(d)
    print "duration T,t",T_d(d),t_d(d)

##########################################################

# rocket travels for T years system time
def rocket_flies_for_T(T):
    print "rocket time           ",T
    print "time on earth         ",t_T(T)
    print "distance travelled    ",s_T(T)
    print "velocity              ",v_T(T)
    print "gamma                 ",gamma_T(T)
    print "acceleration observed ",a_t(t_T(T))

# spacetrip with landing 
def spacetrip_d(d):
    print "spacetrip: passenger landing in distance d"
    T,t = T_d(d/2.0),t_d(d/2.0)
    print "passenger ages for",2.0*T
    print "earth ages for    ",2.0*t
    print "max. velocity     ",v_T(T)