Velocity/Displacement Equations for Rockets

from math import *


t_f = 1913.87
I_sp = 178444.0
m_dot = -651.71
m_0 = 2166828.0

g_0 = -9.80665
c = 299792458.0


def v(t,v_0=0.0):
    return -g_0*I_sp*log(1.0+m_dot/m_0*t) + v_0

def x(t,v_0=0.0):
    a = 1.0 + (m_dot/m_0)*t
    def fn(u):
        return u*log(u) - u
    return (m_0/m_dot) * ( -g_0*I_sp*(fn(a)-fn(1.0)) + v_0*(a-1.0) )


print("Velocity:")
print("    v(0  ) = %f"%v(0.0))
print("    v(t_f) = %f"%v(t_f))
print()
print("Displacement:")
print("    x(0             ) = %f, %f"%( x(0.0           ), x(0.0           )/c ))
print("    x(t_f           ) = %f, %f"%( x(t_f           ), x(t_f           )/c ))
print("    x(0,  -1500000.0) = %f, %f"%( x(0.0,-1500000.0), x(0.0,-1500000.0)/c ))
print("    x(t_f,-1500000.0) = %f, %f"%( x(t_f,-1500000.0), x(t_f,-1500000.0)/c ))