SolPath

What Is This?

SolPath plans point-to-point missions between the planets for a spacecraft that accelerates continuously — a brachistochrone trajectory. Pick an origin, a destination, a departure date, and a constant acceleration, and SolPath computes the flight path, travel time, and relativistic effects.

Flip And Burn

A constant-thrust ship doesn't coast. It accelerates toward the target for the first half of the trip, performs a 180° flip maneuver, then decelerates for the second half, arriving at rest relative to the destination. The animation shows the full sequence: the exhaust plume, the mid-course flip, and the deceleration burn. At accelerations near 1 g, even Mars is only days away.

Planetary Positions

Planet positions are computed from Keplerian orbital elements with secular rates, so departure and arrival geometry reflect where the planets actually are on your chosen date — including how far the destination moves during the trip.

The Solar Exclusion Zone

Trajectories are kept at least 0.35 AU from Sol. When a direct path would pass closer, SolPath reroutes it — either with a waypoint stop (two full brachistochrone legs with a stop at a tangent waypoint) or a smooth arc that skirts the boundary without stopping. The dashed ring marks the boundary, annotated with Sol's Schwarzschild radius and the tidal force at the ring.

Relativity

Every mission reports both observer time and ship time. At high accelerations over long distances, the ship's peak speed becomes a meaningful fraction of the speed of light, and the Time Dilation panel shows the Lorentz factor and the time saved by the crew.

Tips

• Drag the canvas to pan; scroll or use the corner buttons to zoom.
• Use the scrub bar to seek anywhere in the animation.
• The Share button copies a link that encodes your full mission setup.
• Try Earth → Mars on 2032-07-14 to see a solar detour in action.

Trajectory legs are straight-line kinematics; solar gravity is ignored under thrust. At the accelerations SolPath models, that's a fair approximation — gravity at the exclusion ring is only ~0.005 g.

← Back to About

Brachistochrone Trajectories

From the Greek brachistos (shortest) and chronos (time), a brachistochrone is the fastest possible path between two points. For a spacecraft with unlimited propellant, that means thrusting the entire way: accelerate toward the target to the midpoint, flip 180°, then decelerate to arrive at rest.

For a distance d under constant acceleration a, the trip takes t = 2√(d/a). Doubling the acceleration cuts travel time by only √2, but quadrupling the distance merely doubles it — which is why the outer planets stay surprisingly reachable at 1 g.

The catch is delta-v. A traditional Hohmann transfer to Mars needs a few km/s and months of coasting; a 1 g brachistochrone needs thousands of km/s — far beyond chemical rockets. It's the domain of fusion torches and other speculative drives, which is what makes it fun to plan for.

← Back to About

Keplerian Orbits

Johannes Kepler showed that planets move on ellipses with the Sun at one focus, sweeping out equal areas in equal times. An orbit is fully described by six orbital elements: semi-major axis, eccentricity, inclination, longitude of the ascending node, longitude of perihelion, and mean longitude.

The elements drift slowly as the planets tug on one another, so each one also carries a secular rate — a per-century correction. SolPath stores both for every planet, steps the mean longitude to your chosen date, solves Kepler's equation for the eccentric anomaly, and converts to a position in the ecliptic plane.

That's why departure and arrival geometry change with the date: the planets really are where the ephemeris puts them, and the destination keeps moving while you fly.

← Back to About

The Schwarzschild Radius

The Schwarzschild radius is the size an object would have to be squeezed to for its escape velocity to reach the speed of light — the radius of a black hole's event horizon: r_s = 2GM/c².

For Sol it's about 2.95 km. Compress the entire Sun — 333,000 Earth masses — into a ball smaller than a city and it would become a black hole. Shown at the exclusion ring purely for scale: the danger at 0.35 AU is heat and radiation, not gravity.

The tidal force shown alongside it is the difference in solar pull across a radial metre, 2GM/r³ — about 10⁻¹² m/s² at the ring. Utterly negligible for a spacecraft; near a stellar-mass black hole's horizon the same formula is what tears things apart.

← Back

Delta-v

Delta-v (Δv) is the total change in velocity a mission demands — every speed-up, slow-down, and course change added together. It's the true currency of spaceflight: the rocket equation says the propellant needed grows exponentially with the ratio of Δv to exhaust velocity, so small increases in Δv quickly become enormous increases in fuel.

A brachistochrone spends the entire trip thrusting, so its Δv is roughly twice the peak speed: accelerate to it, then shed all of it again. For Earth → Mars at 1 g that's a few megameters per second — which is why the Mission Summary quotes Δv in Mm/s, a unit no chemical rocket will ever need. A Hohmann transfer to Mars, by comparison, costs about 6 km/s: roughly a thousand times less.

Chemical engines exhaust at ~4.5 km/s, so a Mm/s-class budget is hopeless for them — the propellant would outweigh the observable universe. Constant thrust at 1 g assumes something far beyond today's engines: fusion torches, beamed power, or other drives that trade science fiction for arithmetic.

← Back

Time Dilation

Special relativity says a moving clock runs slow. The factor is the Lorentz γ = 1/√(1 − v²/c²): at everyday speeds it's indistinguishable from 1, but as speed approaches light-speed it grows without bound. The crew doesn't notice anything odd on board — their clocks, hearts, and coffee all run normally. It's only when compared against clocks at home that less time has passed for the ship.

That's why every mission reports two durations. Observer time is the trip as measured from the solar system at large; ship time is what the crew's calendar shows on arrival. The Time Dilation panel shows the peak γ and the time the crew "saved" by traveling fast.

For inner-planet hops the effect is tiny — γ ≈ 1.00002 on a 1 g Mars run, saving the crew mere seconds. Push to the outer planets at high acceleration and peak speed reaches several percent of c, where the savings grow to hours. And this is no illusion: the crew genuinely ages less. Fly far enough, fast enough, and you arrive measurably younger than your twin who stayed home.

← Back

The Flip Maneuver

A ship that accelerated the whole way would streak past its destination at megameters per second. To arrive at rest, the second half of the trip must be spent slowing down — and since a rocket can only push along its engine axis, slowing down means physically turning the ship around so the engine faces the direction of travel.

So at the midpoint the engine cuts out, the ship rotates 180°, and the burn resumes — now as deceleration. During the rotation the ship coasts and the crew is briefly weightless; before and after, the steady thrust presses them to the deck at a comfortable 1 g, like gravity. The animation shows the whole sequence: plume forward, the slow tumble, plume aft.

When the mission caps peak speed, the profile gains a cruise phase: accelerate, coast at the cap, flip at the end of the cruise, then brake. The white dot on the trajectory marks the flip point — always at the midpoint of a pure brachistochrone leg, but pushed later when a cruise phase intervenes.