Travel Time to Alpha Centauri - In Python

The star Alpha Centauri. Image Credit: Author

After reading @procrastilearner's article Kill Time At Work With Recreational Math: Let's Travel To Alpha Centauri! I decided to have an attempt at coding his excel sheet to calculate travel time to Alpha Centauri in Python (which I am very new at).

To quickly recap, the original problem was to calculate the travel time it would take to travel to Alpha Centauri. By travel time, I mean the time experienced by the travelers. We will also assume that the spacecraft has the ability to maintain an acceleration/deceleration of 1G for the entire journey.

As it turns out this program (listed below) does indeed give the expected answer of 3.6 years. Incidentally, for observers on earth, the journey would take 6 years. This is the effect of time dilation due to Special Relativity.

For reference here are @procrastilearner’s articles.

• Intuitive Special Relativity - Time Dilation
• Kill Time At Work With Recreational Math: Let's Travel To Alpha Centauri!

And here is the code.

# Compute ship travel time to Alpha Centauri based on constant 1g acceleration and deceleration

import math

# Convert meters to light years
def m2ly(m):
    return(m/9454254955488000.0)

# Convert seconds to years
def sec2year(sec):
    return(sec/(3600*24*365.25))

# velocity in ms
def lorenzfactor(v):
    c = 299792458.0
    return(1 / math.sqrt(1 - (v * v) / (c * c)))

# velocity in ms
def compositionofvelocities(u_,v):
    c = 299792458.0
    return((u_+v)/(1 + u_*v/(c*c)))

counter = 1
ts = 0
ts_incr = 1000.0

# initial distance travelled of ship
d = 0.0

# initial velocity of ship
v1 = 0.0

# initial time of ship
t_s = 0.0

# target distance in m (half distance to Alpha Centauri
d_target = 2.15 * 9454254955488000.0

while (d < d_target):
    counter = counter + 1
# compute lorentz factor for current velocity
    lorentz = lorenzfactor(v1)
# increment earth time
    ts_previous = ts
    ts = ts + ts_incr
# increment ship time
    t_s = t_s + ts_incr / lorentz
    a = 9.8 / lorentz
# velocity increment
    v2 = a * ts_incr
# New velocity based on composition of velocities
    v1_previous = v1
    v1 = compositionofvelocities(v1,v2)

# Compute new distance
    d = d + 0.5 * (v1_previous + v1) * (ts - ts_previous)

# Final time and distance (time to accelerate and to deccelerate
print("Time taken ="+str(2*sec2year(t_s))+" years")