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Relativistic Rocket Kinematics

Python, 93 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93``` ```# Relativistic Rocket Kinematics # FB - 20130609 import math print "Coordinate Time passed (for observer) to reach given speed (velocity):" print "v0 = 0" g = float(raw_input("Constant Proper Acceleration in g: ")) a = g * 9.8 # meters / second ** 2 a = a / 3e8 # light-second / second ** 2 a = a * 3.15e7 # light-year / year ** 2 # a = float(raw_input("Constant Proper Acceleration: ")) v = float(raw_input("Speed in c: ")) tc = v / a / math.sqrt(1.0 - v * v) print str(tc) + " years" print print "Proper Time passed for the traveller:" print "v0 = 0" # g = float(raw_input("Constant Proper Acceleration in g: ")) # a = g * 9.8 # meters / second ** 2 # a = a / 3e8 # light-second / second ** 2 # a = a * 3.15e7 # light-year / year ** 2 # a = float(raw_input("Constant Proper Acceleration: ")) # tc = float(raw_input("Coordinate Time passed for the observer in years: ")) tp = math.asinh(a * tc) / a print str(tp) + " years" ##print ##print "Distance travelled at given time:" ##print "v0 = 0" ##a = float(raw_input("Constant Proper Acceleration: ")) ##t = float(raw_input("Time: ")) ##x = (math.sqrt(1.0 + a * a * t * t) - 1.0) / a ##print x ##print ##print "Coordinate Time passed for distant observer:" ##print "v0 = 0" ##a = float(raw_input("Constant Proper Acceleration: ")) ##t = float(raw_input("Proper Time passed for the traveller: ")) ##tc = math.sinh(a * t) / a ##print tc ##print ##print "Coordinate Time passed to reach given distance:" ##print "v0 = 0" ##a = float(raw_input("Constant Proper Acceleration: ")) ##x = float(raw_input("Distance: ")) ##tc = (math.sqrt(1.0 + a * a * x * x) - 1.0) / a ##print tc ##print ##print "Speed at given time:" ##print "v0 = 0" ##a = float(raw_input("Constant Proper Acceleration: ")) ##t = float(raw_input("Time: ")) ##v = a * t / math.sqrt(1.0 + a * a * t * t) ##print v ##print ##print "Speed at given time under constant force:" ##print "v0 = 0" ##f = float(raw_input("Force: ")) ##m = float(raw_input("Mass: ")) ##t = float(raw_input("Time: ")) ##v1 = f * t / math.sqrt(m * m - (f * t / c) ** 2.0) ##v2 = f * t / m / math.sqrt(1.0 + (f / m / c) ** 2.0 * t * t) ##print v1, v2 ##print ##print "Distance travelled at given time under constant force:" ##print "v0 = 0" ##f = float(raw_input("Force: ")) ##m = float(raw_input("Mass: ")) ##t = float(raw_input("Time: ")) ##x = c * (m * c / f) * (math.sqrt(1.0 + (f / m / c) ** 2.0 * t * t) - 1.0) ##print x ##print ##print "Acceleration at given time under constant force:" ##print "v0 = 0" ##f = float(raw_input("Force: ")) ##m = float(raw_input("Mass: ")) ##t = float(raw_input("Time: ")) ##a = f / m / math.sqrt(1.0 + (f / m / c) ** 2.0 * t * t) ** 3.0 ##print a ##print ##print "Time it takes to reach given speed (velocity) under constant force:" ##print "v0 = 0" ##f = float(raw_input("Force: ")) ##m = float(raw_input("Mass: ")) ##v = float(raw_input("Speed: ")) ##t = math.sqrt(v * v * m * m * c * c / (f * f * (c * c - v * v))) ##print t ##print ##print "Time to travel given distance under constant force:" ##print "v0 = 0" ##f = float(raw_input("Force: ")) ##m = float(raw_input("Mass: ")) ##x = float(raw_input("Distance: ")) ##t = math.sqrt(((x * f / m + 1.0) ** 2.0 - 1.0) * m * m * c * c / f * f ) ##print t ``` FB36 (author) 10 years, 5 months ago

For example, how long it would take to reach 99.9% of speed of light using a rocket engine that provides 1 g constant acceleration (from viewpoint of the traveller(s)):

Coordinate Time passed (for observer) to reach given speed (velocity):

v0 = 0

Constant Proper Acceleration in g: 1

Speed in c: 0.999

21.71419414 years

Proper Time passed for the traveller:

v0 = 0

3.69310123154 years FB36 (author) 10 years, 5 months ago

Since we are assuming 1 g constant acceleration, the rocket would also provide artificial gravity for the travellers!

http://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration FB36 (author) 10 years, 5 months ago

Imagine a wide UFO shaped spaceship with engines underneath.

A passenger standing in a room looking out the window on the side of the ship would see stars like long vertical strings moving downwards; not like moving sideways in the movies! Created by FB36 on Sun, 9 Jun 2013 (MIT)

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