The rocket impulse problem: the rocket changes its mass to accelerate

physics-rocket-principles.py

# G acceleration of earth (m/s^2)
G_EARTH = 9.81
# How many times the iteration is repeated (s)
DELAY = 0.001
# Start mass of Rocket (kg)
START_MASS = 775000
# End mass of the Rocket (all fuel burnt) (kg)
END_MASS = 265143
# Velocity of the gas (relative to the rocket) (m/s)
V_REL = 3248 
# Mass loss per second (burned fuel per second) (kg)
FUEL_LOSS = 3922

# Delta mass loss in flight (kg)
delta_mass = 0
# Velocity while flying (m/s)
velocity = 0
# Mass loss per delay time (iteration time) (kg)
fuel_loss_delay = FUEL_LOSS * DELAY


def get_endvelocity(delta_mass, velocity):
  """ 
  Calculates the endvelocity of the rocket in a given timespan
  :param delta_mass: the mass lost since start (burned gas)
  :param velocity: the beginn veloity 
  """
  mass_beginn = START_MASS - delta_mass
  g_force = mass_beginn * G_EARTH
  
  endvelocity = \
    (g_force * DELAY - fuel_loss_delay * V_REL + \
      (fuel_loss_delay - mass_beginn) * velocity) \
        / (fuel_loss_delay - mass_beginn)
    
  return endvelocity

# calculating the time iterative
while START_MASS - delta_mass > END_MASS:
  print velocity
  velocity = get_endvelocity(delta_mass, velocity)
  delta_mass += fuel_loss_delay