~ $ cd projects/rocinante && cat README.md

A relativistic rocket

A ship that can keep its engine burning does not fly the way a probe does. It speeds up to halfway, turns round, and slows down the rest. Near the speed of light its own clock falls behind the ones at home, so a trip has two lengths. Here they are side by side, for one ship, to ten places:

to	distance	on board	at home	top speed	fuel burnt
the Moon	384,400 km	6.3 hours	6.3 hours	34 km/s	9.3 t
Mars	0.52 au	3.8 days	3.8 days	478 km/s	133 t
Jupiter	4.2 au	11 days	11 days	1,360 km/s	376 t
Saturn	8.5 au	15 days	15 days	1,934 km/s	533 t
Pluto	38.5 au	32 days	32 days	1.4% of c	1,123 t
Proxima Centauri	4.24 light-years	68 years	68 years	6.3% of c	all 5,000 t, then coasts
Sirius	8.58 light-years	137 years	137 years	6.3% of c	all 5,000 t, then coasts
Epsilon Eridani	10.52 light-years	168 years	168 years	6.3% of c	all 5,000 t, then coasts
the centre of the galaxy	26,000 light-years	414,743 years	415,558 years	6.3% of c	all 5,000 t, then coasts
Andromeda	2.5 million light-years	40 million years	40 million years	6.3% of c	all 5,000 t, then coasts

To Proxima Centauri: speed against the ship's clock

Press a row to draw that trip. The ship it opens with is a fusion torch: thirty thousand tonnes, a sixth of it fuel, a third of a g.

Things to try

It owns the solar system and nothing else. Mars in under four days, Pluto in a month, on a thousand tonnes of fuel at most. Proxima Centauri takes sixty-eight years: it burns half its fuel in the first ten weeks, reaches 6% of the speed of light, and coasts with the engine off for sixty-seven years. At that speed the two clocks still agree.
Give it fuel. Slide it up until the row for Proxima stops saying coasts: twenty ships' worth of fuel for every ship. The trip drops to seven years on board and eight and a half at home. This is the rocket equation: fuel has to carry the fuel.
Make it perfect: exhaust at 100% of c, one g, and all the fuel the slider has. Now the clocks part. Proxima is 3.5 years on board and 5.9 at home. The centre of the galaxy is 20 years on board and 26,002 at home, and Andromeda is 29. You could go, inside a working life; nobody you knew would hear of it. The fuel for Andromeda is six million million ships for every ship, with an engine nobody knows how to build.

What it is not

Straight lines from a standing start: no orbits, no launch windows, no gravity wells, and the planets are taken at the gap between their orbit and ours. No shielding either, and at these speeds the thin gas between the stars arrives as hard radiation. The arithmetic is the relativistic rocket of the Usenet Physics FAQ, and its table of trips at one g is what this page's tests are checked against.

Where it comes from

This is the arithmetic of the Rocinante Simulator, which I built in October 2025: the solar system and the thirty nearest stars in three dimensions, a ship to configure, and a sphere showing how far it can reach. Go there to fly it. This page keeps only the sums, written again for this site with nothing underneath.