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β˜€οΈ Solar Sail Simulator

No fuel β€” only sunlight. Photon radiation pressure slowly pushes a reflective sail outward on a spiralling Keplerian orbit. RK4 integration, AU / year units.

Sail Parameters

Simulation

Telemetry

Distance1.00 AU
Speed29.8 km/s
Sail accelβ€” ΞΌm/sΒ²
Elapsed0.00 yr
Max dist1.00 AU
πŸš€ ESCAPED INNER SYSTEM
Tip: Ξ± β‰ˆ 35Β° maximises tangential thrust for outward spiral. Ξ± = 0Β° gives maximum radial push. Negative Ξ± spirals inward toward the Sun.

About this simulation

This simulator integrates the trajectory of a solar sail spacecraft using a fourth-order Runge-Kutta (RK4) solver in AU/year units, starting from a circular Earth-like orbit at 1 AU with orbital velocity 2Ο€ AU/yr. Each step combines solar gravity with a photon radiation pressure force proportional to cosΒ²(pitch)/rΒ², where the sail's normal vector is tilted by a pitch angle Ξ± relative to the radial direction. Tuning sail area, spacecraft mass, and pitch angle changes how quickly the craft spirals outward past Mars and toward Jupiter's orbit.

🔬 What it shows

A reflective sail starting in Earth's orbit spirals outward under continuous photon pressure, its trail color-coded by distance from blue near 1 AU to red past 5 AU. An escape badge lights up once the craft passes 3 AU.

🎮 How to use

Drag the Area A and Mass m sliders to change the sail's area-to-mass ratio, which sets the characteristic acceleration a_c at 1 AU. The Pitch Ξ± slider tilts the sail normal between the radial and tangential directions; Speed multiplies RK4 steps per frame, and Reset restarts from the circular orbit.

💡 Did you know?

Sunlight actually pushes things β€” at 1 AU the solar radiation pressure is about 4.56 micronewtons per square metre, tiny per unit area but enough to slowly spiral a large, light sail out of the solar system without any propellant.

Frequently asked questions

Why does the pitch angle matter so much?

The sail's thrust magnitude scales with cosΒ²(pitch), so a flat sail facing the Sun (Ξ± = 0Β°) gets maximum radial push but no tangential component to raise orbital energy. Around Ξ± β‰ˆ 35Β° the balance between thrust magnitude and its tangential projection is close to optimal for spiraling outward efficiently, which is why it's the default value.

What happens with a negative pitch angle?

A negative Ξ± tilts the sail's normal the other way, giving the tangential thrust component a retrograde direction. That removes orbital energy instead of adding it, so the spacecraft spirals inward toward the Sun rather than escaping outward.

Why use RK4 instead of a simpler integrator?

The fourth-order Runge-Kutta method evaluates the combined gravity-plus-sail acceleration at four points per step and combines them with weighted averaging, giving much better long-term accuracy than a basic Euler step. That matters here because the simulation runs thousands of steps at a fixed timestep of 0.002 years while the craft's radius and sail thrust change continuously.

How do sail area and mass affect the trajectory?

The characteristic acceleration a_c is proportional to area divided by mass, so a light, large sail escapes far faster than a heavy, small one. Increasing Area A or decreasing Mass m raises the sail acceleration reading in the telemetry panel and shortens the time needed to reach the 3 AU escape threshold.

Why does the craft occasionally reset itself?

If a chosen pitch angle drives the spacecraft inward and its distance from the Sun drops below 0.05 AU, the simulation treats that as falling into the Sun and automatically calls resetSim() to restart from the 1 AU circular orbit. This safety check prevents the RK4 integrator from breaking down near the singular 1/rΒ² gravity term.