The energy
One half v squared, relativistically corrected.
The kinetic energy required per kilogram of final velocity is one half v squared, with a relativistic correction. Everything else in interstellar flight is a design choice. This is not.
| Speed | Velocity | KE per kg | KE per kg (GWh) | Crossing to Proxima |
|---|---|---|---|---|
| 0.001c | 3.00 × 10⁵ m/s | 4.5 × 10¹⁰ J | 0.012 | 4,250 yr |
| 0.005c | 1.50 × 10⁶ m/s | 1.1 × 10¹² J | 0.31 | 850 yr |
| 0.01c | 3.00 × 10⁶ m/s | 4.5 × 10¹² J | 1.25 | 425 yr |
| 0.05c | 1.50 × 10⁷ m/s | 1.1 × 10¹⁴ J | 31 | 85 yr |
| 0.10c | 3.00 × 10⁷ m/s | 4.5 × 10¹⁴ J | 126 | 42 yr |
| 0.20c | 6.00 × 10⁷ m/s | 1.85 × 10¹⁵ J | 515 | 21 yr |
Measured physics. The Lorentz factor at 0.2c is 1.0206. Crossing times are one-way to Proxima Centauri at 4.2465 light-years and exclude acceleration distance, which is negligible at these speeds.
Two comparators
An electrical economy, and a small truck.
The United States generates roughly 4,000 terawatt-hours of electricity per year, which is 4 million gigawatt-hours. Divided by 515 gigawatt-hours per kilogram, that entire annual output, converted with perfect efficiency, accelerates about 7.8 tons to 0.2c. At a realistic 20 percent coupling efficiency, 1.6 tons.
That is the whole American electrical economy for a year, and it buys a small truck moving fast.
Now run it the other way. A 10,000-ton generation ship at 0.01c requires 4.5 × 10¹⁹ joules of kinetic energy, which is about 7 percent of current world annual primary energy consumption. It arrives at Alpha Centauri in 425 years.
Patience beats mass reduction
Velocity is quadratic; mass is linear.
Put those two results next to each other, because their relationship is the most counterintuitive thing on this page. The energy cost of a slow, massive interstellar mission is modest. The energy cost of a fast, tiny one is enormous.
Velocity enters as a square and mass enters linearly, so patience is worth vastly more than mass reduction. A civilization that could tolerate a 425-year transit could send a small city for a fraction of a year of its energy budget.
The barrier to the generation ship is therefore not energy. It is governance. A 425-year mission requires a chartering institution that persists for 425 years and a crew society that remains functional and loyal to an original purpose across roughly 17 generations, with no possibility of correction and no meaningful communication. Nothing in human institutional history suggests this is achievable.
The energy was never the problem. That is worth stating plainly because the popular framing of interstellar flight is almost entirely about power, and the power is the tractable part. What is intractable is holding a purpose.
The coupling ceiling
20 percent, and no design improves it.
The second irreducible quantity belongs to the beam.
A photon of energy E carries momentum E over c. A perfectly reflecting sail therefore receives a force of twice the incident power over c. The power delivered into the sail’s kinetic energy is that force times the sail velocity, which is 2β times the incident power — so the instantaneous coupling efficiency equals twice the ratio of sail speed to light speed.
Integrate over a burn at constant power and constant mass, where β grows linearly with time, and the average coupling over the whole acceleration is simply the final β.
At 0.2c, the maximum possible beam-to-kinetic coupling efficiency is 20 percent. This is not an engineering figure. It is a consequence of photons carrying E over c of momentum, and no sail design, coating, or geometry improves it. Four fifths of every joule generated leaves as light that has done its job and moved on. Any interstellar energy budget that assumes better than this is wrong.
The exponent where programs die
Deceleration, not acceleration.
For any rocket, the mass ratio is the exponential of the velocity change divided by the exhaust velocity. A flyby needs one velocity change. An orbiter needs two. A round trip needs four.
| Mission | Velocity changes | Mass ratio | Verdict |
|---|---|---|---|
| 0.1c flyby | 1 | e², about 7.4 | Achievable |
| 0.1c arrival at rest | 2 | e⁴, about 55 | Hard but not absurd |
| 0.1c round trip | 4 | e⁸, about 2,981 | Dead |
Halve the exhaust velocity to 0.025c and those numbers become 55, 2,981, and 9 million. The exponent is where interstellar programs die, and it is why the deceleration question rather than the acceleration question determines what kind of mission is possible.
Three families
They do not resemble each other.
The flyby. Grams to kilograms, 0.1c to 0.2c, beam-driven, no deceleration, one pass, statistical redundancy across thousands of craft. Achievable within the century.
The arrival. Tons, 0.05c or slower, requiring either a nuclear deceleration stage or a passive braking mechanism at the far end. Plausibly started within the century, arriving in the next.
The settlement. Thousands of tons, 0.01c or slower, energetically modest and institutionally impossible on any timescale worth reasoning about.
Most of this section concerns the first family, because it is the only one that fits inside 2100, and the infrastructure that makes the second family a 2100s decision rather than a 2200s one.