User:JDBPhysicist/Sandbox

Physics
Solar sails are propelled by radiation pressure, the force exerted by light reflecting from the sails. Photons carry momentum which is proportional to the frequency of the radiation:
 * $$p = \frac{h}{\lambda}$$

Consider in an inertial reference frame, a photon, with momentum perpendicular to the sail surface pi before the reflection andpr after the reflection. Not all photons are reflected, some are absorbed by the surface, ... coefficient of reflection... Momentum must be conserved in the interaction between the sail and the radiation; therefore the momentum imparted on the sail must equal the difference in momentum between the incident and reflected photons:
 * $$p = \frac{h}{\lambda} + \frac{h}{\lambda}$$

Energy E = pc therefore :
 * $$E = \frac{hc}{\lambda} + \frac{hc}{\lambda}$$

Radiation pressure increases proportionally to the area of the sail illuminated by the radiation.

There are two sources of solar forces: radiation pressure, and solar wind. Radiation pressure is much stronger than wind pressure.

In 1924, the Russian space engineer Friedrich Zander proposed that, since light provides a small amount of thrust, this effect could be used as a form of space propulsion requiring no fuel. Einstein proposed (and experiments confirm) that photons have a momentum p=E/c; therefore, each light photon absorbed by or reflecting from a surface exerts a small amount of  radiation pressure. This results in forces of about 4.57x10−6 N/m2 for absorbing surfaces perpendicular to the radiation in Earth orbit, and a little less than twice as much if the radiation is reflected. This was proven experimentally by Russian physicist Pyotr Nikolaevich Lebedev in 1900, and independently by Nichols and Hull at Dartmouth in 1901 using a Nichols radiometer.

Charged particles from the solar wind are able to cause geomagnetic storms which can knock out power grids on Earth, and point the tails of comets away from the Sun. The solar wind averages 6.7 billion tons per hour at 520 km/s with "slow" low energy coronal ejections reaching 400 km/s and "fast," higher energy ejections averaging 750 km/s. At the distance of the Earth, this results in average solar wind pressure of 3.4×10−9 N/m2, and is three orders of magnitude less than the photonic radiation pressure. Still the solar wind dominates many phenomena because its interaction cross section with gases and charged particles is about 109 times larger than that of the photons.

Both of these forces are small and decrease with the inverse square distance from the Sun. Even large sails produce minute acceleration, but over time, sails can build up considerable speeds. Because the force on the sails and the force of gravity from the Sun both vary as inverse square functions, solar sail vessels can be rated by the ratio of the sail's force divided by the gravitational force. Solar sail vessels with the same rating are able to follow the same trajectories.

Changing course trajectories can be accomplished in two ways. First, tilting the sail with respect to the light source changes the direction of acceleration because the force on a sail from reflected radiation and wind acts in a direction perpendicular to its surface. Smaller auxiliary vanes can be used to gently pull the main sail into its new position (see the vanes on the illustration labeled Cosmos 1, above). Second, gravity from a nearby mass, such as a star or planet, will alter the direction of a spaceship. When orbiting a star or planet, sails can be used to slow down and spiral inward, or to increase the velocity and spiral outward. If the planet has moons or the star has planets, these techniques can be used to achieve slingshots around these bodies.