Solar Sail Acceleration Calculator Formula

Understand the math behind the solar sail acceleration calculator. Each variable explained with a worked example.

Use the Solar Sail Acceleration Calculator

Formulas Used

Sail Acceleration

acceleration = 2 * 1361 * sail_area / (2.998e8 * spacecraft_mass * pow(distance_au, 2))

Acceleration (micro-g)

accel_micro_g = 2 * 1361 * sail_area / (2.998e8 * spacecraft_mass * pow(distance_au, 2)) / 9.80665 * 1e6

Variables

VariableDescriptionDefault
sail_areaSail Area(m2)10000
spacecraft_massTotal Spacecraft Mass(kg)100
distance_auDistance from Sun(AU)1

How It Works

Solar Sail Acceleration

A perfectly reflecting solar sail receives momentum from reflected sunlight.

Formula

a = 2S * A / (c * m * d squared)

  • *S* = 1361 W/m2 (solar constant at 1 AU)
  • *A* = sail area
  • *c* = speed of light (2.998 x 10^8 m/s)
  • *m* = total mass
  • *d* = distance from the Sun in AU

    • The factor of 2 accounts for perfect reflection (momentum change = 2p).

    Worked Example

    10 000 m2 sail, 100 kg spacecraft, at 1 AU.

    sail_area = 10000spacecraft_mass = 100distance_au = 1
    1. 01a = 2 * 1361 * 10000 / (2.998e8 * 100 * 1)
    2. 02a = 27 220 000 / 2.998e10
    3. 03a = 9.08e-4 m/s2
    4. 04About 92.6 micro-g

    Frequently Asked Questions

    How fast can a solar sail go?

    Acceleration is continuous so speed builds up over time. After months, a sail can reach speeds unattainable by chemical rockets, especially for interplanetary missions.

    Does a solar sail work far from the Sun?

    Yes, but acceleration decreases with the square of the distance. Beyond about 5 AU, solar pressure becomes very weak.

    Has a solar sail ever been tested?

    Yes. JAXA's IKAROS (2010) was the first successful solar sail in interplanetary space. The Planetary Society's LightSail 2 (2019) demonstrated sail propulsion in Earth orbit.

    Ready to run the numbers?

    Open Solar Sail Acceleration Calculator