Space Travel Calculator
Calculate interstellar travel times with relativistic effects and fuel requirements
Spaceship and Destination Parameters
1.00g • 1g = 9.81 m/s² (Earth gravity)
Mass of the spaceship without fuel
Select target destination for your space journey
Calculation Options
Travel Results
Relativistic Kinetic Energy: 2.03 × 10^20 J
Max Velocity: 2.85 × 10^8 m/s
Required Fuel Mass: 5.36 × 10^3 kg
Fuel-to-Payload Ratio: 5.36:1
Travel Analysis
Example: Journey to Alpha Centauri
Mission Parameters
Destination: Alpha Centauri (4.37 light years)
Acceleration: 1g (9.81 m/s²)
Spaceship Mass: 1,000 kg
Mission: Arrive and stop
Classical Physics
Travel Time: ~2,200 years
Max Velocity: ~3000c (!)
Violates relativity
Relativistic Physics
Time in Ship: ~3.6 years
Time on Earth: ~6.0 years
Max Velocity: ~95% c
Fuel Needed: ~5,200 tons
Space Travel Facts
Speed of Light
299,792,458 m/s
Ultimate speed limit
Earth Gravity
9.81 m/s²
Comfortable acceleration
Lorentz Factor
γ = 1/√(1-v²/c²)
Relativistic effects
Relativistic Effects
Time Dilation: Time slows down at high speeds
Length Contraction: Distances appear shorter
Mass-Energy: Infinite energy needed for light speed
Fuel Requirements: Exponentially increase with speed
Understanding Interstellar Space Travel
Relativistic Rocket Equations
For interstellar travel, we must use Einstein's special relativity. The classical equations fail dramatically at high speeds, predicting impossible velocities exceeding light speed.
Key Formulas (Arrive and Stop):
T = (2c/a) × asinh(at/2c)
t = (2c/a) × sinh(aT/2c)
v = c × tanh(aT/2c)
d = (2c²/a) × (cosh(aT/2c) - 1)
T = time in spaceship, t = time on Earth, v = max velocity, d = distance, a = acceleration, c = speed of light
Time Dilation Effect
Due to time dilation, the crew ages much slower than people on Earth. This makes interstellar travel theoretically possible within a human lifetime, though Earth time passes much faster.
Fuel Requirements:
M = m(e^(aT/c) - 1)
M = fuel mass, m = payload mass, assumes perfect efficiency
Challenge: Fuel requirements grow exponentially with speed, making near-light-speed travel extremely demanding.