Which book?

Achieving a velocity of 0.5 times the speed of light (ccc) for space travel involves solving advanced challenges in physics and engineering. The Python script below creates a simplified optimization framework to analyze the propulsion needed. It uses physics principles like relativistic mass-energy equivalence and propulsion mechanisms such as fusion or antimatter engines.

This code assumes you have the theoretical fuel and energy to achieve the speed, but it abstracts away complex challenges like time dilation, cosmic radiation, and material limitations.

Python Code

import numpy as np
import matplotlib.pyplot as plt

# Constants
c = 3e8  # Speed of light (m/s)
target_speed = 0.5 * c  # Target speed (0.5c)
ship_mass = 1e5  # Mass of the spacecraft without fuel (kg)
fuel_efficiency = 1e-3  # Fuel conversion efficiency (e.g., antimatter ~0.1, fusion ~0.001)
exhaust_velocity = 1e7  # Exhaust velocity of the propulsion system (m/s)
specific_impulse = exhaust_velocity / 9.81  # Specific impulse (seconds)

# Functions
def relativistic_mass(speed, rest_mass):
    """Calculate relativistic mass."""
    gamma = 1 / np.sqrt(1 - (speed / c) ** 2)
    return gamma * rest_mass

def fuel_needed(final_speed, ship_mass, exhaust_velocity):
    """Estimate fuel required using the Tsiolkovsky rocket equation."""
    delta_v = final_speed
    mass_ratio = np.exp(delta_v / exhaust_velocity)
    fuel_mass = ship_mass * (mass_ratio - 1)
    return fuel_mass

# Optimization
def optimize_propulsion(target_speed, ship_mass, exhaust_velocity, fuel_efficiency):
    fuel_mass = fuel_needed(target_speed, ship_mass, exhaust_velocity)
    energy_required = fuel_mass * fuel_efficiency * c**2  # Total energy for propulsion
    return fuel_mass, energy_required

# Perform calculations
fuel_mass, energy_required = optimize_propulsion(target_speed, ship_mass, exhaust_velocity, fuel_efficiency)

# Display results
print(f"Target speed: {target_speed / c:.2f}c")
print(f"Required fuel mass: {fuel_mass:.2e} kg")
print(f"Energy required: {energy_required:.2e} joules")

# Visualization
speeds = np.linspace(0, 0.5 * c, 100)
fuel_masses = [fuel_needed(speed, ship_mass, exhaust_velocity) for speed in speeds]

plt.figure(figsize=(10, 6))
plt.plot(speeds / c, fuel_masses, label='Fuel Mass Required')
plt.xlabel('Speed as a Fraction of Light Speed (v/c)')
plt.ylabel('Fuel Mass (kg)')
plt.title('Fuel Requirement vs. Speed')
plt.legend()
plt.grid()
plt.show()

How it Works:

Relativistic Mass: Accounts for relativistic effects as the spacecraft approaches significant fractions of the speed of light.
Tsiolkovsky Rocket Equation: Estimates fuel requirements based on the propulsion system's exhaust velocity and initial mass.
Energy Requirement: Evaluates energy needs assuming the specified fuel efficiency.

Limitations:

Idealized Assumptions: Assumes perfect efficiency and ignores engineering constraints.
Simplified Physics: Doesn't account for external factors like gravity, drag, or realistic propulsion systems.
Energy Storage: No consideration for how energy would be stored or delivered.

Would you like more refinement or details on specific subsystems?

FIRE ALL THE PHYSICISTS

I mean, saying it would take half of forever with existing technology, when we do not have the technology to do it in the first place, seems a bit redundant. There are any number of hypothetical technologies for travel to relatively nearby stars that, while we don't have them presently, at least do not violate physics and are more an issue of requiring a civilization of much larger scale than ours to afford to build them rather than one of if they're physically possible.

An analogy I once saw was this: suppose you were to go back in time to meet a medieval blacksmith, and you show him the blueprints for a modern jetliner. You might, with a lot of explaining of the relevant physics and engineering behind all the parts, be able to convince the guy that the machine could work if constructed. But, he'd have no idea of the process for how many of the parts are made, or the materials they're made from, and if you included all that information too, the whole process would be so expensive and the size of the economy back then so small that in all likelihood, not even the richest kingdom on earth in his day could possibly afford to actually build and operate one. However, if the blacksmith took all that information and concluded "this can never happen, it's just too hard", time would prove him wrong.

perpetually within the next 10 years

I think you’re forgetting Stargate technology…

Grok 2.0 alone will move heaven and Earth to reach alien civilizations. It's sole reason for that will be to insult them. But hey, a motivation is a motivation.

Terraforming would seem a bit unnecessary if you can send a crewed ship there. Manned interstellar travel, unless we're wrong about the whole speed of light thing, is going to take decades at least to reach the very nearest stars (I'd imagine that it is more likely we'd go to those stars first, and only reach Trappist when people from those stars later launch their own ships, until eventually the outer edge of settled space reaches 40ly).

That implies that, if you can send some colony ship to another star, you necessarily have the technology to build a space habitat that can sustain large numbers of humans in sufficient comfort to run a small civilization and all relevant industry, self-sufficiently using only the materials available in space from asteroids and such as inputs. You have this tech first, because the colony ship is itself just one or more of these habitats, on top of some massive propulsion system.

As such, why even bother with terraforming planets? That's a process that may potentially take millennia to truly finish, longer than it took your ship to even get there with some of the possible propulsion options, will only be viable on a fraction of worlds, and will still get you a place that probably does not have an earth like day or gravity or any number of other differences. You would then be back in the bottom of a gravity well, which requires a ton of energy expenditure to get back into space again. Why not instead, find some asteroids and comets in your target system, there's probably going to be some around somewhere if our solar system is any indication, and build more of those habitats as needed.