Using the following equations and values, you can calculate the force of sunlight on and acceleration of the spacecraft:
- Force (F) = 2(P x A)/c
- Acceleration (a) = F/M
At 1 astronomical unit (AU), the power of sunlight is about 131 watts/foot2 (1,400 watts/meter2). Our spacecraft weighs 2.2-lb (1-kg) and has a sail area of 0.38 mi2 (1 km2 or 1-million m2), so:
- P (power) = 1,400 watts/m2
- A (area) = 1-million m2
- c (speed of light) = 3x108 m/s
- M (mass) = 1 kg
This works out to a force (F) of about 2 lb or 9 newtons (N). This force leads to an acceleration (a) of about 29 ft/s 2 (9 m/s2), slightly less than the acceleration due to Earth's gravity. In comparison, a space-shuttle main engine can produce 367,000 lb (1.67-million N) of force during liftoff and 462,000 lb (2.1-million N) of thrust in a vacuum.
Cruising by Sunlight
Maneuvering a solar-sail spacecraft requires balancing two factors: the direction of the solar sail relative to the sun and the orbital speed of the spacecraft. By changing the angle of the sail with respect to the sun, you change the direction of the force exerted by sunlight.
When the spacecraft is in orbit around the Earth or sun, it is traveling in a circular or elliptical path at a given speed and distance. To go to a higher orbit (travel farther away from the object), you angle the solar sail with respect to the sun so that the pressure generated by sunlight is in the direction of your orbital motion. The force accelerates the spacecraft, increases the speed of its orbit and the spacecraft moves into a higher orbit. In contrast, if you want to go to a lower orbit (closer to the object), you angle the sail with respect to the sun so that the pressure generated by the sunlight is opposite the direction of your orbital motion. The force then decelerates the spacecraft, decreases the speed of its orbit and the spacecraft drops into a lower orbit.
The pressure of sunlight decreases with the square of the distance from the sun. Therefore, sunlight exerts greater pressure closer to the sun than farther away. Future solar-sail spacecraft may take advantage of this fact by first dropping to an orbit close to the sun -- a solar fly-by -- and using the greater sunlight pressure to get a bigger boost of acceleration at the start of the mission. This is called a powered perihelion maneuver.